Confinement-deconfinement transitions in Z 2 gauge theories, and deconfined criticality
|
|
- Polly Walsh
- 5 years ago
- Views:
Transcription
1 HARVARD Confinement-deconfinement transitions in Z 2 gauge theories, and deconfined criticality Indian Institute of Science Education and Research, Pune Subir Sachdev November 15, 2017 Talk online: sachdev.physics.harvard.edu
2 1. Z2 lattice gauge theory and topological order 2. The Ising* confinement transition 3. Odd Z2 lattice gauge theory and deconfined criticality with an emergent U(1) gauge field 4. Z2 lattice gauge theory with fermions at half-filling, and deconfined criticality with an emergent SU(2) gauge field
3 1. Z2 lattice gauge theory and topological order 2. The Ising* confinement transition 3. Odd Z2 lattice gauge theory and deconfined criticality with an emergent U(1) gauge field 4. Z2 lattice gauge theory with fermions at half-filling, and deconfined criticality with an emergent SU(2) gauge field
4 Z2 lattice gauge theory (Wegner, 1971) z H = X z z z z g X i x z z z G i = x x x x Gauss s Law: [H, G i ]=0, G i =1
5 Z2 lattice gauge theory (Wegner, 1971) W C = Y C z C Deconfined phase W C Perimeter Law Confined phase W C Area Law g
6 Topological order V x = Y Cx x, V y = Y Cy x C y C y C x W x = Y C x z, W y = Y C y z C x V x W y = W y V x, V y W x = W x V y and all other pairs commute. On a torus, there are two additional independent operators, V x and V y which commute with the Hamiltonian: [H, V x ]=[H, V y ]=0 Deconfined phase W C Perimeter Law Confined phase W C Area Law g
7 Topological order V x = Y Cx x, V y = Y Cy x C y C y C x W x = Y C x z, W y = Y C y z C x V x W y = W y V x, V y W x = W x V y and all other pairs commute. On a torus, there are two additional independent operators, V x and V y which commute with the Hamiltonian: [H, V x ]=[H, V y ]=0 Deconfined phase. 4-fold degenerate ground state: V x = ±1, V y = ±1. Can take linear combinations to make eigenstates with W x = ±1, W y = ±1. Topological order Confined phase. Unique ground state has V x = 1, V y = 1. No topological order g
8 Topological order V x = Y Cx x, V y = Y Cy x C y C y C x W x = Y C x z, W y = Y C y z C x V x W y = W y V x, V y W x = W x V y and all other pairs commute. On a torus, there are two additional independent operators, V x and V y which commute with the Hamiltonian: [H, V x ]=[H, V y ]=0 Topological phase has degenerate states with Z 2 flux W = ±1 through the holes of the torus (N. Read and S.S., 1991)
9 Topological order V x = Y Cx x, V y = Y Cy x C y C y C x W x = Y C x z, W y = Y C y z C x V x W y = W y V x, V y W x = W x V y and all other pairs commute. On a torus, there are two additional independent operators, V x and V y which commute with the Hamiltonian: [H, V x ]=[H, V y ]=0 Deconfined phase. 4-fold degenerate ground state: V x = ±1, V y = ±1. Can take linear combinations to make eigenstates with W x = ±1, W y = ±1. Topological order Confined phase. Unique ground state has V x = 1, V y = 1. No topological order g This criterion can distinguish the phases when dynamical (or even gapless) matter fields are present
10 1. Z2 lattice gauge theory and topological order 2. The Ising* confinement transition 3. Odd Z2 lattice gauge theory and deconfined criticality with an emergent U(1) gauge field 4. Z2 lattice gauge theory with fermions at half-filling, and deconfined criticality with an emergent SU(2) gauge field
11 H = X z z z z g X i x G i =1 Kramers-Wannier-Wegner duality, Ising criticality Deconfined phase. 4-fold degenerate ground state: V x = ±1, V y = ±1. Can take linear combinations to make eigenstates with W x = ±1, W y = ±1. Topological order Confined phase. Unique ground state has V x = 1, V y = 1. No topological order g This criterion can distinguish the phases when dynamical (or even gapless) matter fields are present
12 Embed in a compact U(1) gauge theory Define z e ia and impose A =0, by adding a potential cos(2a). Then make a gauge transformation A µ! A µ µ /2, and make dynamical to make the Hamiltonian gauge invariant. In this manner the Z 2 gauge theory becomes a compact U(1) gauge theory with a charge 2 Higgs field: 2 L = X 4 ~! 3 2 A i + 1 i 5 X cos( ~ A) ~ J X cos( ~ i 2 A ~ i ) i i E. Fradkin and S. Shenker, Phys Rev D 19, 3682 (1979) Now we take the naive continuum limit with the Higgs field obtain a theory of complex scalar coupled to a U(1) gauge field e i, and L = (@ µ 2iA µ ) 2 + s 2 + u e 2 ( A ) 2 However, this turns continuum theory out to be incorrect: we cannot ignore the monopoles is the compact U(1) gauge field, A µ near the confinement transition.
