Ultra-quantum metals. Subir Sachdev February 5, 2018 Simons Foundation, New York HARVARD

Transcription

1 Ultra-quantum metals Subir Sachdev February 5, 2018 Simons Foundation, New York HARVARD

2 <latexit sha1_base64="k7jx8efbma2lrujxy27hncmbd18=">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</latexit> Ubiquitous Strange, Bad, Incoherent, or Ultra-quantum metal has a resistivity,, which obeys T, and in some cases h/e 2 (in two dimensions), where h/e 2 is the quantum unit of resistance.

3 Ultra-quantum metals just got stranger B-linear magnetoresistance!? Ba-122 LSCO I. M. Hayes et. al., Nat. Phys P. Giraldo-Gallo et. al., arxiv:

4 Ultra-quantum metals just got stranger Scaling between B and T!? Ba-122 Ba-122 I. M. Hayes et. al., Nat. Phys. 2016

5 Interactions between L. Balents, J. McGreevy, S. Sachdev, T. Senthil (partly nucleated by student, Aavishkar Patel) Quantum spin liquids and the metal-insulator transition in doped semiconductors, Andrew C. Potter, Maissam Barkeshli, John McGreevy, T. Senthil, Phys. Rev. Lett. 109, (2012). A strongly correlated metal built from Sachdev-Ye-Kitaev models, Xue-Yang Song, Chao-Ming Jian, Leon Balents, Phys. Rev. Lett. 119, (2017). Magnetotransport in a model of a disordered strange metal, Aavishkar A. Patel, John McGreevy, Daniel P. Arovas, Subir Sachdev, arxiv: Translationally invariant non-fermi liquid metals with critical Fermi-surfaces: Solvable models, Debanjan Chowdhury, Yochai Werman, Erez Berg, T. Senthil, arxiv:

6 H = The Sachdev-Ye-Kitaev (SYK) model 1 (2N) 3/2 NX i,j,k,`=1 U ij;k` f i f j f k f` µ X i f i f i X Pick a set of random positions

7 The SYK model H = 1 (2N) 3/2 NX i,j,k,`=1 U ij;k` f i f j f k f` µ X i f i f i X Place electrons randomly on some sites

8 The SYK model H = 1 (2N) 3/2 NX i,j,k,`=1 U ij;k` f i f j f k f` µ X i f i f i X Entangle electrons pairwise randomly

9 The SYK model H = 1 (2N) 3/2 NX i,j,k,`=1 U ij;k` f i f j f k f` µ X i f i f i X Entangle electrons pairwise randomly

10 The SYK model H = 1 (2N) 3/2 NX i,j,k,`=1 U ij;k` f i f j f k f` µ X i f i f i X Entangle electrons pairwise randomly

11 The SYK model H = 1 (2N) 3/2 NX i,j,k,`=1 U ij;k` f i f j f k f` µ X i f i f i X Entangle electrons pairwise randomly

12 The SYK model H = 1 (2N) 3/2 NX i,j,k,`=1 U ij;k` f i f j f k f` µ X i f i f i X Entangle electrons pairwise randomly

13 The SYK model H = 1 (2N) 3/2 NX i,j,k,`=1 U ij;k` f i f j f k f` µ X i f i f i X Entangle electrons pairwise randomly

14 The SYK model H = 1 (2N) 3/2 NX i,j,k,`=1 U ij;k` f i f j f k f` µ X i f i f i X This describes both a strange metal and a black hole!

