Modern Physics of the Condensed State: Strong Correlations and Quantum Topology

TL;DR

This review explores how modern ideas of unconventional quantum states, topological phenomena, and strong correlations advance understanding of condensed matter physics, emphasizing quantum fluctuations, phase transitions, and exotic states.

Contribution

It synthesizes recent developments in topological and strongly correlated quantum states, highlighting their theoretical frameworks and implications for condensed matter physics.

Findings

Topological states and spin liquids are central to modern condensed matter theory.

Quantum fluctuations and phase transitions are influenced by topological and frustration effects.

Exotic non-Fermi-liquid states challenge traditional electronic theories.

Abstract

The topic of the review is the application of new ideas of unconventional quantum states to the physics of condensed matter, in particular of solid state, in the context of modern field theory. A comparison is made with classical papers on many-electron theory, including the formalism of many-electron operators. The essentially many-particle nature of the ground state, individual and collective excitations, and quantum fluctuations in the systems under consideration, as well as quantum phase transitions are discussed with an emphasis on topological aspects and with allowance for the effects of frustration. Variational approaches and representations of auxiliary particles, corresponding mean-field approximation and gauge field theory, confinement-deconfinement problem, violation of the Fermi-liquid picture, and exotic non-Fermi-liquid states are considered. An overview is given of the modern theory of entangled topological states, formation of spin liquid, strings and string networks.