13 Particle-vortex duality But we proceed anyway, and perform a Dasgupta-Halperin-Peskin particlevortex duality on L. This requires a complex scalar which creates a vortex with flux, and the dual theory is el µ 2 + es 2 + eu 4. Now we have to impose the requirement that vortices with flux and flux are the same i.e. allow 2 monopoles to be created from the vacuum. This modifies the Lagrangian to el µ 2 + es 2 + eu 4 ( 2 +( ) 2 ). Finally, we write = + i#. Thefield has a smaller mass then #, and so we can integrated out # to obtain the final correct dual theory el = (@ µ ) 2 + es 2 + eu 4. This is the promised dual Ising theory of the confinement-deconfinement transition. The field creates the vison particle. The refers to the fact that a single vison cannot be created locally, and this changes some topological properties on compact spaces.
14 H = X z z z z g X i x G i =1 Kramers-Wannier-Wegner duality, Ising criticality Deconfined phase. 4-fold degenerate ground state: V x = ±1, V y = ±1. Can take linear combinations to make eigenstates with W x = ±1, W y = ±1. Topological order Confined phase. Unique ground state has V x = 1, V y = 1. No topological order g This criterion can distinguish the phases when dynamical (or even gapless) matter fields are present
15 1. Z2 lattice gauge theory and topological order 2. The Ising* confinement transition 3. Odd Z2 lattice gauge theory and deconfined criticality with an emergent U(1) gauge field 4. Z2 lattice gauge theory with fermions at half-filling, and deconfined criticality with an emergent SU(2) gauge field
16 Symmetry-enriched topological (SET) order H = X z z z z X g x, G i = 1 i
17 Symmetry-enriched topological (SET) order H = X z z z z g X i x, G i = 1 Deconfined phase. 4-fold degenerate ground state: V x = ±1, V y = ±1. Can take linear combinations to make eigenstates with W x = ±1, W y = ±1. Topological order Confined phase. Broken symmetry and valence bond solid (VBS) order g (R. Jalabert and S.S., 1991; T. Senthil, A. Vishwanath, L. Balents, S. S. and M.P.A. Fisher, 2004)
18 Symmetry-enriched topological (SET) order H = X and deconfined criticality z z z z X g x, G i = 1 i Deconfined quantum criticality with a U(1) gauge theory and a charge 2 complex scalar Deconfined phase. 4-fold degenerate ground state: V x = ±1, V y = ±1. Can take linear combinations to make eigenstates with W x = ±1, W y = ±1. Topological order Confined phase. Broken symmetry and valence bond solid (VBS) order g (R. Jalabert and S.S., 1991; T. Senthil, A. Vishwanath, L. Balents, S. S. and M.P.A. Fisher, 2004)
19 Berry phases suppress monopoles at the critical point Embedding the Z 2 gauge theory in a compact U(1) gauge theory as before, the G i = 1 background charges lead to a source term for A (a Polyakov loop) 2 L = X 4 ~! 3 2 A i + 1 i 5 X cos( ~ A) ~ J X cos( ~ i 2 A ~ i ) i i + i X i ( 1) i x+i y A i Performing the Dasgupta-Halperin duality transform directly on this lattice model with the source term, we now find a dual vortex theory in which only quadrupled monopoles are permitted. el µ 2 + es 2 + eu 4 4( 8 +( ) 8 ). The 4 coupling is known to be irrelevant at the (Wilson-Fisher) critical point, and so monopoles can be ignored in the critical theory! Undualizing back to the original theory, this means that it is now valid to take the naive continuum limit of L to obtain the deconfined critical theory with a U(1) gauge field L = (@ µ 2iA µ ) 2 + s 2 + u e 2 ( A ) 2.
