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WORLD SCIENTIFIC eBooks

Low-dimensional quantum field theories for condensed matter physicists : lecture notes of ICTP Summer Course, Trieste, Italy, September 1992

Stig Lundqvist, G. Morandi, Lu Yu

Published Jan 1, 1995• 18 citations
OpenAlex

Abstract

Some geometry and toplogy, G. Marmo and G. Morandi gauge symmetries, toplogy and quantisation, A.P. Balachandran the Chern-Simons-Landau-Ginzburg theory of the fractional quantum Hall effect, S.C. Zhang universitality in the fractional quantum hall, E. Fradkin and A. Lopez anyons and anyon superconductivity, A.L. Fetter bosonization - how to make it work for you in condensed matter, R. Shankar methods of conformal field theory in condensed matter physics, A.W.W. Ludwig integrable models in condensed matter physics, N. Andrei quantum antiferromagnets in two dimensions, S. Sachdev.

Related papers

Integrable Models in Condensed Matter Physics

Natan Andrei

This is an expanded version of the lectures given at the Trieste Summer School 1992 on Low-dimensional Quantum Field Theories for Condensed Matter Physicists.

arXiv:cond-mat/9408101•Feb 1, 1995•66 citations

Proceedings of the Sixth Physics Summer School, Modern Perspectives in Many-Body Physics, the Australian National University Canberra, Australia 11-29 January 1993

Manas Pratim Das, Jagadishwar Mahanty

Introductory many-body theory, D.J. Thouless collective description of many-body systems, R.M. Dreizler fermi liquid theory, D. Pines theory of fractional quantum hall effect, A.H. MacDonald numerical methods for problems of interacting many electron systems, D.J. Scalapino supersymmetry in nuclear and condensed matter physics, A.B. Balantekin strongly coupled plasmas, K.I. Golden fractional quantum hall effect and electron solid, R.G. Clark models to treat strong electronic correlations, M.P. Das physics of anyons, R.B. Laughlin. (Part contents).

WORLD SCIENTIFIC eBooks•Jan 1, 1994•0 citations

Strongly correlated electron systems II : proceedings of the Adriatico Research Conference and Miniworkshop, ICTP, Trieste, Italy, 18 June - 27 July 1990

G. Baskaran

Open questions related with heavy electrons, H.R. Ott electron spectroscopy of strongly correlated systems, J.W. Allen single hole in 1D and 2D hubbard model, S. Sorella surface acoustic wave studies of the FQHE, R.L. Willett Chern-Simons-Landau-Ginzburg theory of the FQHE and its experimental prediction, S.C. Zhang magnetic fluctuations in La2-xSrxCuO4, G. Aeppli single particle spectral function for the large U Hubbard model, P. Wolfe strongly correlated systems in infinite dimensions and their zero-dimensional counterpart, G. Kotliar stable hc-e vortices in a gauge theory of superconductivity in strongly correlated systems, S. Sachdev electronic mechanisms for superconductivity in doped C60, G. Baskaran weakly correlated electrons - many questions and few answers, H.J. Schulz normal state properties of the high Tc oxides - gauge theories, L. Loffe single particle and optical gaps in charge-transfer insulators, Y. Bang et al a renormalization group approach for many-Fermion problems, R. Shankar spin singlet quantum hall effect and nonabelian Landau-Ginzburg theory, A. Balatsky De Haas-Van Alphen and Shubnikov-De Haas oscillations in strongly correlated electron gas, P. Lederer et al strongly correlated Fermi liquid and the normal state of high Tc superconductors, Z. Wang determinant Monte Carlo for the Hubbard model with arbitrarily gauged auxiliary fields, A.M. Tremblay spin-charged coupling in doped Mott insulators, J. Wheatley.

