AdS/CFT and condensed matter
|
|
- Wilfrid Warner
- 6 years ago
- Views:
Transcription
1 AdS/CFT and condensed matter Reviews: arxiv: arxiv: arxiv: (with Markus Mueller) Talk online: sachdev.physics.harvard.edu HARVARD
2 Lars Fritz, Harvard Victor Galitski, Maryland Max Metlitski, Harvard Eun Gook Moon, Harvard Markus Mueller, Trieste Yang Qi, Harvard Frederik Denef, Harvard Sean Hartnoll, Harvard Christopher Herzog, Princeton Pavel Kovtun, Victoria Dam Son, Washington Joerg Schmalian, Iowa Cenke Xu, Harvard HARVARD
3 Outline A. Relativistic field theories of quantum phase transitions 1. Coupled dimer antiferromagnets 2. Triangular lattice antiferromagnets 3. Graphene 4. AdS/CFT and quantum critical transport
4 B. Finite density quantum matter
5 Outline B. Finite density quantum matter 1. Graphene Fermi surfaces and Fermi liquids 2. Quantum phase transitions of Fermi liquids Pomeranchuk instability and spin density waves; Fermi surfaces and non-fermi liquids 3. AdS2 theory 4. Cuprate superconductivity
6 Outline B. Finite density quantum matter 1. Graphene Fermi surfaces and Fermi liquids 2. Quantum phase transitions of Fermi liquids Pomeranchuk instability and spin density waves; Fermi surfaces and non-fermi liquids 3. AdS2 theory 4. Cuprate superconductivity
7 Quantum phase transition in graphene T (K) Quantum critical Dirac liquid Hole Fermi liquid 1 n (1 + λ ln Λ n ) Electron Fermi liquid n /m 2
8 Electron Green s function in Fermi liquid (T=0) G(k, ω) = Z ω v F (k k F ) iω 2 F ( k k F ω ) +...
9 Electron Green s function in Fermi liquid (T=0) G(k, ω) = Z ω v F (k k F ) iω 2 F ( k k F ω Green s function has a pole in the LHP at ) +... ω = v F (k k F ) iα(k k F ) Pole is at ω = 0 precisely at k = k F i.e. on a sphere of radius k F in momentum space. This is the Fermi surface. Im(ω) Re(ω)
10 Outline B. Finite density quantum matter 1. Graphene Fermi surfaces and Fermi liquids 2. Quantum phase transitions of Fermi liquids Pomeranchuk instability and spin density waves; Fermi surfaces and non-fermi liquids 3. AdS2 theory 4. Cuprate superconductivity
11 Outline B. Finite density quantum matter 1. Graphene Fermi surfaces and Fermi liquids 2. Quantum phase transitions of Fermi liquids Pomeranchuk instability and spin density waves; Fermi surfaces and non-fermi liquids 3. AdS2 theory 4. Cuprate superconductivity
12 Quantum criticality of Pomeranchuk instability y x Fermi surface with full square lattice symmetry
13 Quantum criticality of Pomeranchuk instability y x Spontaneous elongation along x direction: Ising order parameter φ > 0.
14 Quantum criticality of Pomeranchuk instability y x Spontaneous elongation along y direction: Ising order parameter φ < 0.
15 Quantum criticality of Pomeranchuk instability φ =0 φ 0 λ c λ Pomeranchuk instability as a function of coupling λ
16 Quantum criticality of Pomeranchuk instability T Quantum critical T c φ =0 λ c φ 0 λ Phase diagram as a function of T and λ
17 Quantum criticality of Pomeranchuk instability T Quantum critical T c Classical d=2 Ising criticality φ =0 λ c φ 0 λ Phase diagram as a function of T and λ
18 Quantum criticality of Pomeranchuk instability T Quantum critical T c φ =0 D=2+1 λ Ising criticality c? φ 0 λ Phase diagram as a function of T and λ
19 Quantum criticality of Pomeranchuk instability Effective action for Ising order parameter S φ = d 2 [ rdτ ( τ φ) 2 + c 2 ( φ) 2 +(λ λ c )φ 2 + uφ 4]
20 Quantum criticality of Pomeranchuk instability Effective action for Ising order parameter S φ = d 2 rdτ [ ( τ φ) 2 + c 2 ( φ) 2 +(λ λ c )φ 2 + uφ 4] Effective action for electrons: S c = dτ N f i c iα τ c iα i<j t ij c iα c iα α=1 N f dτc kα ( τ + ε k ) c kα α=1 k
21 Quantum criticality of Pomeranchuk instability Coupling between Ising order and electrons S φc = γ dτ φ N f (cos k x cos k y )c kα c kα α=1 k for spatially independent φ φ > 0 φ < 0
22 Quantum criticality of Pomeranchuk instability Coupling between Ising order and electrons S φc = γ dτ N f φ q (cos k x cos k y )c k+q/2,α c k q/2,α α=1 k,q for spatially dependent φ φ > 0 φ < 0
23 Quantum criticality of Pomeranchuk instability S φ = d 2 [ rdτ ( τ φ) 2 + c 2 ( φ) 2 +(λ λ c )φ 2 + uφ 4] S c = S φc = γ N f α=1 k dτ N f α=1 dτc kα ( τ + ε k ) c kα φ q (cos k x cos k y )c k+q/2,α c k q/2,α k,q Quantum critical field theory Z = DφDc iα exp ( S φ S c S φc )
24 Quantum criticality of Pomeranchuk instability Hertz theory Integrate out c α fermions and obtain non-local corrections to φ action δs φ N f γ 2 d 2 q 4π 2 dω 2π φ(q, ω) 2[ ω q + q2] +... This leads to a critical point with dynamic critical exponent z = 3 and quantum criticality controlled by the Gaussian fixed point.
25 Quantum criticality of Pomeranchuk instability Hertz theory 1 N f (q 2 + ω /q) Self energy of c α fermions to order 1/N f Σ c (k, ω) i N f ω 2/3 This leads to the Green s function G(k, ω) 1 ω v F (k k F ) i N f ω 2/3 Note that the order 1/N f term is more singular in the infrared than the bare term; this leads to problems in the bare 1/N f expansion in terms that are dominated by low frequency fermions.