20 RG flow of L el µ 2 + es 2 + eu 4 4( 8 +( ) 8 ). VBS 4 Z 2 Neel 0 topological order Critical complex scalar and U(1) gauge field ges c g es U(1) spin Free photon/ Goldstone liquid
21 Symmetry-enriched topological (SET) order H = X and deconfined criticality z z z z X g x, G i = 1 i Deconfined quantum criticality with a U(1) gauge theory and a charge 2 complex scalar Deconfined phase. 4-fold degenerate ground state: V x = ±1, V y = ±1. Can take linear combinations to make eigenstates with W x = ±1, W y = ±1. Topological order Confined phase. Broken symmetry and valence bond solid (VBS) order g (R. Jalabert and S.S., 1991; T. Senthil, A. Vishwanath, L. Balents, S. S. and M.P.A. Fisher, 2004)
22 1. Z2 lattice gauge theory and topological order 2. The Ising* confinement transition 3. Odd Z2 lattice gauge theory and deconfined criticality with an emergent U(1) gauge field 4. Z2 lattice gauge theory with fermions at half-filling, and deconfined criticality with an emergent SU(2) gauge field
23 Fermionic matter at half filling H = X z z z z g X i x t X hiji i z ij j Deconfined phase. Massless Dirac fermions Topological order Confined phase. Fermion pairing and superconductivity g S. Gazit, M. Randeria, and A. Vishwanath, Nature Physics 13, 484 (2017)
24 Fermionic matter at half filling H = X z z z z g X i x t X hiji i z ij j Deconfined quantum criticality with a SU(2) gauge theory and a critical SO(3) Higgs scalar Deconfined phase. Massless Dirac fermions Topological order Confined phase. Fermion pairing and superconductivity g S. Gazit, M. Randeria, and A. Vishwanath, Nature Physics 13, 484 (2017) S. Gazit, F. F. Assaad, Chong Wang, S. Sachdev, and A. Vishwanath, to appear
25 1. Z2 lattice gauge theory and topological order 2. The Ising* confinement transition 3. Odd Z2 lattice gauge theory and deconfined criticality with an emergent U(1) gauge field 4. Z2 lattice gauge theory with fermions at half-filling, and deconfined criticality with an emergent SU(2) gauge field
Quantum Monte Carlo study of a Z 2 gauge theory containing phases with and without a Luttinger volume Fermi surface
Quantum Monte Carlo study of a Z 2 gauge theory containing phases with and without a Luttinger volume Fermi surface V44.00011 APS March Meeting, Los Angeles Fakher Assaad, Snir Gazit, Subir Sachdev, Ashvin
More informationDeconfined Quantum Critical Points
Deconfined Quantum Critical Points Leon Balents T. Senthil, MIT A. Vishwanath, UCB S. Sachdev, Yale M.P.A. Fisher, UCSB Outline Introduction: what is a DQCP Disordered and VBS ground states and gauge theory
More informationLecture 2: Deconfined quantum criticality
Lecture 2: Deconfined quantum criticality T. Senthil (MIT) General theoretical questions Fate of Landau-Ginzburg-Wilson ideas at quantum phase transitions? (More precise) Could Landau order parameters
More informationZ 2 topological order near the Neel state on the square lattice
HARVARD Z 2 topological order near the Neel state on the square lattice Institut für Theoretische Physik Universität Heidelberg April 28, 2017 Subir Sachdev Talk online: sachdev.physics.harvard.edu Shubhayu
More informationDeconfined Quantum Critical Points
Deconfined Quantum Critical Points Outline: with T. Senthil, Bangalore A. Vishwanath, UCB S. Sachdev, Yale L. Balents, UCSB conventional quantum critical points Landau paradigm Seeking a new paradigm -
More informationEmergent gauge fields and the high temperature superconductors
HARVARD Emergent gauge fields and the high temperature superconductors Unifying physics and technology in light of Maxwell s equations The Royal Society, London November 16, 2015 Subir Sachdev Talk online:
More informationProperties of monopole operators in 3d gauge theories
Properties of monopole operators in 3d gauge theories Silviu S. Pufu Princeton University Based on: arxiv:1303.6125 arxiv:1309.1160 (with Ethan Dyer and Mark Mezei) work in progress with Ethan Dyer, Mark
More informationSPT: a window into highly entangled phases
SPT: a window into highly entangled phases T. Senthil (MIT) Collaborators: Chong Wang, A. Potter Why study SPT? 1. Because it may be there... Focus on electronic systems with realistic symmetries in d
More information(Effective) Field Theory and Emergence in Condensed Matter
