Modern Physics of the Condensed State: Strong Correlations and Quantum Topology
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Modern Physics of the Condensed State: Strong Correlations and Quantum Topology V. Yu. Irkhinа, * and Yu. N. Skryabinа а
Mikheev Institute of Metal Physics, Ural Branch, Russian Academy of Sciences, Ekaterinburg, 620108 Russia *e-mail: [email protected] Received December 4, 2018; revised December 14, 2018; accepted January 9, 2019
Abstract—The theme of this survey is the application of new ideas of uncommon quantum states to the physics of the condensed state, in particular, of solids, in the context of the contemporary field theory. A comparison is performed with the classical works on the many-electron theory, including the formalism of manyelectron operators. Principally, the many-particle nature of the ground state, individual and collective excitations, and quantum fluctuations in the systems in question are discussed, as well as quantum phase transitions (mainly, the topological aspects considering the effects of frustration). The variational approaches and the concepts of auxiliary particles, the corresponding mean-field approximations, the theory of gauge fields, the problem of confinement–deconfinement, the breakdown of the Fermi-liquid behavior, and exotic nonFermi liquid states are considered. A survey of the contemporary theory of the entangled topological states, formation of spin liquid, strings, and string networks is given. Keywords: quantum topology, quantum phase transitions, many-electron operators, auxiliary particles, spin liquid, strings, string networks DOI: 10.1134/S0031918X19060061
CONTENTS 1. INTRODUCTION 1.1. Quantum Phases and the Concept of Quantum Topology 1.2. Quantum Phase Transitions 2. DEVELOPMENT OF THE CONCEPTS AND METHODS OF MANY-ELECTRON THEORY 2.1. Second Quantization: Fermions and Many-Electron Operators 2.2. Variational Approaches 2.3. Concepts of Auxiliary Particles 2.4. The t–J Model and the s–d Exchange Model with Strong Correlations 3. FERMI LIQUID AND NON-FERMI LIQUID PHASES 3.1. Mean-Field Theory and Gauge Fields 3.2. Confinement and Deconfinement 3.3. Dirac Fermions and Algebraic Spin Liquid 3.4. Model of Phase Strings 3.5. Frustrations in Kondo Lattices 3.6. Fractionalized Fermi Liquid 4. THEORY OF QUANTUM PHASE TRANSITIONS. SPIN LIQUID AND TOPOLOGICAL ORDER 4.1. Deconfinement Quantum Criticality 4.2. Higgs Criticality
4.3. Quantum Phase Transitions and Incoherent States in Conducting Magnets 4.4. Superconductivity and Topological Order 5. LATTICE GAUGE THEORIES AND STRINGS 5.1. Condensation of String Networks 5.2. Tensor Networks 6. CONCLUSIONS 1. INTRODUCTION The 2016 Nobel Prize in Physics was awarded for the theoretical discoveries of topological phase transitions and topological phases of matter, for the works carried out in 1970–1980, which “opened the secrets of exotic matter.” In the time that passed since the pioneer works of D. Haldane, M. Kosterlitz, and D. Thouless, considerable progress was achieved in the physics of the condensed state connected with the application of new, substantially quantum topological concepts, such as to
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