WORLD SCIENTIFIC eBooks•Jan 1, 1991•0 citations

Field Theories of Condensed Matter Systems

Eduardo Fradkin

ForewordIntroductionThe Hubbard ModelThe Magnetic Instability of the Fermi SystemOne-Dimensional Quantum AntiferromagnetsSigma Models, Topological Terms and Spin LiquidsThe Spin Liquid StatesChiral Spin States and AnyonsAnyon SuperconductivityTopology and Quantum Hall EffectThe Fractal Quantum Hall Effect

•Jan 1, 2007•1,082 citations

Fractionalized Fermi liquids and the cuprate phase diagram

Pietro M. Bonetti, Maine Christos, Alexander Nikolaenko +2 more

Abstract We review a theoretical framework for the cuprate superconductors, rooted in a fractionalized Fermi liquid (FL*) description of the intermediate-temperature pseudogap phase at low doping. The FL* theory predicted hole pockets each of fractional area p / 8 at hole doping p , in contrast to the area p / 4 in spin density wave theory. Magnetotransport measurements, including observation of the Yamaji angle, show clear evidence of hole pocket quasiparticles which can tunnel coherently between square lattice layers, and are consistent with the FL* description. The FL* phase of a single-band model is described using a layer construction with a pair of ancilla qubits on each site: the Ancilla layer model (ALM). Its mean field theory yields hole pockets of area p / 8 , and matches the gapped photoemission spectrum in the anti-nodal region of the Brillouin zone. Fluctuations are described by the SU(2) gauge theory of a background spin liquid with critical Dirac spinons. A Monte Carlo study of the thermal SU(2) gauge theory transforms the hole pockets into Fermi arcs in photoemission. One route to confinement of FL* upon lowering temperature yields a d -wave superconductor via a Kosterlitz–Thouless transition of h / ( 2 e ) vortices, with nodal Bogoliubov quasiparticles featuring anisotropic velocities and vortices surrounded by charge order halos. An alternative route yields a charge-ordered metallic state that has quantum oscillations consistent with observations. These confinement transitions are driven by the condensation of a SU(2) fundamental Higgs field, which also provides a fractionalized description of intertwined orders. Increasing doping from the FL* phase in the ALM drives a transition to a conventional FL at large doping, passing through an intermediate strange metal regime. We formulate a theory of the FL*-FL metal-metal transition without a symmetry-breaking order parameter, using a critical quantum ‘charge’ liquid of mobile electrons in the presence of disorder, developed via an extension of the Sachdev–Ye–Kitaev model to two spatial dimensions. At low temperatures, and across optimal and over doping, we address the regimes of extended non-FL behavior by Griffiths effects near quantum phase transitions in disordered metals. Partly based on lectures by S S at Boulder School 2025, Dynamics of Strongly Correlated Electrons , 14–18 July. Lecture videos . Joint ICTP-WE Heraeus School and Workshop on Advances in Quantum Matter: Pushing the Boundaries , ICTP, Trieste, 4, 6 August 2025. Lecture videos . School on Quantum Dynamics of Matter, Light and Information , ICTP, Trieste, 18, 19 August 2025. Lecture videos . Croucher Advanced Study Institute for Fractional Chern Insulators , University of Hong Kong, 4, 5 September 2025. Lecture slides . Advanced School and Conference on Quantum Matter , ICTP Trieste, 1–12 December 2025. Lecture Notes . Lecture videos .