(Effective) Field Theory and Emergence in Condensed Matter T. Senthil (MIT) Effective field theory in condensed matter physics Microscopic models (e.g, Hubbard/t-J, lattice spin Hamiltonians, etc) `Low
More informationCritical Spin-liquid Phases in Spin-1/2 Triangular Antiferromagnets. In collaboration with: Olexei Motrunich & Jason Alicea
Critical Spin-liquid Phases in Spin-1/2 Triangular Antiferromagnets In collaboration with: Olexei Motrunich & Jason Alicea I. Background Outline Avoiding conventional symmetry-breaking in s=1/2 AF Topological
More information(Im)possible emergent symmetry and conformal bootstrap
(Im)possible emergent symmetry and conformal bootstrap Yu Nakayama earlier results are based on collaboration with Tomoki Ohtsuki Phys.Rev.Lett. 117 (2016) Symmetries in nature The great lesson from string
More informationSmall and large Fermi surfaces in metals with local moments
Small and large Fermi surfaces in metals with local moments T. Senthil (MIT) Subir Sachdev Matthias Vojta (Augsburg) cond-mat/0209144 Transparencies online at http://pantheon.yale.edu/~subir Luttinger
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 informationUniversal phase transitions in Topological lattice models
Universal phase transitions in Topological lattice models F. J. Burnell Collaborators: J. Slingerland S. H. Simon September 2, 2010 Overview Matter: classified by orders Symmetry Breaking (Ferromagnet)
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 information2. Spin liquids and valence bond solids
Outline 1. Coupled dimer antiferromagnets Landau-Ginzburg quantum criticality 2. Spin liquids and valence bond solids (a) Schwinger-boson mean-field theory - square lattice (b) Gauge theories of perturbative
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 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 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 informationDual vortex theory of doped antiferromagnets
Dual vortex theory of doped antiferromagnets Physical Review B 71, 144508 and 144509 (2005), cond-mat/0502002, cond-mat/0511298 Leon Balents (UCSB) Lorenz Bartosch (Harvard) Anton Burkov (Harvard) Predrag
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 informationBoson Vortex duality. Abstract
Boson Vortex duality Subir Sachdev Department of Physics, Harvard University, Cambridge, Massachusetts, 0238, USA and Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada (Dated:
More informationMany faces of Mirror Symmetries
Many faces of Mirror Symmetries Huajia Wang University of llinois at Urbana Champaign S. Kachru, M. Mulligan, G.Torroba, H. Wang, arxiv: 1608.05077 S. Kachru, M. Mulligan, G.Torroba, H. Wang, arxiv: 1609.02149
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 informationCriticality in topologically ordered systems: a case study
Criticality in topologically ordered systems: a case study Fiona Burnell Schulz & FJB 16 FJB 17? Phases and phase transitions ~ 194 s: Landau theory (Liquids vs crystals; magnets; etc.) Local order parameter
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 informationFractional quantum Hall effect and duality. Dam T. Son (University of Chicago) Canterbury Tales of hot QFTs, Oxford July 11, 2017
Fractional quantum Hall effect and duality Dam T. Son (University of Chicago) Canterbury Tales of hot QFTs, Oxford July 11, 2017 Plan Plan General prologue: Fractional Quantum Hall Effect (FQHE) Plan General
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 theory of vortices in d-wave superconductors
Quantum theory of vortices in d-wave superconductors Physical Review B 71, 144508 and 144509 (2005), Annals of Physics 321, 1528 (2006), Physical Review B 73, 134511 (2006), cond-mat/0606001. Leon Balents
More informationDualities, Old and New. David Tong: MIT Pappalardo Fellow,
Dualities, Old and New David Tong: MIT Pappalardo Fellow, 2001-2004 Quantum Field Theory Quantum Field Theory... is hard 1. Numerics: How to Proceed? How to Proceed? 1. Numerics: 2. Toy Models (e.g. supersymmetry)
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 informationIs the composite fermion a Dirac particle?
Is the composite fermion a Dirac particle? Dam T. Son GGI conference Gauge/gravity duality 2015 Ref.: 1502.03446 Plan Plan Fractional quantum Hall effect Plan Fractional quantum Hall effect Composite fermion
More informationIs the composite fermion a Dirac particle?