15 The SYK model Feynman graph expansion in U ijk`, and graph-by-graph average, yields exact equations in the large N limit: G(i!) = 1 i! + µ (i!) G( =0 )=Q., ( ) = U 2 G 2 ( )G( ) S. Sachdev and J. Ye, Phys. Rev. Lett. 70, 3339 (1993)

16 The SYK model Feynman graph expansion in U ijk`, and graph-by-graph average, yields exact equations in the large N limit: G(i!) = 1 i! + µ (i!) X G( =0 )=Q., ( ) = U 2 G 2 ( )G( ) Low frequency analysis shows that the solutions must be gapless and obey (z) =µ 1 Ap z +..., G(z) = A pz where A = e i /4 ( /U 2 ) 1/4 at half-filling. The ground state is a non-fermi liquid, with a continuously variable density Q. <latexit sha1_base64="0uo4waqgszzn7hs7cocap/zkzug=">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</latexit> <latexit sha1_base64="0uo4waqgszzn7hs7cocap/zkzug=">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</latexit> S. Sachdev and J. Ye, Phys. Rev. Lett. 70, 3339 (1993)

17 The SYK model Many-body level spacing 2 N = e N ln 2 Non-quasiparticle excitations with spacing e Ns 0 There are 2 N many body levels with energy E, which do not admit a quasiparticle decomposition. Shown are all values of E for a single cluster of size N = 12. The T! 0 state has an entropy S GP S = Ns 0 with s 0 = G + ln(2) 4 < ln 2 = where G is Catalan s constant, for the half-filled case Q =1/2. GPS: A. Georges, O. Parcollet, and S. Sachdev, PRB 63, (2001) W. Fu and S. Sachdev, PRB 94, (2016)

18 The SYK model Many-body level spacing 2 N = e N ln 2 There are 2 N many body levels with energy E, which do not admit a quasiparticle decomposition. Shown are all values of E for a single cluster of size N = 12. The T! 0 state has an entropy S GP S = Ns 0 with s 0 = G + ln(2) 4 < ln 2 = Non-quasiparticle excitations with spacing e Ns 0 W. Fu and S. Sachdev, PRB 94, (2016) where G is Catalan s constant, for the half-filled case Q =1/2. GPS: A. Georges, O. Parcollet, and S. Sachdev, PRB 63, (2001) For SYK models with N =2supersymmetry,GPS=BPS <latexit sha1_base64="hy0bptipu7u4cqjcamcnhahepgg=">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</latexit> <latexit sha1_base64="hy0bptipu7u4cqjcamcnhahepgg=">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</latexit>

19 The SYK model Low energy, many-body density of states (E) e Ns 0 sinh( p 2(E E 0 )N ) D. Stanford and E. Witten, A. M. Garica-Garcia, J.J.M. Verbaarschot, D. Bagrets, A. Altland, and A. Kamenev, Low temperature entropy S = Ns 0 + N T +... T = 0 fermion Green s function G( ) 1/2 at large. (Fermi liquids with quasiparticles have G( ) 1/ ) T>0Green sfunction has conformal invariance G (T/sin( k B T /~)) 1/2 A. Georges and O. Parcollet PRB 59, 5341 (1999) The last property indicates eq ~/(k B T ), and this has been found in a recent numerical study. A. Eberlein, V. Kasper, S. Sachdev, and J. Steinberg, arxiv:

20 Black holes Black holes have an entropy and a temperature, T H = ~c 3 /(8 GMk B ). The entropy is proportional to their surface area. They relax to thermal equilibrium in a time ~/(k B T H ).

21 LIGO September 14, 2015 The ring-down is predicted by General Relativity to happen in a time 8 GM c 3 8 milliseconds. Curiously this happens to equal ~ k B T H : so the ring down can also be viewed as the approach of a quantum system to thermal equilibrium at the fastest possible rate.!