26 Quantum criticality of Pomeranchuk instability 1 N f (q 2 + ω /q) 1 ω v F (k k F ) i N f ω 2/3 The infrared singularities of fermion particle-hole pairs are most severe on planar graphs: these all contribute at leading order in 1/N f. Sung-Sik Lee, arxiv:
27 Γ Γ
28 Fermi surfaces in electron- and hole-doped cuprates Γ Hole states occupied Electron states occupied Effective Hamiltonian for quasiparticles: Γ H 0 = i<j t ij c iα c iα k ε k c kα c kα with t ij non-zero for first, second and third neighbor, leads to satisfactory agreement with experiments. The area of the occupied electron states, A e, from Luttinger s theory is A e = { 2π 2 (1 p) for hole-doping p 2π 2 (1 + x) for electron-doping x The area of the occupied hole states, A h, which form a closed Fermi surface and so appear in quantum oscillation experiments is A h =4π 2 A e.
29 Spin density wave theory A spin density wave (SDW) is the spontaneous appearance of an oscillatory spin polarization. The electron spin polarization is written as S(r, τ) = ϕ (r, τ)e ik r where ϕ is the SDW order parameter, and K is a fixed ordering wavevector. For simplicity we will consider the case of K =(π, π), but our treatment applies to general K.
30 Spin density wave theory In the presence of spin density wave order, ϕ at wavevector K = (π, π), we have an additional term which mixes electron states with momentum separated by K H sdw = ϕ c k,α σ αβc k+k,β k,α,β where σ are the Pauli matrices. The electron dispersions obtained by diagonalizing H 0 + H sdw for ϕ (0, 0, 1) are E k± = ε k + ε k+k 2 ± (εk ε k+k 2 ) + ϕ 2 This leads to the Fermi surfaces shown in the following slides for electron and hole doping.
31 Spin density wave theory in hole-doped cuprates Increasing SDW order Γ S. Sachdev, A. V. Chubukov, and A. Sokol, Phys. Rev. B 51, (1995). A. V. Chubukov and D. K. Morr, Physics Reports 288, 355 (1997).
32 Spin density wave theory in hole-doped cuprates Increasing SDW order Γ Γ S. Sachdev, A. V. Chubukov, and A. Sokol, Phys. Rev. B 51, (1995). A. V. Chubukov and D. K. Morr, Physics Reports 288, 355 (1997).
33 Spin density wave theory in hole-doped cuprates Increasing SDW order Electron pockets Γ Γ Γ Hole pockets S. Sachdev, A. V. Chubukov, and A. Sokol, Phys. Rev. B 51, (1995). A. V. Chubukov and D. K. Morr, Physics Reports 288, 355 (1997).
34 Spin density wave theory in hole-doped cuprates Increasing SDW order Γ Γ Γ Γ Hole pockets SDW order parameter is a vector, ϕ, whose amplitude vanishes at the transition to the Fermi liquid. S. Sachdev, A. V. Chubukov, and A. Sokol, Phys. Rev. B 51, (1995). A. V. Chubukov and D. K. Morr, Physics Reports 288, 355 (1997).
35 Spin density wave theory In the presence of spin density wave order, ϕ at wavevector K =(π, π), we have an additional term which mixes electron states with momentum separated by K H sdw = ϕ k,α,β c k,α σ αβc k+k,β where σ are the Pauli matrices. At the quantum critical point for the onset of SDW order, we integrate out the fermions and derive an effective action functional for ϕ.
36 Spin density wave theory This functional has the form S = d 2 q 4π 2 ] dω 2π ϕ (q, ω) 2[ r + q 2 + χ(k, ω) + u d 2 xdτ( ϕ 2 (x, τ)) The susceptibility, χ, has a non-analytic dependence on ω because of Landau damping: χ(k, ω) =χ 0 + χ 1 ω +... This leads to a critical point with dynamic critical exponent z = 2, and upper-critical dimension d = 2.
37 Spin density wave theory This functional has the form S = d 2 q 4π 2 ] dω 2π ϕ (q, ω) 2[ r + q 2 + χ(k, ω) + u d 2 xdτ( ϕ 2 (x, τ)) The susceptibility, χ, has a non-analytic dependence on ω because of Landau damping: However, the higher order corrections require summation of all planar graphs, χ(k, ω) =χ 0 + χ 1 ω +... as in the Pomeranchuk instability. M. Metlitski This leads to a critical point with dynamic critical exponent z = 2, and upper-critical dimension d = 2.
38 Outline B. Finite density quantum matter 1. Graphene Fermi surfaces and Fermi liquids 2. Quantum phase transitions of Fermi liquids Pomeranchuk instability and spin density waves; Fermi surfaces and non-fermi liquids 3. AdS2 theory 4. Cuprate superconductivity
39 Outline B. Finite density quantum matter 1. Graphene Fermi surfaces and Fermi liquids 2. Quantum phase transitions of Fermi liquids Pomeranchuk instability and spin density waves; Fermi surfaces and non-fermi liquids 3. AdS2 theory 4. Cuprate superconductivity
40 Conformal field theory in 2+1 dimensions at T =0 Einstein gravity on AdS 4
41 Conformal field theory in 2+1 dimensions at T>0 Einstein gravity on AdS 4 with a Schwarzschild black hole
42 Conformal field theory in 2+1 dimensions at T>0, with a non-zero chemical potential, µ and applied magnetic field, B Einstein gravity on AdS 4 with a Reissner-Nordstrom black hole carrying electric and magnetic charges
43 AdS4-Reissner-Nordstrom black hole ) ds 2 = (f(r)dτ L2 2 r 2 + dr2 f(r) + dx2 + dy 2, ( f(r) = 1 1+ (r2 +µ 2 + r+b 4 2 )( ) ) 3 r γ 2 + (r2 +µ 2 + r+b 4 2 ) r + γ [ 2 A = iµ 1 r ] dτ + Bx dy. T = 1 4πr + r + (3 r2 +µ 2 γ 2 r4 +B 2 γ 2 ). ( r r + ) 4,
44 Examine free energy and Green s function of a probe particle T. Faulkner, H. Liu, J. McGreevy, and D. Vegh, arxiv: F. Denef, S. Hartnoll, and S. Sachdev, arxiv:
45 Short time behavior depends upon conformal AdS4 geometry near boundary T. Faulkner, H. Liu, J. McGreevy, and D. Vegh, arxiv: F. Denef, S. Hartnoll, and S. Sachdev, arxiv:
46 Long time behavior depends upon near-horizon geometry of black hole T. Faulkner, H. Liu, J. McGreevy, and D. Vegh, arxiv: F. Denef, S. Hartnoll, and S. Sachdev, arxiv:
47 Radial direction of gravity theory is measure of energy scale in CFT T. Faulkner, H. Liu, J. McGreevy, and D. Vegh, arxiv: F. Denef, S. Hartnoll, and S. Sachdev, arxiv:
48 AdS4-Reissner-Nordstrom black hole ) ds 2 = (f(r)dτ L2 2 r 2 + dr2 f(r) + dx2 + dy 2, ( f(r) = 1 1+ (r2 +µ 2 + r+b 4 2 )( ) ) 3 r γ 2 + (r2 +µ 2 + r+b 4 2 ) r + γ [ 2 A = iµ 1 r ] dτ + Bx dy. T = 1 4πr + r + (3 r2 +µ 2 γ 2 r4 +B 2 γ 2 ). ( r r + ) 4,
49 AdS2 x R 2 near-horizon geometry r r + 1 ζ ds 2 = R2 ζ 2 ( dτ 2 + dζ 2) + r2 + R 2 ( dx 2 + dy 2)
50 Infrared physics of Fermi surface is linked to the near horizon AdS2 geometry of Reissner-Nordstrom black hole T. Faulkner, H. Liu, J. McGreevy, and D. Vegh, arxiv:
51 AdS4 Geometric interpretation of RG flow T. Faulkner, H. Liu, J. McGreevy, and D. Vegh, arxiv:
52 AdS2 x R2 Geometric interpretation of RG flow T. Faulkner, H. Liu, J. McGreevy, and D. Vegh, arxiv:
53 Green s function of a fermion T. Faulkner, H. Liu, J. McGreevy, and D. Vegh, arxiv: G(k, ω) 1 ω v F (k k F ) iω θ(k) See also M. Cubrovic, J Zaanen, and K. Schalm, arxiv:
54 Green s function of a fermion T. Faulkner, H. Liu, J. McGreevy, and D. Vegh, arxiv: G(k, ω) 1 ω v F (k k F ) iω θ(k) Similar to non-fermi liquid theories of Fermi surfaces coupled to gauge fields, and at quantum critical points
55 Free energy from gravity theory The free energy is expressed as a sum over the quasinormal frequencies, z l, of the black hole. Here l represents any set of quantum numbers: F boson = T l F fermion = T l ln ln ( ( z l 2πT Γ ( izl 2πT ( ) ) Γ izl 2 2πT ) ) 2 Application of this formula shows that the fermions exhibit the dhva quantum oscillations with expected period (2π/(Fermi surface ares)) in 1/B, but with an amplitude corrected from the Fermi liquid formula of Lifshitz- Kosevich. F. Denef, S. Hartnoll, and S. Sachdev, arxiv:
56 Outline B. Finite density quantum matter 1. Graphene Fermi surfaces and Fermi liquids 2. Quantum phase transitions of Fermi liquids Pomeranchuk instability and spin density waves; Fermi surfaces and non-fermi liquids 3. AdS2 theory 4. Cuprate superconductivity
57 Outline B. Finite density quantum matter 1. Graphene Fermi surfaces and Fermi liquids 2. Quantum phase transitions of Fermi liquids Pomeranchuk instability and spin density waves; Fermi surfaces and non-fermi liquids 3. AdS2 theory 4. Cuprate superconductivity
58 The cuprate superconductors
59 Γ Γ
60 The cuprate superconductors Multiple quantum phase transitions involving at least two order parameters (antiferromagnetism and superconductivity) and a topological change in the Fermi surface
61 Crossovers in transport properties of hole-doped cuprates * coh? (K) ( ) S-shaped + 2 or A F M upturns in ( ) -wave SC Hole doping (1 < < 2) 2 FL? N. E. Hussey, J. Phys: Condens. Matter 20, (2008)
62 Quantum critical Classical spin waves Dilute triplon gas Neel order
63 Crossovers in transport properties of hole-doped cuprates Strange metal T (K) A F M d-wave SC Hole doping x x m Strange metal: quantum criticality of optimal doping critical point at x = x m?
64 Only candidate quantum critical point observed at low T Strange metal T (K) x s A F M d-wave SC Hole doping x Spin density wave order present below a quantum critical point at x = x s with x s 0.12 in the La series of cuprates
65 Γ Γ
66 Theory of quantum criticality in the cuprates Small Fermi pockets Strange Metal Large Fermi surface Spin density wave (SDW) Underlying SDW ordering quantum critical point in metal at x = x m
67 Evidence for connection between linear resistivity and stripe-ordering in a cuprate with a low Tc Magnetic field of upto 35 T used to suppress superconductivity Linear temperature dependence of resistivity and change in the Fermi surface at the pseudogap critical point of a high-tc superconductor R. Daou, Nicolas Doiron-Leyraud, David LeBoeuf, S. Y. Li, Francis Laliberté, Olivier Cyr-Choinière, Y. J. Jo, L. Balicas, J.-Q. Yan, J.-S. Zhou, J. B. Goodenough & Louis Taillefer, Nature Physics 5, (2009)
68 Spin density wave theory in hole-doped cuprates Increasing SDW order Γ Γ Γ Γ Hole pockets Quantum phase transition involves both a SDW order parameter ϕ, and a topological change in the Fermi surface S. Sachdev, A. V. Chubukov, and A. Sokol, Phys. Rev. B 51, (1995). A. V. Chubukov and D. K. Morr, Physics Reports 288, 355 (1997).
69 Theory of quantum criticality in the cuprates Small Fermi pockets Strange Metal Large Fermi surface Spin density wave (SDW) Underlying SDW ordering quantum critical point in metal at x = x m
70 Theory of quantum criticality in the cuprates Small Fermi pockets with pairing fluctuations Strange Metal Large Fermi surface d-wave superconductor Spin density wave (SDW) Onset of d-wave superconductivity hides the critical point x = x m
71 Theory of quantum criticality in the cuprates Small Fermi pockets with pairing fluctuations Strange Metal Large Fermi surface d-wave superconductor Spin density wave (SDW) Competition between SDW order and superconductivity moves the actual quantum critical point to x = x s <x m.
72 Theory of quantum criticality in the cuprates Small Fermi pockets with pairing fluctuations Strange Metal Large Fermi surface d-wave superconductor Spin density wave (SDW) Competition between SDW order and superconductivity moves the actual quantum critical point to x = x s <x m.
73 Theory of quantum criticality in the cuprates Small Fermi pockets with pairing fluctuations Strange Metal Large Fermi surface Thermally fluctuating SDW Magnetic quantum criticality Spin gap d-wave superconductor Spin density wave (SDW) Competition between SDW order and superconductivity moves the actual quantum critical point to x = x s <x m.
