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

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 many-electron 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 non-Fermi 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.