22 The SYK model Low energy, many-body density of states (E) e Ns 0 sinh( p 2(E E 0 )N ) D. Stanford and E. Witten, A. M. Garica-Garcia, J.J.M. Verbaarschot, D. Bagrets, A. Altland, and A. Kamenev, Low temperature entropy S = Ns 0 + N T +... T = 0 fermion Green s function G( ) 1/2 at large. (Fermi liquids with quasiparticles have G( ) 1/ ) T>0Green sfunction has conformal invariance G (T/sin( k B T /~)) 1/2 A. Georges and O. Parcollet PRB 59, 5341 (1999) The last property indicates eq ~/(k B T ), and this has been found in a recent numerical study. A. Eberlein, V. Kasper, S. Sachdev, and J. Steinberg, arxiv:

23 Black hole horizon SYK and black holes ~x Black holes with a near-horizon AdS2 geometry (described by quantum gravity in 1+1 spacetime dimensions) match the properties of the 0+1 dimensional SYK model in the previous slide: Ns0 is the Bekenstein-Hawking entropy S. Sachdev, PRL 105, (2010); A. Kitaev (2015); J. Maldacena, D. Stanford, and Zhenbin Yang, arxiv:

24 Infecting a Fermi liquid and making it SYK Mobile electrons (c) interacting with SYK quantum dots (f) with exchange interactions. This yields the first model agreeing with magnetotransport in strange metals! c f Debanjan Chowdhury, Yochai Werman, Erez Berg, T. Senthil, arxiv:

25 Infecting a Fermi liquid and making it SYK Mobile electrons (c) interacting with SYK quantum dots (f) with exchange interactions. This yields the first model agreeing with magnetotransport in strange metals! c f Aavishkar A. Patel, John McGreevy, Daniel P. Arovas, Subir Sachdev, arxiv:

26 Infecting a Fermi liquid and making it SYK Mobile electrons (c) interacting with SYK quantum dots (f) with exchange interactions. This yields the first model agreeing with magnetotransport in strange metals! Large N solution (with or without microscopic disorder) yields a marginal Fermi liquid metal, with conductivities of the form: xx(b,t) = 1 B T L T xy(b,t) = B B T 2 H T where the scaling functions interpolate as L,H(b! 0) constant ; L,H(b!1) 1/b 2 This solution exhibits B/T scaling, but the magnetoresistance xx saturates for B T. <latexit sha1_base64="nvhrmartpt4gwjshxqwwoa/+row=">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</latexit> Aavishkar A. Patel, John McGreevy, Daniel P. Arovas, Subir Sachdev, arxiv:

27 Infecting a Fermi liquid and making it SYK Need mesoscopic disorder to obtain linear-in-b magnetoresistance Current path length increases linearly with B at large B due to local Hall effect, which causes the global resistance to increase linearly with B at large B. Exact numerical solution of charge-transport equations in a random-resistor network. (M. M. Parish and P. Littlewood, Nature 426, 162 (2003))

28 Infecting a Fermi liquid and making it SYK n b /n a =0.8 b/ a =0.8 a =0.1k B T t/100 (B =0.0025) Scaling between B and T (T = t/100) ~ 50 T (a = 3.82 A) Aavishkar A. Patel, John McGreevy, Daniel P. Arovas, Subir Sachdev, arxiv:

29 <latexit sha1_base64="muuuoyjnbgbjqjkic9mruaxqeoe=">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</latexit> This simple two-component model describes a new state of matter which is realized by electrons in the presence of strong interactions and disorder. Can such a model be realized as a fixed-point of a generic theory of strongly-interacting electrons in the presence of disorder? Can we start from a single-band Hubbard model with (or without) disorder, and end up with such two-band fixed point, with emergent local conservation laws?

30 Electrons in doped silicon appear to separate into two components: localized spin moments and itinerant electrons 10' P 2 [ " T(K) F1G. 1. Temperature dependence of normalized susceptibility g/gp, ~; of three Si:P,B samples with dia'erent normalized electron densities, n/n, =0. 58, I.I, and 1.8. Solid lines through data are a guide to the eye. M. J. Hirsch, D.F. Holcomb, R.N. Bhatt, and M.A. Paalanen PRL 68, 1418 (1992) M. Milovanovic, S. Sachdev and R.N. Bhatt, PRL 63, 82 (1989) A.C. Potter, M. Barkeshli, J. McGreevy, T. Senthil, PRL 109, (2012)