arXiv:2508.20164•Reports on Progress in Physics•Mar 17, 2026•6 citations

Low Dimensional Quantum Field Theories for Condensed Matter Physicists

Subir Sachdev A

•Jan 1, 1992•48 citations
Some geometry and toplogy, G. Marmo and G. Morandi gauge symmetries, toplogy and quantisation, A.P. Balachandran the Chern-Simons-Landau-Ginzburg theory of the fractional quantum Hall effect, S.C. Zhang universitality in the fractional quantum hall, E. Fradkin and A. Lopez anyons and anyon superconductivity, A.L. Fetter bosonization - how to make it work for you in condensed matter, R. Shankar methods of conformal field theory in condensed matter physics, A.W.W. Ludwig integrable models in condensed matter physics, N. Andrei quantum antiferromagnets in two dimensions, S. Sachdev.
Introductory many-body theory, D.J. Thouless collective description of many-body systems, R.M. Dreizler fermi liquid theory, D. Pines theory of fractional quantum hall effect, A.H. MacDonald numerical methods for problems of interacting many electron systems, D.J. Scalapino supersymmetry in nuclear and condensed matter physics, A.B. Balantekin strongly coupled plasmas, K.I. Golden fractional quantum hall effect and electron solid, R.G. Clark models to treat strong electronic correlations, M.P. Das physics of anyons, R.B. Laughlin. (Part contents).
Open questions related with heavy electrons, H.R. Ott electron spectroscopy of strongly correlated systems, J.W. Allen single hole in 1D and 2D hubbard model, S. Sorella surface acoustic wave studies of the FQHE, R.L. Willett Chern-Simons-Landau-Ginzburg theory of the FQHE and its experimental prediction, S.C. Zhang magnetic fluctuations in La2-xSrxCuO4, G. Aeppli single particle spectral function for the large U Hubbard model, P. Wolfe strongly correlated systems in infinite dimensions and their zero-dimensional counterpart, G. Kotliar stable hc-e vortices in a gauge theory of superconductivity in strongly correlated systems, S. Sachdev electronic mechanisms for superconductivity in doped C60, G. Baskaran weakly correlated electrons - many questions and few answers, H.J. Schulz normal state properties of the high Tc oxides - gauge theories, L. Loffe single particle and optical gaps in charge-transfer insulators, Y. Bang et al a renormalization group approach for many-Fermion problems, R. Shankar spin singlet quantum hall effect and nonabelian Landau-Ginzburg theory, A. Balatsky De Haas-Van Alphen and Shubnikov-De Haas oscillations in strongly correlated electron gas, P. Lederer et al strongly correlated Fermi liquid and the normal state of high Tc superconductors, Z. Wang determinant Monte Carlo for the Hubbard model with arbitrarily gauged auxiliary fields, A.M. Tremblay spin-charged coupling in doped Mott insulators, J. Wheatley.
Abstract We review a theoretical framework for the cuprate superconductors, rooted in a fractionalized Fermi liquid (FL*) description of the intermediate-temperature pseudogap phase at low doping. The FL* theory predicted hole pockets each of fractional area p / 8 at hole doping p , in contrast to the area p / 4 in spin density wave theory. Magnetotransport measurements, including observation of the Yamaji angle, show clear evidence of hole pocket quasiparticles which can tunnel coherently between square lattice layers, and are consistent with the FL* description. The FL* phase of a single-band model is described using a layer construction with a pair of ancilla qubits on each site: the Ancilla layer model (ALM). Its mean field theory yields hole pockets of area p / 8 , and matches the gapped photoemission spectrum in the anti-nodal region of the Brillouin zone. Fluctuations are described by the SU(2) gauge theory of a background spin liquid with critical Dirac spinons. A Monte Carlo study of the thermal SU(2) gauge theory transforms the hole pockets into Fermi arcs in photoemission. One route to confinement of FL* upon lowering temperature yields a d -wave superconductor via a Kosterlitz–Thouless transition of h / ( 2 e ) vortices, with nodal Bogoliubov quasiparticles featuring anisotropic velocities and vortices surrounded by charge order halos. An alternative route yields a charge-ordered metallic state that has quantum oscillations consistent with observations. These confinement transitions are driven by the condensation of a SU(2) fundamental Higgs field, which also provides a fractionalized description of intertwined orders. Increasing doping from the FL* phase in the ALM drives a transition to a conventional FL at large doping, passing through an intermediate strange metal regime. We formulate a theory of the FL*-FL metal-metal transition without a symmetry-breaking order parameter, using a critical quantum ‘charge’ liquid of mobile electrons in the presence of disorder, developed via an extension of the Sachdev–Ye–Kitaev model to two spatial dimensions. At low temperatures, and across optimal and over doping, we address the regimes of extended non-FL behavior by Griffiths effects near quantum phase transitions in disordered metals. Partly based on lectures by S S at Boulder School 2025, Dynamics of Strongly Correlated Electrons , 14–18 July. Lecture videos . Joint ICTP-WE Heraeus School and Workshop on Advances in Quantum Matter: Pushing the Boundaries , ICTP, Trieste, 4, 6 August 2025. Lecture videos . School on Quantum Dynamics of Matter, Light and Information , ICTP, Trieste, 18, 19 August 2025. Lecture videos . Croucher Advanced Study Institute for Fractional Chern Insulators , University of Hong Kong, 4, 5 September 2025. Lecture slides . Advanced School and Conference on Quantum Matter , ICTP Trieste, 1–12 December 2025. Lecture Notes . Lecture videos .