The Landscape of the Hubbard model HARVARD Talk online: sachdev.physics.harvard.edu Subir Sachdev Highly Frustrated Magnetism 2010 Johns Hopkins University.

Slides:

Advertisements

Similar presentations

One-dimensional approach to frustrated magnets

Advertisements

High T c Superconductors & QED 3 theory of the cuprates Tami Pereg-Barnea

Quantum “disordering” magnetic order in insulators, metals, and superconductors HARVARD Talk online: sachdev.physics.harvard.edu Perimeter Institute, Waterloo,

Antoine Georges Olivier Parcollet Nick Read Subir Sachdev Jinwu Ye Mean field theories of quantum spin glasses Talk online: Sachdev.

Quantum critical phenomena Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu Quantum critical phenomena Talk online: sachdev.physics.harvard.edu.

Frustrated Magnetism, Quantum spin liquids and gauge theories

Pavel Buividovich (Regensburg). They are very similar to relativistic strongly coupled QFT Dirac/Weyl points Dirac/Weyl points Quantum anomalies Quantum.

Quantum Phase Transitions Subir Sachdev Talks online at

Chiral symmetry breaking in graphene: a lattice study of excitonic and antiferromagnetic phase transitions Ulybyshev Maxim, ITEP, MSU.

Detecting collective excitations of quantum spin liquids Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu.

Quantum antiferromagnetism and superconductivity Subir Sachdev Talk online at

AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu.

Subir Sachdev Science 286, 2479 (1999). Quantum phase transitions in atomic gases and condensed matter Transparencies online at

Talk online: : Sachdev Ground states of quantum antiferromagnets in two dimensions Leon Balents Matthew Fisher Olexei Motrunich Kwon Park Subir Sachdev.

Subir Sachdev arXiv: Subir Sachdev arXiv: Loss of Neel order in insulators and superconductors Ribhu Kaul Max Metlitski Cenke Xu.

Quantum effects in Magnetic Salts Part II G. Aeppli London Centre for Nanotechnology.

Fermi surface change across quantum phase transitions Phys. Rev. B 72, (2005) Phys. Rev. B (2006) cond-mat/ Hans-Peter Büchler.

Quantum critical transport, duality, and M-theory hep-th/ Christopher Herzog (Washington) Pavel Kovtun (UCSB) Subir Sachdev (Harvard) Dam Thanh.

Quantum criticality, the cuprate superconductors, and the AdS/CFT correspondence HARVARD Talk online: sachdev.physics.harvard.edu.

Classifying two-dimensional superfluids: why there is more to cuprate superconductivity than the condensation of charge -2e Cooper pairs cond-mat/ ,

Strongly interacting cold atoms Subir Sachdev Talks online at

Dual vortex theory of doped antiferromagnets Physical Review B 71, and (2005), cond-mat/ , cond-mat/ Leon Balents (UCSB) Lorenz.

Anomalous excitation spectra of frustrated quantum antiferromagnets John Fjaerestad University of Queensland Work done in collaboration with: Weihong Zheng,

Breakdown of the Landau-Ginzburg-Wilson paradigm at quantum phase transitions Science 303, 1490 (2004); cond-mat/ cond-mat/ Leon Balents.

Spin Liquid Phases ? Houches/06//2006.

cond-mat/ , cond-mat/ , and to appear

Dual vortex theory of doped antiferromagnets Physical Review B 71, and (2005), cond-mat/ , cond-mat/ Leon Balents (UCSB) Lorenz.

Classifying two-dimensional superfluids: why there is more to cuprate superconductivity than the condensation of charge -2e Cooper pairs cond-mat/ ,

Putting competing orders in their place near the Mott transition cond-mat/ and cond-mat/ Leon Balents (UCSB) Lorenz Bartosch (Yale) Anton.

Magnetic quantum criticality Transparencies online at Subir Sachdev.

The phase diagram of the cuprates and the quantum phase transitions of metals in two dimensions HARVARD Talk online: sachdev.physics.harvard.edu.

LS Cable, a South Korean company based in Anyang-si near Seoul, has ordered three million metres of superconducting wire from US firm American Superconductor.