Is the composite fermion a Dirac particle? Dam T. Son (University of Chicago) Cold atoms meet QFT, 2015 Ref.: 1502.03446 Plan Plan Composite fermion: quasiparticle of Fractional Quantum Hall Effect (FQHE)
More informationEmergent light and the high temperature superconductors
HARVARD Emergent light and the high temperature superconductors Pennsylvania State University State College, January 21, 2016 Subir Sachdev Talk online: sachdev.physics.harvard.edu Maxwell's equations:
More informationLIBERATION ON THE WALLS IN GAUGE THEORIES AND ANTI-FERROMAGNETS
LIBERATION ON THE WALLS IN GAUGE THEORIES AND ANTI-FERROMAGNETS Tin Sulejmanpasic North Carolina State University Erich Poppitz, Mohamed Anber, TS Phys.Rev. D92 (2015) 2, 021701 and with Anders Sandvik,
More informationSupersymmetric Mirror Duality and Half-filled Landau level S. Kachru, M Mulligan, G Torroba and H. Wang Phys.Rev.
Supersymmetric Mirror Duality and Half-filled Landau level S. Kachru, M Mulligan, G Torroba and H. Wang Phys.Rev. B92 (2015) 235105 Huajia Wang University of Illinois Urbana Champaign Introduction/Motivation
More informationSome open questions from the KIAS Workshop on Emergent Quantum Phases in Strongly Correlated Electronic Systems, Seoul, Korea, October 2005.
Some open questions from the KIAS Workshop on Emergent Quantum Phases in Strongly Correlated Electronic Systems, Seoul, Korea, October 2005. Q 1 (Balents) Are quantum effects important for physics of hexagonal
More informationUnderstanding correlated electron systems by a classification of Mott insulators
Understanding correlated electron systems by a classification of Mott insulators Eugene Demler (Harvard) Kwon Park (Maryland) Anatoli Polkovnikov Subir Sachdev T. Senthil (MIT) Matthias Vojta (Karlsruhe)
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 informationParamagnetic phases of Kagome lattice quantum Ising models p.1/16
Paramagnetic phases of Kagome lattice quantum Ising models Predrag Nikolić In collaboration with T. Senthil Massachusetts Institute of Technology Paramagnetic phases of Kagome lattice quantum Ising models
More informationConformal Quantum Criticality Order and Deconfinement in Quantum Dimer Models
Conformal Quantum Criticality Order and Deconfinement in Quantum Dimer Models Eduardo Fradkin Department of Physics University of Illinois at Urbana-Champaign Collaborators Eddy Ardonne, UIUC Paul Fendley,
More informationDetecting boson-vortex duality in the cuprate superconductors
Detecting boson-vortex duality in the cuprate superconductors Physical Review B 71, 144508 and 144509 (2005), cond-mat/0602429 Leon Balents (UCSB) Lorenz Bartosch (Harvard) Anton Burkov (Harvard) Predrag
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 informationClassifying two-dimensional superfluids: why there is more to cuprate superconductivity than the condensation of charge -2e Cooper pairs
Classifying two-dimensional superfluids: why there is more to cuprate superconductivity than the condensation of charge -2e Cooper pairs cond-mat/0408329, cond-mat/0409470, and to appear Leon Balents (UCSB)
More informationGapless Spin Liquids in Two Dimensions
Gapless Spin Liquids in Two Dimensions MPA Fisher (with O. Motrunich, Donna Sheng, Matt Block) Boulder Summerschool 7/20/10 Interest Quantum Phases of 2d electrons (spins) with emergent rather than broken
More informationEntanglement signatures of QED3 in the kagome spin liquid. William Witczak-Krempa
Entanglement signatures of QED3 in the kagome spin liquid William Witczak-Krempa Aspen, March 2018 Chronologically: X. Chen, KITP Santa Barbara T. Faulkner, UIUC E. Fradkin, UIUC S. Whitsitt, Harvard S.