74 Theory of quantum criticality in the cuprates Small Fermi pockets with pairing fluctuations Strange Metal Large Fermi surface Classical spin waves Quantum critical Dilute triplon gas Thermally fluctuating SDW Magnetic quantum criticality Spin gap d-wave superconductor Neel order Criticality of the coupled dimer antiferromagnet at x=xs Spin density wave (SDW) Competition between SDW order and superconductivity moves the actual quantum critical point to x = x s <x m.
75 Theory of quantum criticality in the cuprates ncreasing SDW Small Fermi pockets with pairing fluctuations Strange Metal Large Fermi surface Thermally fluctuating SDW Magnetic quantum criticality Spin gap d-wave superconductor Criticality of the topological change in Fermi surface at x=xm Spin density wave (SDW) Competition between SDW order and superconductivity moves the actual quantum critical point to x = x s <x m.
76 T Small Fermi pockets with pairing fluctuations Strange Metal Large Fermi surface Thermally fluctuating SDW Magnetic quantum criticality Spin gap d-wave SC
77 T Small Fermi pockets with pairing fluctuations Strange Metal Large Fermi surface Thermally fluctuating SDW Magnetic quantum criticality Spin gap d-wave SC SC+ SDW SC SDW (Small Fermi pockets) H M "Normal" (Large Fermi surface)
78 T Small Fermi pockets with pairing fluctuations Strange Metal Large Fermi surface Thermally fluctuating SDW Magnetic quantum criticality Spin gap d-wave SC Change in frequency of quantum oscillations in electron-doped SC+ SDW SDW (Small Fermi pockets) M SC materials identifies xm = H "Normal" (Large Fermi surface)
79 Increasing SDW order Nd 2 x Ce x CuO 4 T. Helm, M. V. Kartsovni, M. Bartkowiak, N. Bittner, M. Lambacher, A. Erb, J. Wosnitza, R. Gross, arxiv:
80 T Neutron scattering at H=0 in same material identifies xs = 0.14 < xm Small Fermi pockets with pairing fluctuations Thermally fluctuating SDW Magnetic quantum criticality Spin gap Strange Metal d-wave SC Large Fermi surface SC+ SDW SC SDW (Small Fermi pockets) H M "Normal" (Large Fermi surface)
81 Nd 2 x Ce x CuO 4 Spin correlation length!/a x=0.038 x=0.075 x=0.106 x=0.129 x=0.134 x=0.145 x=0.150 x= Temperature (K) E. M. Motoyama, G. Yu, I. M. Vishik, O. P. Vajk, P. K. Mang, and M. Greven, Nature 445, 186 (2007).
82 T Small Fermi pockets with pairing fluctuations Strange Metal Large Fermi surface Experiments on Nd 2 x Ce x CuO 4 show that at low fields x s =0.14, while at high fields x m = Thermally fluctuating SDW Magnetic quantum criticality Spin gap SC+ SDW d-wave SC SC SDW (Small Fermi pockets) H M "Normal" (Large Fermi surface)
83 Conclusions General theory of finite temperature dynamics and transport near quantum critical points, with applications to antiferromagnets, graphene, and superconductors
84 Conclusions The AdS/CFT offers promise in providing a new understanding of strongly interacting quantum matter at non-zero density
85 Conclusions Identified quantum criticality in cuprate superconductors with a critical point at optimal doping associated with onset of spin density wave order in a metal Elusive optimal doping quantum critical point has been hiding in plain sight. It is shifted to lower doping by the onset of superconductivity
Strong coupling problems in condensed matter and the AdS/CFT correspondence
Strong coupling problems in condensed matter and the AdS/CFT correspondence Reviews: arxiv:0910.1139 arxiv:0901.4103 Talk online: sachdev.physics.harvard.edu HARVARD Frederik Denef, Harvard Yejin Huh,
More informationQuantum phase transitions of insulators, superconductors and metals in two dimensions
Quantum phase transitions of insulators, superconductors and metals in two dimensions Talk online: sachdev.physics.harvard.edu HARVARD Outline 1. Phenomenology of the cuprate superconductors (and other
More informationQuantum criticality of Fermi surfaces in two dimensions
Quantum criticality of Fermi surfaces in two dimensions Talk online: sachdev.physics.harvard.edu HARVARD Yejin Huh, Harvard Max Metlitski, Harvard HARVARD Outline 1. Quantum criticality of Fermi points:
More informationTheory of the competition between spin density waves and d-wave superconductivity in the underdoped cuprates
HARVARD Theory of the competition between spin density waves and d-wave superconductivity in the underdoped cuprates Talk online: sachdev.physics.harvard.edu HARVARD Where is the quantum critical point
More informationQuantum criticality in the cuprate superconductors. Talk online: sachdev.physics.harvard.edu
Quantum criticality in the cuprate superconductors Talk online: sachdev.physics.harvard.edu The cuprate superconductors Destruction of Neel order in the cuprates by electron doping, R. K. Kaul, M. Metlitksi,
More informationQuantum disordering magnetic order in insulators, metals, and superconductors
Quantum disordering magnetic order in insulators, metals, and superconductors Perimeter Institute, Waterloo, May 29, 2010 Talk online: sachdev.physics.harvard.edu HARVARD Cenke Xu, Harvard arxiv:1004.5431
More informationQuantum criticality of Fermi surfaces
Quantum criticality of Fermi surfaces Subir Sachdev Physics 268br, Spring 2018 HARVARD Quantum criticality of Ising-nematic ordering in a metal y Occupied states x Empty states A metal with a Fermi surface
More informationThe phase diagram of the cuprates and the quantum phase transitions of metals in two dimensions
The phase diagram of the cuprates and the quantum phase transitions of metals in two dimensions Niels Bohr Institute, Copenhagen, May 6, 2010 Talk online: sachdev.physics.harvard.edu HARVARD Max Metlitski,
More informationThe phase diagrams of the high temperature superconductors
The phase diagrams of the high temperature superconductors Talk online: sachdev.physics.harvard.edu HARVARD Max Metlitski, Harvard Eun Gook Moon, Harvard HARVARD The cuprate superconductors Square lattice
More informationSaturday, April 3, 2010
Phys. Rev. Lett. 1990 Superfluid-insulator transition Ultracold 87 Rb atoms - bosons M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature 415, 39 (2002). T σ = 4e2 h Σ Quantum Σ, auniversalnumber.