Quantum theory of vortices and quasiparticles in d-wave superconductors.

Exotic Phases in Quantum Magnets MPA Fisher Outline: 2d Spin liquids: 2 Classes Topological Spin liquids Critical Spin liquids Doped Mott insulators: Conducting.

Deconfined Quantum Critical Points

The phase diagrams of the high temperature superconductors HARVARD Talk online: sachdev.physics.harvard.edu.

Paired electron pockets in the hole-doped cuprates Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu.

Correlated States in Optical Lattices Fei Zhou (PITP,UBC) Feb. 1, 2004 At Asian Center, UBC.

Strong coupling problems in condensed matter and the AdS/CFT correspondence HARVARD arXiv: Reviews: Talk online: sachdev.physics.harvard.edu arXiv:

Quantum criticality of Fermi surfaces in two dimensions HARVARD Talk online: sachdev.physics.harvard.edu.

1 Lattice Quantum Chromodynamics 1- Literature : Lattice QCD, C. Davis Hep-ph/ Burcham and Jobes By Leila Joulaeizadeh 19 Oct

(Simon Fraser University, Vancouver)

Quantum exotic states in correlated topological insulators Su-Peng Kou ( 寇谡鹏 ) Beijing Normal University.

Ashvin Vishwanath UC Berkeley

Strong coupling problems in condensed matter and the AdS/CFT correspondence HARVARD arXiv: Reviews: Talk online: sachdev.physics.harvard.edu arXiv:

Quantum Criticality and Black Holes Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu.

Phys. Rev. Lett M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature 415, 39 (2002). Superfluid-insulator transition.

Deconfined quantum criticality Leon Balents (UCSB) Lorenz Bartosch (Frankfurt) Anton Burkov (Harvard) Matthew Fisher (UCSB) Subir Sachdev (Harvard) Krishnendu.

Frustrated magnetism in 2D Collin Broholm Johns Hopkins University & NIST  Introduction Two types of antiferromagnets Experimental tools  Frustrated.

Quantum criticality, the AdS/CFT correspondence, and the cuprate superconductors HARVARD Talk online: sachdev.physics.harvard.edu.

Deconfined quantum criticality T. Senthil (MIT) P. Ghaemi,P. Nikolic, M. Levin (MIT) M. Hermele (UCSB) O. Motrunich (KITP), A. Vishwanath (MIT) L. Balents,

Lattice gauge theory treatment of Dirac semimetals at strong coupling Yasufumi Araki 1,2 1 Institute for Materials Research, Tohoku Univ. 2 Frontier Research.

Flat Band Nanostructures Vito Scarola

Cenke Xu 许岑珂 University of California, Santa Barbara Stable 2+1d CFT at the Boundary of a Class of 3+1d Symmetry Protected Topological States.

Quantum Criticality and Black Holes Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu.

From the Hubbard model to high temperature superconductivity HARVARD S. Sachdev Talk online: sachdev.physics.harvard.edu.

Condensed matter physics and string theory HARVARD Talk online: sachdev.physics.harvard.edu.

Spin-Orbit Coupling Effects in Bilayer and Optical Lattice Systems

Quantum vortices and competing orders

T. Senthil Leon Balents Matthew Fisher Olexei Motrunich Kwon Park

Quantum phases and critical points of correlated metals

Science 303, 1490 (2004); cond-mat/ cond-mat/

Electrical and thermal transport near quantum phase transitions in condensed matter, and in dyonic black holes Sean Hartnoll (KITP) Pavel.

Breakdown of the Landau-Ginzburg-Wilson paradigm at quantum phase transitions Science 303, 1490 (2004); Physical Review B 70, (2004), 71,

Quantum phases and critical points of correlated metals

Quantum phase transitions and the Luttinger theorem.

Possible realization of SU(2)_2 WZNW Quantum Critical Point in CaCu2O3

Phase structure of graphene from Hybrid Monte-Carlo simulations

Deconfined quantum criticality

Quantum phase transitions out of the heavy Fermi liquid

Presentation transcript:

The Landscape of the Hubbard model HARVARD Talk online: sachdev.physics.harvard.edu Subir Sachdev Highly Frustrated Magnetism 2010 Johns Hopkins University August 1

The Hubbard Model Will study the honeycomb and square lattices.