More informationFractional quantum Hall effect and duality. Dam Thanh Son (University of Chicago) Strings 2017, Tel Aviv, Israel June 26, 2017
Fractional quantum Hall effect and duality Dam Thanh Son (University of Chicago) Strings 2017, Tel Aviv, Israel June 26, 2017 Plan Fractional quantum Hall effect Halperin-Lee-Read (HLR) theory Problem
More informationA Brief Introduction to Duality Web
A Brief Introduction to Duality Web WeiHan Hsiao a a Department of Physics, The University of Chicago E-mail: weihanhsiao@uchicago.edu Abstract: This note is prepared for the journal club talk given on
More informationSubir Sachdev. Talk online: sachdev.physics.harvard.edu
HARVARD Gauge theory for the cuprates near optimal doping Developments in Quantum Field Theory and Condensed Matter Physics Simons Center for Geometry and Physics, Stony Brook University November 7, 2018
More informationQuantum theory of vortices and quasiparticles in d-wave superconductors
Quantum theory of vortices and quasiparticles in d-wave superconductors Quantum theory of vortices and quasiparticles in d-wave superconductors Physical Review B 73, 134511 (2006), Physical Review B 74,
More informationTopological symmetry and (de)confinement in gauge theories and spin systems
Topological symmetry and (de)confinement in gauge theories and spin systems Mithat Ünsal, SLAC, Stanford University based on arxiv:0804.4664 QCD* parts with M. Shifman Thanks to Eun-ah Kim, B. Marston,
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 informationVI.D Self Duality in the Two Dimensional Ising Model
VI.D Self Duality in the Two Dimensional Ising Model Kramers and Wannier discovered a hidden symmetry that relates the properties of the Ising model on the square lattice at low and high temperatures.
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 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 informationUnderstanding correlated electron systems by a classification of Mott insulators
Understanding correlated electron systems by a classification of Mott insulators Eugene Demler (Harvard) Kwon Park (Maryland) Anatoli Polkovnikov Subir Sachdev T. Senthil (MIT) Matthias Vojta (Karlsruhe)
More informationThink Globally, Act Locally
Think Globally, Act Locally Nathan Seiberg Institute for Advanced Study Quantum Fields beyond Perturbation Theory, KITP 2014 Ofer Aharony, NS, Yuji Tachikawa, arxiv:1305.0318 Anton Kapustin, Ryan Thorngren,
More informationWhich Spin Liquid Is It?
Which Spin Liquid Is It? Some results concerning the character and stability of various spin liquid phases, and Some speculations concerning candidate spin-liquid phases as the explanation of the peculiar
More informationNon-magnetic states. The Néel states are product states; φ N a. , E ij = 3J ij /4 2 The Néel states have higher energy (expectations; not eigenstates)
Non-magnetic states Two spins, i and j, in isolation, H ij = J ijsi S j = J ij [Si z Sj z + 1 2 (S+ i S j + S i S+ j )] For Jij>0 the ground state is the singlet; φ s ij = i j i j, E ij = 3J ij /4 2 The
More informationEffective Field Theories of Topological Insulators
Effective Field Theories of Topological Insulators Eduardo Fradkin University of Illinois at Urbana-Champaign Workshop on Field Theoretic Computer Simulations for Particle Physics and Condensed Matter
More informationTopological order in quantum matter
HARVARD Topological order in quantum matter Indian Institute of Science Education and Research, Pune Subir Sachdev November 13, 2017 Talk online: sachdev.physics.harvard.edu 1. Classical XY model in 2
More informationarxiv: v1 [cond-mat.str-el] 6 Jul 2011
Phase Diagram of the Kane-Mele-Hubbard model arxiv:1107.145v1 [cond-mat.str-el] 6 Jul 011 Christian Griset 1 and Cenke Xu 1 1 Department of Physics, University of California, Santa Barbara, CA 93106 (Dated:
More informationG2 gauge theories. Axel Maas. 14 th of November 2013 Strongly-Interacting Field Theories III Jena, Germany
G2 gauge theories Axel Maas 14 th of November 2013 Strongly-Interacting Field Theories III Jena, Germany Overview Why G2? Overview Why G2? G2 Yang-Mills theory Running coupling [Olejnik, Maas JHEP'08,
More informationSuperinsulator: a new topological state of matter
Superinsulator: a new topological state of matter M. Cristina Diamantini Nips laboratory, INFN and Department of Physics and Geology University of Perugia Coll: Igor Lukyanchuk, University of Picardie
More informationQuantum Choreography: Exotica inside Crystals
Quantum Choreography: Exotica inside Crystals U. Toronto - Colloquia 3/9/2006 J. Alicea, O. Motrunich, T. Senthil and MPAF Electrons inside crystals: Quantum Mechanics at room temperature Quantum Theory
More informationBraid Group, Gauge Invariance and Topological Order
Braid Group, Gauge Invariance and Topological Order Yong-Shi Wu Department of Physics University of Utah Topological Quantum Computing IPAM, UCLA; March 2, 2007 Outline Motivation: Topological Matter (Phases)
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 informationVI.D Self Duality in the Two Dimensional Ising Model
VI.D Self Duality in the Two Dimensional Ising Model Kramers and Wannier discovered a hidden symmetry that relates the properties of the Ising model on the square lattice at low and high temperatures.