More informationQuantum criticality and the phase diagram of the cuprates
Quantum criticality and the phase diagram of the cuprates Talk online: sachdev.physics.harvard.edu HARVARD Victor Galitski, Maryland Ribhu Kaul, Harvard Kentucky Max Metlitski, Harvard Eun Gook Moon, Harvard
More informationQuantum criticality, the AdS/CFT correspondence, and the cuprate superconductors
Quantum criticality, the AdS/CFT correspondence, and the cuprate superconductors Talk online: sachdev.physics.harvard.edu HARVARD Frederik Denef, Harvard Max Metlitski, Harvard Sean Hartnoll, Harvard Christopher
More informationSign-problem-free Quantum Monte Carlo of the onset of antiferromagnetism in metals
Sign-problem-free Quantum Monte Carlo of the onset of antiferromagnetism in metals Subir Sachdev sachdev.physics.harvard.edu HARVARD Max Metlitski Erez Berg HARVARD Max Metlitski Erez Berg Sean Hartnoll
More informationQuantum matter & black hole ringing
Quantum matter & black hole ringing Sean Hartnoll Harvard University Work in collaboration with Chris Herzog and Gary Horowitz : 0801.1693, 0810.1563. Frederik Denef : 0901.1160. Frederik Denef and Subir
More informationMetals without quasiparticles
Metals without quasiparticles A. Review of Fermi liquid theory B. A non-fermi liquid: the Ising-nematic quantum critical point C. Fermi surfaces and gauge fields Metals without quasiparticles A. Review
More information3. Quantum matter without quasiparticles
1. Review of Fermi liquid theory Topological argument for the Luttinger theorem 2. Fractionalized Fermi liquid A Fermi liquid co-existing with topological order for the pseudogap metal 3. Quantum matter
More informationThe Superfluid-Insulator transition
The Superfluid-Insulator transition Boson Hubbard model M.P. A. Fisher, P.B. Weichmann, G. Grinstein, and D.S. Fisher, Phys. Rev. B 40, 546 (1989). Superfluid-insulator transition Ultracold 87 Rb atoms
More informationThe underdoped cuprates as fractionalized Fermi liquids (FL*)
The underdoped cuprates as fractionalized Fermi liquids (FL*) R. K. Kaul, A. Kolezhuk, M. Levin, S. Sachdev, and T. Senthil, Physical Review B 75, 235122 (2007) R. K. Kaul, Y. B. Kim, S. Sachdev, and T.
More informationQuantum oscillations & black hole ringing
Quantum oscillations & black hole ringing Sean Hartnoll Harvard University Work in collaboration with Frederik Denef : 0901.1160. Frederik Denef and Subir Sachdev : 0908.1788, 0908.2657. Sept. 09 ASC,
More informationQuantum critical transport and AdS/CFT
Quantum critical transport and AdS/CFT Lars Fritz, Harvard Sean Hartnoll, Harvard Christopher Herzog, Princeton Pavel Kovtun, Victoria Markus Mueller, Trieste Joerg Schmalian, Iowa Dam Son, Washington
More informationGeneral relativity and the cuprates
General relativity and the cuprates Gary T. Horowitz and Jorge E. Santos Department of Physics, University of California, Santa Barbara, CA 93106, U.S.A. E-mail: gary@physics.ucsb.edu, jss55@physics.ucsb.edu
More informationQuantum phase transitions of insulators, superconductors and metals in two dimensions
Quantum phase transitions of insulators, superconductors and metals in two dimensions Talk online: sachdev.physics.harvard.edu HARVARD Outline 1. Phenomenology of the cuprate superconductors (and other
More informationA non-fermi liquid: Quantum criticality of metals near the Pomeranchuk instability
A non-fermi liquid: Quantum criticality of metals near the Pomeranchuk instability Subir Sachdev sachdev.physics.harvard.edu HARVARD y x Fermi surface with full square lattice symmetry y x Spontaneous
More informationRecent Developments in Holographic Superconductors. Gary Horowitz UC Santa Barbara
Recent Developments in Holographic Superconductors Gary Horowitz UC Santa Barbara Outline 1) Review basic ideas behind holographic superconductors 2) New view of conductivity and the zero temperature limit
More informationQuantum bosons for holographic superconductors
Quantum bosons for holographic superconductors Sean Hartnoll Harvard University Work in collaboration with Chris Herzog and Gary Horowitz : 0801.1693, 0810.1563. Frederik Denef : 0901.1160. Frederik Denef
More informationQuantum phase transitions and Fermi surface reconstruction
Quantum phase transitions and Fermi surface reconstruction Talk online: sachdev.physics.harvard.edu HARVARD Max Metlitski Matthias Punk Erez Berg HARVARD 1. Fate of the Fermi surface: reconstruction or
More informationTalk online at
Talk online at http://sachdev.physics.harvard.edu Outline 1. CFT3s in condensed matter physics Superfluid-insulator and Neel-valence bond solid transitions 2. Quantum-critical transport Collisionless-t0-hydrodynamic
More informationTheory of the Nernst effect near the superfluid-insulator transition
Theory of the Nernst effect near the superfluid-insulator transition Sean Hartnoll (KITP), Christopher Herzog (Washington), Pavel Kovtun (KITP), Marcus Mueller (Harvard), Subir Sachdev (Harvard), Dam Son
More informationHolography of compressible quantum states
Holography of compressible quantum states New England String Meeting, Brown University, November 18, 2011 sachdev.physics.harvard.edu HARVARD Liza Huijse Max Metlitski Brian Swingle Compressible quantum
More informationThe onset of antiferromagnetism in metals: from the cuprates to the heavy fermion compounds
The onset of antiferromagnetism in metals: from the cuprates to the heavy fermion compounds Twelfth Arnold Sommerfeld Lecture Series January 31 - February 3, 2012 sachdev.physics.harvard.edu HARVARD Max
More informationQuantum Melting of Stripes
Quantum Melting of Stripes David Mross and T. Senthil (MIT) D. Mross, TS, PRL 2012 D. Mross, TS, PR B (to appear) Varieties of Stripes Spin, Charge Néel 2π Q c 2π Q s ``Anti-phase stripes, common in La-based
More informationQuantum matter and gauge-gravity duality
Quantum matter and gauge-gravity duality Institute for Nuclear Theory, Seattle Summer School on Applications of String Theory July 18-20 Subir Sachdev HARVARD Outline 1. Conformal quantum matter 2. Compressible
More informationQuantum phase transitions in condensed matter
Quantum phase transitions in condensed matter The 8th Asian Winter School on Strings, Particles, and Cosmology, Puri, India January 11-18, 2014 Subir Sachdev Talk online: sachdev.physics.harvard.edu HARVARD
More informationExotic phases of the Kondo lattice, and holography
Exotic phases of the Kondo lattice, and holography Stanford, July 15, 2010 Talk online: sachdev.physics.harvard.edu HARVARD Outline 1. The Anderson/Kondo lattice models Luttinger s theorem 2. Fractionalized
More informationHolographic superconductors
Holographic superconductors Sean Hartnoll Harvard University Work in collaboration with Chris Herzog and Gary Horowitz : 0801.1693, 0810.1563. Frederik Denef : 0901.1160. Frederik Denef and Subir Sachdev