1. Honeycomb lattice: semi-metal and antiferromagnetism Dirac fermions and the Gross-Neveu model 2. Spin liquids Unified formulation as a SO(4) gauge theory 3. Instabilities of spin liquids Geometric phases, valence bond solids, and other competing orders Outline

Cenke Xu Harvard UCSB Liang Fu Harvard Physical Review Letters 105, (2010) and to appear

Outline 1. Honeycomb lattice: semi-metal and antiferromagnetism Dirac fermions and the Gross-Neveu model 2. Spin liquids Unified formulation as a SO(4) gauge theory 3. Instabilities of spin liquids Geometric phases, valence bond solids, and other competing orders

The Hubbard Model

Graphene

Semi-metal with massless Dirac fermions Brilluoin zone

Graphene Dirac semi-metal Insulating antiferromagnet with Neel order

Brilluoin zone

Outline 1. Honeycomb lattice: semi-metal and antiferromagnetism Dirac fermions and the Gross-Neveu model 2. Spin liquids Unified formulation as a SO(4) gauge theory 3. Instabilities of spin liquids Geometric phases, valence bond solids, and other competing orders

Outline 1. Honeycomb lattice: semi-metal and antiferromagnetism Dirac fermions and the Gross-Neveu model 2. Spin liquids Unified formulation as a SO(4) gauge theory 3. Instabilities of spin liquids Geometric phases, valence bond solids, and other competing orders

Quantum “disordering” magnetic order

S. Sachdev, M. A. Metlitski, Y. Qi, and S. Sachdev Phys. Rev. B 80, (2009)

Quantum “disordering” magnetic order

Projected fermion wavefunctions (Fisher, Wen, Lee, Kim,Senthil)

Projected fermion wavefunctions neutral fermionic spinons (Fisher, Wen, Lee, Kim,Senthil)

Projected fermion wavefunctions charged slave boson/rotor (Fisher, Wen, Lee, Kim,Senthil)

Projected fermion wavefunctions (Fisher, Wen, Lee, Kim,Senthil)

Projected fermion wavefunctions (Fisher, Wen, Lee, Kim,Senthil)

Projected fermion wavefunctions (Fisher, Wen, Lee, Kim,Senthil)

Unified spin liquid theory

By breaking SO(4) gauge with different Higgs fields, we can reproduce essentially all earlier theories of spin liquids. We also find many new spin liquid phases, some with Majorana fermion excitations which carry neither spin nor charge

Quantum “disordering” magnetic order

Phase diagram “Frustration”

Phase diagram “Frustration”

Phase diagram “Frustration” Semi-metal

Phase diagram “Frustration” Semi-metal Insulator with Neel order

Phase diagram “Frustration” Semi-metal Insulator with Neel order

Phase diagram “Frustration” Semi-metal Insulator with Neel order Spin liquid: CFT of SU(2) QCD with N f =4 massless Dirac quarks

Phase diagram “Frustration” Semi-metal Insulator with Neel order Spin liquid: CFT of SU(2) QCD with N f =4 massless Dirac quarks

Phase diagram “Frustration” Semi-metal Insulator with Neel order Spin liquid: CFT of SU(2) QCD with N f =4 massless Dirac quarks Confining insulator with VBS (kekule) order

Outline 1. Honeycomb lattice: semi-metal and antiferromagnetism Dirac fermions and the Gross-Neveu model 2. Spin liquids Unified formulation as a SO(4) gauge theory 3. Instabilities of spin liquids Geometric phases, valence bond solids, and other competing orders

Outline 1. Honeycomb lattice: semi-metal and antiferromagnetism Dirac fermions and the Gross-Neveu model 2. Spin liquids Unified formulation as a SO(4) gauge theory 3. Instabilities of spin liquids Geometric phases, valence bond solids, and other competing orders

“Frustration” S=1/2 square lattice antiferromagnetic insulator

Phase diagram “Frustration” Semi-metal Insulator with Neel order Spin liquid: CFT of SU(2) QCD with N f =4 massless Dirac quarks Confining insulator with VBS (kekule) order