31 Magnetic excitations are localized (eigenmodes of the spin susceptibility) Charged fermionic excitations are extended (eigenmodes of the electron Hamiltonian) M. Milovanovic, S. Sachdev and R.N. Bhatt, PRL 63, 82 (1989)

32 <latexit sha1_base64="fo91dwskzs4pr/lzhpdfdyle7si=">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</latexit> Many-body quantum chaos and transport Using holographic analogies, Shenker, Stanford, Maldacena introduced the Lyapunov time, L,thetime over which a generic many-body quantum system loses memory of its initial state (defined via an outof-time-order (OTOC) correlator), and established a shortest-possible time to reach quantum chaos L ~ 2 k B T A related bound was proposed earlier (Sachdev, 1999). The SYK model, and black holes in Einstein gravity, saturate this bound.

33 <latexit sha1_base64="rhtlzneykppqwlj1lmqohawsjp8=">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</latexit> Many-body quantum chaos and transport Much theoretical work has examined connections between this chaos bound, and measurable transport co-e cients. The most robust connection is to the thermal di usivity, D T D T v 2 B L (Kapitulnik) where v B is the butterfly velocity at which chaos propagates. A. A. Patel and S. Sachdev, PNAS 114, 1844 (2017) M. Blake, R. A. Davison, and S. Sachdev, PRD 96, (2017)

34 <latexit sha1_base64="c70wv0ds5ti9hj5mdninck/7mmq=">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</latexit> Many-body quantum chaos and transport A quantum hydrodynamical description for scrambling and many-body chaos Mike Blake, Hyunseok Lee, and Hong Liu arxiv: A direct connection was established between the energy di usion mode and the OTOCs measuring chaos. This assumes dominance of the energy di usion mode up to energies of order k B T, which is beyond the hydrodynamic regime. Such a dominance holds in SYK models and holographic theories, and can be expected more generally in ultra-quantum metals without quasiparticle excitations.

35 Non-zero density of fermions strongly coupled to gauge fields, (in the presence of disorder)

36 <latexit sha1_base64="pskis3wp903mnhhacg4i6epd0io=">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</latexit> Non-zero density of fermions strongly coupled to gauge fields, (in the presence of disorder) Half-filled Landau level (Son) Surfaces of (correlated) topological insulators Strange metal state of high (Son) temperature superconductors Pseudogap state of hole-doped cuprates

37 <latexit sha1_base64="pskis3wp903mnhhacg4i6epd0io=">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</latexit> Non-zero density of fermions strongly coupled to gauge fields, (in the presence of disorder) Half-filled Landau level (Son) Surfaces of (correlated) topological insulators Strange metal state of high temperature superconductors Pseudogap state of hole-doped cuprates

38 SM FL YBa 2 Cu 3 O 6+x Figure: K. Fujita and J. C. Seamus Davis

39 SM FL YBa 2 Cu 3 O 6+x Deconfinement transition of a gauge theory? Figure: K. Fujita and J. C. Seamus Davis

40 <latexit sha1_base64="pskis3wp903mnhhacg4i6epd0io=">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</latexit> Non-zero density of fermions strongly coupled to gauge fields, (in the presence of disorder) Half-filled Landau level (Son) Surfaces of (correlated) topological insulators Strange metal state of high temperature superconductors Pseudogap state of hole-doped cuprates

41 <latexit sha1_base64="8bjcuulnfkn/rzb5/mvhsg1uero=">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</latexit> Non-zero density of fermions strongly coupled to gauge fields, (in the presence of disorder) Distinct phases of the gauge theory can be distinguished even in the presence of disorder Is the usual confinement/higgs/deconfinement criterion general enough in the presence of disorder? Novel critical points or phases?