More informationGordon Research Conference Correlated Electron Systems Mount Holyoke, June 27, 2012
Entanglement, holography, and strange metals Gordon Research Conference Correlated Electron Systems Mount Holyoke, June 27, 2012 Lecture at the 100th anniversary Solvay conference, Theory of the Quantum
More informationFrom the pseudogap to the strange metal
HARVARD From the pseudogap to the strange metal S. Sachdev, E. Berg, S. Chatterjee, and Y. Schattner, PRB 94, 115147 (2016) S. Sachdev and S. Chatterjee, arxiv:1703.00014 APS March meeting March 13, 2017
More informationEmergent Quantum Criticality
(Non-)Fermi Liquids and Emergent Quantum Criticality from gravity Hong Liu Massachusetts setts Institute te of Technology HL, John McGreevy, David Vegh, 0903.2477 Tom Faulkner, HL, JM, DV, to appear Sung-Sik
More informationEntanglement, holography, and strange metals
Entanglement, holography, and strange metals University of Cologne, June 8, 2012 Subir Sachdev Lecture at the 100th anniversary Solvay conference, Theory of the Quantum World, chair D.J. Gross. arxiv:1203.4565
More informationTopological order in the pseudogap metal
HARVARD Topological order in the pseudogap metal High Temperature Superconductivity Unifying Themes in Diverse Materials 2018 Aspen Winter Conference Aspen Center for Physics Subir Sachdev January 16,
More informationarxiv: v1 [cond-mat.str-el] 7 Oct 2009
Finite temperature dissipation and transport near quantum critical points Subir Sachdev Department of Physics, Harvard University, Cambridge MA 02138 (Dated: Oct 5, 2009) arxiv:0910.1139v1 [cond-mat.str-el]
More informationA quantum dimer model for the pseudogap metal
A quantum dimer model for the pseudogap metal College de France, Paris March 27, 2015 Subir Sachdev Talk online: sachdev.physics.harvard.edu HARVARD Andrea Allais Matthias Punk Debanjan Chowdhury (Innsbruck)
More informationQuantum entanglement and the phases of matter
Quantum entanglement and the phases of matter IISc, Bangalore January 23, 2012 sachdev.physics.harvard.edu HARVARD Outline 1. Conformal quantum matter Entanglement, emergent dimensions and string theory
More informationSupplementary Information for. Linear-T resistivity and change in Fermi surface at the pseudogap critical point of a high-t c superconductor
NPHYS-2008-06-00736 Supplementary Information for Linear-T resistivity and change in Fermi surface at the pseudogap critical point of a high-t c superconductor R. Daou 1, Nicolas Doiron-Leyraud 1, David
More informationQuantum matter without quasiparticles: SYK models, black holes, and the cuprate strange metal
Quantum matter without quasiparticles: SYK models, black holes, and the cuprate strange metal Workshop on Frontiers of Quantum Materials Rice University, Houston, November 4, 2016 Subir Sachdev Talk online:
More informationGlobal phase diagrams of two-dimensional quantum antiferromagnets. Subir Sachdev Harvard University
Global phase diagrams of two-dimensional quantum antiferromagnets Cenke Xu Yang Qi Subir Sachdev Harvard University Outline 1. Review of experiments Phases of the S=1/2 antiferromagnet on the anisotropic
More informationStrange metal from local quantum chaos
Strange metal from local quantum chaos John McGreevy (UCSD) hello based on work with Daniel Ben-Zion (UCSD) 2017-08-26 Compressible states of fermions at finite density The metallic states that we understand
More informationQuantum phase transitions in condensed matter physics, with connections to string theory
Quantum phase transitions in condensed matter physics, with connections to string theory sachdev.physics.harvard.edu HARVARD High temperature superconductors Cuprates High temperature superconductors Pnictides
More informationIdeas on non-fermi liquid metals and quantum criticality. T. Senthil (MIT).
Ideas on non-fermi liquid metals and quantum criticality T. Senthil (MIT). Plan Lecture 1: General discussion of heavy fermi liquids and their magnetism Review of some experiments Concrete `Kondo breakdown
More informationNematic and Magnetic orders in Fe-based Superconductors
Nematic and Magnetic orders in Fe-based Superconductors Cenke Xu Harvard University Collaborators: Markus Mueller, Yang Qi Subir Sachdev, Jiangping Hu Collaborators: Subir Sachdev Markus Mueller Yang Qi
More informationTalk online: sachdev.physics.harvard.edu
Talk online: sachdev.physics.harvard.edu Particle theorists Condensed matter theorists Quantum Entanglement Hydrogen atom: Hydrogen molecule: = _ = 1 2 ( ) Superposition of two electron states leads to
More informationQuantum mechanics without particles
Quantum mechanics without particles Institute Lecture, Indian Institute of Technology, Kanpur January 21, 2014 sachdev.physics.harvard.edu HARVARD Outline 1. Key ideas from quantum mechanics 2. Many-particle
More informationTheory of Quantum Matter: from Quantum Fields to Strings
Theory of Quantum Matter: from Quantum Fields to Strings Salam Distinguished Lectures The Abdus Salam International Center for Theoretical Physics Trieste, Italy January 27-30, 2014 Subir Sachdev Talk
More informationStrange metals and gauge-gravity duality
Strange metals and gauge-gravity duality Loughborough University, May 17, 2012 Subir Sachdev Lecture at the 100th anniversary Solvay conference, Theory of the Quantum World, chair D.J. Gross. arxiv:1203.4565
More informationEntanglement, holography, and strange metals
Entanglement, holography, and strange metals PCTS, Princeton, October 26, 2012 Subir Sachdev Talk online at sachdev.physics.harvard.edu HARVARD Liza Huijse Max Metlitski Brian Swingle Complex entangled
More informationQuantum phases of antiferromagnets and the underdoped cuprates. Talk online: sachdev.physics.harvard.edu
Quantum phases of antiferromagnets and the underdoped cuprates Talk online: sachdev.physics.harvard.edu Outline 1. Coupled dimer antiferromagnets Landau-Ginzburg quantum criticality 2. Spin liquids and
More informationQuantum critical transport, duality, and M-theory
Quantum critical transport, duality, and M-theory hep-th/0701036 Christopher Herzog (Washington) Pavel Kovtun (UCSB) Subir Sachdev (Harvard) Dam Thanh Son (Washington) Talks online at http://sachdev.physics.harvard.edu
More informationQuantum Phase Transitions
Quantum Phase Transitions Subir Sachdev Talks online at http://sachdev.physics.harvard.edu What is a phase transition? A change in the collective properties of a macroscopic number of atoms What is a quantum
More informationJ. McGreevy, arxiv Wednesday, April 18, 2012
r J. McGreevy, arxiv0909.0518 Consider the metric which transforms under rescaling as x i ζx i t ζ z t ds ζ θ/d ds. This identifies z as the dynamic critical exponent (z = 1 for relativistic quantum critical
More informationA New look at the Pseudogap Phase in the Cuprates.