More informationSymmetry protected topological phases in quantum spin systems
10sor network workshop @Kashiwanoha Future Center May 14 (Thu.), 2015 Symmetry protected topological phases in quantum spin systems NIMS U. Tokyo Shintaro Takayoshi Collaboration with A. Tanaka (NIMS)
More informationFermi liquid theory. Abstract
Fermi liquid theory Subir Sachdev Department of Physics, Harvard University, Cambridge, Massachusetts, 02138, USA and Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada (Dated:
More informationValence Bonds in Random Quantum Magnets
Valence Bonds in Random Quantum Magnets theory and application to YbMgGaO 4 Yukawa Institute, Kyoto, November 2017 Itamar Kimchi I.K., Adam Nahum, T. Senthil, arxiv:1710.06860 Valence Bonds in Random Quantum
More informationSymmetry Protected Topological Phases of Matter
Symmetry Protected Topological Phases of Matter T. Senthil (MIT) Review: T. Senthil, Annual Reviews of Condensed Matter Physics, 2015 Topological insulators 1.0 Free electron band theory: distinct insulating
More informationGeneralized Global Symmetries
Generalized Global Symmetries Anton Kapustin Simons Center for Geometry and Physics, Stony Brook April 9, 2015 Anton Kapustin (Simons Center for Geometry and Physics, Generalized StonyGlobal Brook) Symmetries
More informationThink Globally, Act Locally
Think Globally, Act Locally Nathan Seiberg Institute for Advanced Study Quantum Fields beyond Perturbation Theory, KITP 2014 Ofer Aharony, NS, Yuji Tachikawa, arxiv:1305.0318 Anton Kapustin, Ryan Thorngren,
More informationSpin liquids on ladders and in 2d
Spin liquids on ladders and in 2d MPA Fisher (with O. Motrunich) Minnesota, FTPI, 5/3/08 Interest: Quantum Spin liquid phases of 2d Mott insulators Background: Three classes of 2d Spin liquids a) Topological
More informationBosonization of lattice fermions in higher dimensions
Bosonization of lattice fermions in higher dimensions Anton Kapustin California Institute of Technology January 15, 2019 Anton Kapustin (California Institute of Technology) Bosonization of lattice fermions
More informationSubir Sachdev Harvard University
Quantum phase transitions of correlated electrons and atoms Subir Sachdev Harvard University Course at Harvard University: Physics 268r Classical and Quantum Phase Transitions. MWF 10 in Jefferson 256
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 informationSymmetries Then and Now
Symmetries Then and Now Nathan Seiberg, IAS 40 th Anniversary conference Laboratoire de Physique Théorique Global symmetries are useful If unbroken Multiplets Selection rules If broken Goldstone bosons
More informationIsing Lattice Gauge Theory with a Simple Matter Field
Ising Lattice Gauge Theory with a Simple Matter Field F. David Wandler 1 1 Department of Physics, University of Toronto, Toronto, Ontario, anada M5S 1A7. (Dated: December 8, 2018) I. INTRODUTION Quantum
More informationSupersymmetric Gauge Theories in 3d
Supersymmetric Gauge Theories in 3d Nathan Seiberg IAS Intriligator and NS, arxiv:1305.1633 Aharony, Razamat, NS, and Willett, arxiv:1305.3924 3d SUSY Gauge Theories New lessons about dynamics of quantum
More informationarxiv: v1 [cond-mat.str-el] 6 May 2010
MIT-CTP/4147 Correlated Topological Insulators and the Fractional Magnetoelectric Effect B. Swingle, M. Barkeshli, J. McGreevy, and T. Senthil Department of Physics, Massachusetts Institute of Technology,
More informationSpin liquids in frustrated magnets
May 20, 2010 Contents 1 Frustration 2 3 4 Exotic excitations 5 Frustration The presence of competing forces that cannot be simultaneously satisfied. Heisenberg-Hamiltonian H = 1 J ij S i S j 2 ij The ground
More informationOrganizing Principles for Understanding Matter
Organizing Principles for Understanding Matter Symmetry Conceptual simplification Conservation laws Distinguish phases of matter by pattern of broken symmetries Topology Properties insensitive to smooth
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 informationwith four spin interaction Author(s) Tsukamoto, M.; Harada, K.; Kawashim (2009). doi: / /150/
Title Quantum Monte Carlo simulation of S with four spin interaction Author(s) Tsukamoto, M.; Harada, K.; Kawashim Citation Journal of Physics: Conference Seri Issue Date 2009 URL http://hdl.handle.net/2433/200787
More informationQuarks, Leptons and Gauge Fields Downloaded from by on 03/13/18. For personal use only.