42 A solvable model Fractionalize the electron (c i, i =1...N, =1...M) into an orthogonal fermion f i and an Ising spin i z = ±1: c i = This introduces a Z 2 gauge invariance z i f i z i! i z i, f i! i f i The solvable model is (closely related to) the N!1, M!1limit of H = X µf i f i g i x i + p 1 X z z t ij i j f i f j + 1 X p J ij f i f i f j f j NM NM i,j (Senthil, Metlitski, Vishwanath, Sachdev ) where t ij and J ij are random numbers. What is the fate of the Z 2 gauge theory as a function of the coupling g? i,j

43 A solvable model Fractionalize the electron (c i, i =1...N, =1...M) into an orthogonal fermion f i and an Ising spin i z = ±1: c i = This introduces a Z 2 gauge invariance z i f i z i! i z i, f i! i f i The solvable model is (closely related to) the N!1, M!1limit of H = X µf i f i g i x i + p 1 X z z t ij i j f i f j + 1 X p J ij f i f i f j f j NM NM i,j (Senthil, Metlitski, Vishwanath, Sachdev ) where t ij and J ij are random numbers. What is the fate of the Z 2 gauge theory as a function of the coupling g? i,j

44 <latexit sha1_base64="du47f7vjqkj5ijvhrhydnbqckp0=">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</latexit> <latexit sha1_base64="uipqfli2sv3p+6x1xepmimn1ykw=">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</latexit> <latexit sha1_base64="z/w7rvojjt1g12b0lgxypniawlc=">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</latexit> <latexit sha1_base64="2mrnkh2ivjctmqnorg3ix6n58gq=">aaacchicdvdltgjbejz1ifhcpxqzccae1gvr9eb04letv0iaknmhgymzs5uzxpvs+aipxvuzpbmv/ovf4s84iczqtjjoklxd6e4kyikmet6bmzu9mzs3n1nili4tr6zm1tyvtzrodj6pzktratmghqifbuqoxxpygeiobvcni792ddqisf3giizwyhpkdavnacw/unztfdq5vofuh5yoygfuc70xlcnvvsovjxynsp5mcnbovtc7eu9cumglm6zr9gjspuyj4bkg2wziigb8ivwgyaliizhwoj52slet0qhdsntssmfq94muhcymwsb2hgz75rc3ev/yggl2d1upuhgcopjnom4ikuz09dntca0c5casxrwwt1lez5pxtplkmwzsekqh/bsjcis3omp3pgv3x6ihtegrbvo/8uvukeudl/lv40lugbjjtsgokzikqzjtckz8wokg9+sbpdp3zppz7lx8tk45k5kn8gpo6wf5qzo+</latexit> A solvable model There is no confining/higgs phase, but there is a phase transition between a deconfined phase and a critical-higgs phase. Critical-Higgs point. f gapless and critical. z gapless and critical. Deconfined phase: a critical orthogonal metal. f gapless and critical. z gapped. Critical-Higgs phase. f gapless and critical. z gapless and critical. g c 1/g (Wenbo Fu, Yingfei Gu, SS, G. Tarnopolsky)