A New look at the Pseudogap Phase in the Cuprates. Patrick Lee MIT Common themes: 1. Competing order. 2. superconducting fluctuations. 3. Spin gap: RVB. What is the elephant? My answer: All of the above!
More informationRelativistic magnetotransport in graphene
Relativistic magnetotransport in graphene Markus Müller in collaboration with Lars Fritz (Harvard) Subir Sachdev (Harvard) Jörg Schmalian (Iowa) Landau Memorial Conference June 6, 008 Outline Relativistic
More informationQuantum Oscillations, Magnetotransport and the Fermi Surface of cuprates Cyril PROUST
Quantum Oscillations, Magnetotransport and the Fermi Surface of cuprates Cyril PROUST Laboratoire National des Champs Magnétiques Intenses Toulouse Collaborations D. Vignolles B. Vignolle C. Jaudet J.
More informationMean field theories of quantum spin glasses
Mean field theories of quantum spin glasses Antoine Georges Olivier Parcollet Nick Read Subir Sachdev Jinwu Ye Talk online: Sachdev Classical Sherrington-Kirkpatrick model H = JS S i j ij i j J ij : a
More informationQuantum entanglement and the phases of matter
Quantum entanglement and the phases of matter Stony Brook University February 14, 2012 sachdev.physics.harvard.edu HARVARD Quantum superposition and entanglement Quantum Superposition The double slit experiment
More informationQuantum entanglement and the phases of matter
Quantum entanglement and the phases of matter University of Toronto March 22, 2012 sachdev.physics.harvard.edu HARVARD Sommerfeld-Bloch theory of metals, insulators, and superconductors: many-electron
More informationPhase diagram of the cuprates: Where is the mystery? A.-M. Tremblay
Phase diagram of the cuprates: Where is the mystery? A.-M. Tremblay I- Similarities between phase diagram and quantum critical points Quantum Criticality in 3 Families of Superconductors L. Taillefer,
More informationSYK models and black holes
SYK models and black holes Black Hole Initiative Colloquium Harvard, October 25, 2016 Subir Sachdev Talk online: sachdev.physics.harvard.edu HARVARD Wenbo Fu, Harvard Yingfei Gu, Stanford Richard Davison,
More informationQuantum entanglement and the phases of matter
Quantum entanglement and the phases of matter Imperial College May 16, 2012 Lecture at the 100th anniversary Solvay conference, Theory of the Quantum World, chair D.J. Gross. arxiv:1203.4565 sachdev.physics.harvard.edu
More informationCan superconductivity emerge out of a non Fermi liquid.
Can superconductivity emerge out of a non Fermi liquid. Andrey Chubukov University of Wisconsin Washington University, January 29, 2003 Superconductivity Kamerling Onnes, 1911 Ideal diamagnetism High Tc
More informationSpin liquids on the triangular lattice
Spin liquids on the triangular lattice ICFCM, Sendai, Japan, Jan 11-14, 2011 Talk online: sachdev.physics.harvard.edu HARVARD Outline 1. Classification of spin liquids Quantum-disordering magnetic order
More informationAdS/CFT and holographic superconductors
AdS/CFT and holographic superconductors Toby Wiseman (Imperial) In collaboration with Jerome Gauntlett and Julian Sonner [ arxiv:0907.3796 (PRL 103:151601, 2009), arxiv:0912.0512 ] and work in progress
More informationProbing Universality in AdS/CFT
1 / 24 Probing Universality in AdS/CFT Adam Ritz University of Victoria with P. Kovtun [0801.2785, 0806.0110] and J. Ward [0811.4195] Shifmania workshop Minneapolis May 2009 2 / 24 Happy Birthday Misha!
More informationCondensed Matter Physics in the City London, June 20, 2012
Entanglement, holography, and the quantum phases of matter Condensed Matter Physics in the City London, June 20, 2012 Lecture at the 100th anniversary Solvay conference, Theory of the Quantum World arxiv:1203.4565
More informationQuantum phase transitions in condensed matter
Quantum phase transitions in condensed matter The 8th Asian Winter School on Strings, Particles, and Cosmology, Puri, India January 11-18, 2014 Subir Sachdev Talk online: sachdev.physics.harvard.edu HARVARD
More informationStates of quantum matter with long-range entanglement in d spatial dimensions. Gapped quantum matter Spin liquids, quantum Hall states
States of quantum matter with long-range entanglement in d spatial dimensions Gapped quantum matter Spin liquids, quantum Hall states Conformal quantum matter Graphene, ultracold atoms, antiferromagnets
More informationComplex entangled states of quantum matter, not adiabatically connected to independent particle states. Compressible quantum matter
Complex entangled states of quantum matter, not adiabatically connected to independent particle states Gapped quantum matter Z2 Spin liquids, quantum Hall states Conformal quantum matter Graphene, ultracold
More informationElectronic quasiparticles and competing orders in the cuprate superconductors
Electronic quasiparticles and competing orders in the cuprate superconductors Andrea Pelissetto Rome Subir Sachdev Ettore Vicari Pisa Yejin Huh Harvard Harvard Gapless nodal quasiparticles in d-wave superconductors
More informationThe Nernst effect in high-temperature superconductors
The Nernst effect in high-temperature superconductors Iddo Ussishkin (University of Minnesota) with Shivaji Sondhi David Huse Vadim Oganesyan Outline Introduction: - High-temperature superconductors: physics
More informationFermi Surface Reconstruction and the Origin of High Temperature Superconductivity
Fermi Surface Reconstruction and the Origin of High Temperature Superconductivity Mike Norman Materials Science Division Argonne National Laboratory & Center for Emergent Superconductivity Physics 3, 86
More informationThe Hubbard model in cold atoms and in the high-tc cuprates
The Hubbard model in cold atoms and in the high-tc cuprates Daniel E. Sheehy Aspen, June 2009 Sheehy@LSU.EDU What are the key outstanding problems from condensed matter physics which ultracold atoms and
More informationQuantum entanglement and the phases of matter
Quantum entanglement and the phases of matter University of Cincinnati March 30, 2012 sachdev.physics.harvard.edu HARVARD Sommerfeld-Bloch theory of metals, insulators, and superconductors: many-electron
More informationQuantum phase transitions and the Luttinger theorem.