QUARKS, LEPTONS & GAUGE FIELDS 2nd edition Kerson Huang Professor of Physics Mussuchusetts Institute qf Technology Y 8 World Scientific Singapore New Jersey London Hong Kong Publirhed by World Scientific
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 informationThe Role Of Magnetic Monopoles In Quark Confinement (Field Decomposition Approach)
The Role Of Magnetic Monopoles In Quark Confinement (Field Decomposition Approach) IPM school and workshop on recent developments in Particle Physics (IPP11) 2011, Tehran, Iran Sedigheh Deldar, University
More informationQuantum spin liquids and the Mott transition. T. Senthil (MIT)
Quantum spin liquids and the Mott transition T. Senthil (MIT) Friday, December 9, 2011 Band versus Mott insulators Band insulators: even number of electrons per unit cell; completely filled bands Mott
More informationThe Half-Filled Landau Level
Nigel Cooper Department of Physics, University of Cambridge Celebration for Bert Halperin s 75th January 31, 2017 Chong Wang, Bert Halperin & Ady Stern. [C. Wang, NRC, B. I. Halperin & A. Stern, arxiv:1701.00007].
More informationChern-Simons Theory and Its Applications. The 10 th Summer Institute for Theoretical Physics Ki-Myeong Lee
Chern-Simons Theory and Its Applications The 10 th Summer Institute for Theoretical Physics Ki-Myeong Lee Maxwell Theory Maxwell Theory: Gauge Transformation and Invariance Gauss Law Charge Degrees of
More informationt Hooft-Polyakov Monopoles on the Lattice
t Hooft-Polyakov Monopoles on the Lattice Davis,Kibble,Rajantie&Shanahan, JHEP11(2000) Davis,Hart,Kibble&Rajantie, PRD65(2002) Rajantie, in progress 19 May 2005 University of Wales, Swansea Introduction
More informationQuantum Field Theory. Kerson Huang. Second, Revised, and Enlarged Edition WILEY- VCH. From Operators to Path Integrals
Kerson Huang Quantum Field Theory From Operators to Path Integrals Second, Revised, and Enlarged Edition WILEY- VCH WILEY-VCH Verlag GmbH & Co. KGaA I vh Contents Preface XIII 1 Introducing Quantum Fields
More informationSPIN LIQUIDS AND FRUSTRATED MAGNETISM
SPIN LIQUIDS AND FRUSTRATED MAGNETISM Classical correlations, emergent gauge fields and fractionalised excitations John Chalker Physics Department, Oxford University For written notes see: http://topo-houches.pks.mpg.de/
More informationXY model: particle-vortex duality. Abstract
XY model: particle-vortex duality Subir Sachdev Department of Physics, Harvard University, Cambridge, Massachusetts, 02138, USA Dated: February 7, 2018) Abstract We consider the classical XY model in D
More informationTopology and Chern-Simons theories. Abstract
Topology and Chern-Simons theories Subir Sachdev Department of Physics, Harvard University, Cambridge, Massachusetts, 02138, USA and Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5,
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 informationQuantum spin systems - models and computational methods
Summer School on Computational Statistical Physics August 4-11, 2010, NCCU, Taipei, Taiwan Quantum spin systems - models and computational methods Anders W. Sandvik, Boston University Lecture outline Introduction
More informationA Dirac Spin Liquid May Fill the Gap in the Kagome Antiferromagnet
1 A Dirac Spin Liquid May Fill the Gap in the Kagome Antiferromagnet A. Signatures of Dirac cones in a DMRG study of the Kagome Heisenberg model, Yin- Chen He, Michael P. Zaletel, Masaki Oshikawa, and
More information