45 <latexit sha1_base64="du47f7vjqkj5ijvhrhydnbqckp0=">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</latexit> <latexit sha1_base64="uipqfli2sv3p+6x1xepmimn1ykw=">aaacjhicdvfdi9nafj3erzv+bhufvrgssj5odtrsdkweruh2cywtu9cu7mrykww7myszg9cs+uxv9eeif8fj0wuvvtbwoofce4dz40pji4x99/wbn2/dvrnzn7h3/8hd3d6jx59twrsbm1gq0pzh3iksgmyoucf5zyaxsykz+pjdq599awnlqu9xvcgi4jmwqrqchbxsfyt0kxucgopthaxqaakuqsh1krxu2cgxzdjlq9zteexjgile23jhujrcw9moozhgfyb2ugldceg6v8b14uilc2gcvxd1ejn4f7+tw2wvz0i2ngyni9qc4wq8cebwxaam0uhintun2zpz9n5gssnqwv1ckg7tfmaqxdtcuokk1kfuw6i4uoqzzb3uvac7adabreklxyq0ly17gumg/b2j4yw1qyj2zojjbv/wwvjf2rzg9hdrsf3vcfp0i9jausxpmz5npagbauua75kgiuegc3q3ciil7oa6w7yjel7iluzcnmyutqveu4suy6d/b7nh+czkn4b9o/fbqhbie/kcvcqdmivh5jickbkr5ie35z31nvm7/th/67/rrl637dkjf5t/8rdolmbo</latexit> <latexit sha1_base64="z/w7rvojjt1g12b0lgxypniawlc=">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</latexit> <latexit sha1_base64="2mrnkh2ivjctmqnorg3ix6n58gq=">aaacchicdvdltgjbejz1ifhcpxqzccae1gvr9eb04letv0iaknmhgymzs5uzxpvs+aipxvuzpbmv/ovf4s84iczqtjjoklxd6e4kyikmet6bmzu9mzs3n1nili4tr6zm1tyvtzrodj6pzktratmghqifbuqoxxpygeiobvcni792ddqisf3giizwyhpkdavnacw/unztfdq5vofuh5yoygfuc70xlcnvvsovjxynsp5mcnbovtc7eu9cumglm6zr9gjspuyj4bkg2wziigb8ivwgyaliizhwoj52slet0qhdsntssmfq94muhcymwsb2hgz75rc3ev/yggl2d1upuhgcopjnom4ikuz09dntca0c5casxrwwt1lez5pxtplkmwzsekqh/bsjcis3omp3pgv3x6ihtegrbvo/8uvukeudl/lv40lugbjjtsgokzikqzjtckz8wokg9+sbpdp3zppz7lx8tk45k5kn8gpo6wf5qzo+</latexit> A solvable model There is no confining/higgs phase, but there is a phase transition between a deconfined phase and a critical-higgs phase. Distinct exponents Critical-Higgs point. f gapless and critical. z gapless and critical. Deconfined phase: a critical orthogonal metal. f gapless and critical. z gapped. Critical-Higgs phase. f gapless and critical. z gapless and critical. g c 1/g (Wenbo Fu, Yingfei Gu, SS, G. Tarnopolsky)

46 <latexit sha1_base64="g0am6ho2e7vx53epw3xykyamo98=">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</latexit> Thoughts on field theories of ultra-quantum metals Breakdown of quasiparticles requires strong coupling to a low energy collective mode In all known cases, we can write down the singular processes in terms of a continuum field theory of the fermions near the Fermi surface coupled to the collective mode. In all known cases, the continuum critical theory has a conserved total (pseudo-) momentum, P ~, which commutes with the Hamiltonian. This momentum may not be equal to the crystal momentum of the underlying lattice model.

47 <latexit sha1_base64="szc+obw1wr/hdkokgkvymuoxd94=">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</latexit> Thoughts on field theories of ultra-quantum metals As long as J, ~ P ~ 6=0(where J ~ is the electrical current) the d.c. resistivity of the critical theory is exactly zero. This is the case even though the electron self energy can be highly singular and there are no fermionic quasiparticles (many well-known papers on non-fermi liquid transport ignore this point.) We need to include additional (dangerously) irrelevant umklapp corrections to obtain a non-zero resistivity. Because these additional corrections are irrelevant, it is di cult to see how they can induce a linear-in-t resistivity.

48 Thoughts on field theories of ultra-quantum metals Theories of metallic states without quasiparticles in the presence of disorder Well-known perturbative theory of disordered metals has 2 classes of known fixed points, the insulator at strong disorder, and the metal at weak disorder. The latter state has long-lived, extended quasiparticle excitations (which are not plane waves). Needed: a metallic fixed point at intermediate disorder and strong interactions without quasiparticle excitations. Although disorder is present, it largely self-averages at long scales. SYK models