Quantum phase transitions and the Luttinger theorem. Leon Balents (UCSB) Matthew Fisher (UCSB) Stephen Powell (Yale) Subir Sachdev (Yale) T. Senthil (MIT) Ashvin Vishwanath (Berkeley) Matthias Vojta (Karlsruhe)
More informationQuantum Criticality. S. Sachdev and B. Keimer, Physics Today, February Talk online: sachdev.physics.harvard.edu HARVARD. Thursday, May 5, 2011
Quantum Criticality S. Sachdev and B. Keimer, Physics Today, February 2011 Talk online: sachdev.physics.harvard.edu HARVARD What is a quantum phase transition? Non-analyticity in ground state properties
More informationGauge/Gravity Duality: Applications to Condensed Matter Physics. Johanna Erdmenger. Julius-Maximilians-Universität Würzburg
Gauge/Gravity Duality: Applications to Condensed Matter Physics. Johanna Erdmenger Julius-Maximilians-Universität Würzburg 1 New Gauge/Gravity Duality group at Würzburg University Permanent members 2 Gauge/Gravity
More informationTopological order in insulators and metals
HARVARD Topological order in insulators and metals 34th Jerusalem Winter School in Theoretical Physics New Horizons in Quantum Matter December 27, 2016 - January 5, 2017 Subir Sachdev Talk online: sachdev.physics.harvard.edu
More informationQuantum Criticality and Black Holes
Quantum Criticality and Black Holes ubir Sachde Talk online at http://sachdev.physics.harvard.edu Quantum Entanglement Hydrogen atom: Hydrogen molecule: = _ = 1 2 ( ) Superposition of two electron states
More informationLattice modulation experiments with fermions in optical lattices and more
Lattice modulation experiments with fermions in optical lattices and more Nonequilibrium dynamics of Hubbard model Ehud Altman Weizmann Institute David Pekker Harvard University Rajdeep Sensarma Harvard
More informationCold atoms and AdS/CFT
Cold atoms and AdS/CFT D. T. Son Institute for Nuclear Theory, University of Washington Cold atoms and AdS/CFT p.1/27 History/motivation BCS/BEC crossover Unitarity regime Schrödinger symmetry Plan Geometric
More informationDetecting collective excitations of quantum spin liquids. Talk online: sachdev.physics.harvard.edu
Detecting collective excitations of quantum spin liquids Talk online: sachdev.physics.harvard.edu arxiv:0809.0694 Yang Qi Harvard Cenke Xu Harvard Max Metlitski Harvard Ribhu Kaul Microsoft Roger Melko
More informationThermo-electric transport in holographic systems with moment
Thermo-electric Perugia 2015 Based on: Thermo-electric gauge/ models with, arxiv:1406.4134, JHEP 1409 (2014) 160. Analytic DC thermo-electric conductivities in with gravitons, arxiv:1407.0306, Phys. Rev.
More informationAdS/CFT and condensed matter. Talk online: sachdev.physics.harvard.edu
AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Particle theorists Sean Hartnoll, KITP Christopher Herzog, Princeton Pavel Kovtun, Victoria Dam Son, Washington Condensed matter theorists
More informationHolographic transport with random-field disorder. Andrew Lucas
Holographic transport with random-field disorder Andrew Lucas Harvard Physics Quantum Field Theory, String Theory and Condensed Matter Physics: Orthodox Academy of Crete September 1, 2014 Collaborators
More informationQuantum phase transitions in Mott insulators and d-wave superconductors
Quantum phase transitions in Mott insulators and d-wave superconductors Subir Sachdev Matthias Vojta (Augsburg) Ying Zhang Science 286, 2479 (1999). Transparencies on-line at http://pantheon.yale.edu/~subir
More informationHow to get a superconductor out of a black hole
How to get a superconductor out of a black hole Christopher Herzog Princeton October 2009 Quantum Phase Transition: a phase transition between different quantum phases (phases of matter at T = 0). Quantum
More informationRevealing fermionic quantum criticality from new Monte Carlo techniques. Zi Yang Meng ( 孟子杨 )
Revealing fermionic quantum criticality from new Monte Carlo techniques Zi Yang Meng ( 孟子杨 ) http://ziyangmeng.iphy.ac.cn Collaborators and References Xiao Yan Xu Zi Hong Liu Chuang Chen Gao Pei Pan Yang
More informationSign-problem-free quantum Monte Carlo of the onset of antiferromagnetism in metals
arxiv:1206.0742v2 [cond-mat.str-el] 8 Nov 2012 Sign-problem-free quantum Monte Carlo of the onset of antiferromagnetism in metals Erez Berg, 1,2 Max A. Metlitski, 3 Subir Sachdev 1,4 1 Department of Physics,
More informationQuantum Monte Carlo investigations of correlated electron systems, present and future. Zi Yang Meng ( 孟子杨 )
Quantum Monte Carlo investigations of correlated electron systems, present and future Zi Yang Meng ( 孟子杨 ) http://ziyangmeng.iphy.ac.cn Collaborators Xiao Yan Xu Yoni Schattner Zi Hong Liu Erez Berg Chuang
More informationTuning order in cuprate superconductors
Tuning order in cuprate superconductors arxiv:cond-mat/0201401 v1 23 Jan 2002 Subir Sachdev 1 and Shou-Cheng Zhang 2 1 Department of Physics, Yale University, P.O. Box 208120, New Haven, CT 06520-8120,
More informationTopological order in quantum matter
HARVARD Topological order in quantum matter Stanford University Subir Sachdev November 30, 2017 Talk online: sachdev.physics.harvard.edu Mathias Scheurer Wei Wu Shubhayu Chatterjee arxiv:1711.09925 Michel
More informationarxiv: v1 [hep-th] 16 Feb 2010
Condensed matter and AdS/CFT Subir Sachdev arxiv:1002.2947v1 [hep-th] 16 Feb 2010 Lectures at the 5th Aegean summer school, From gravity to thermal gauge theories: the AdS/CFT correspondence, Adamas, Milos
More information