The quantum phases of matter

TL;DR

This paper surveys various quantum phases of matter, focusing on entanglement, classification, and recent theoretical and experimental advances, including topological, conformal, and compressible quantum phases and their potential gravitational duals.

Contribution

It provides a comprehensive classification and discussion of quantum matter phases, connecting theoretical models with experimental systems and exploring gauge-gravity duality applications.

Findings

Gapped quantum matter includes Z_2 spin liquids linked to topological field theories.

Conformal quantum matter occurs at quantum critical points in lattice models.

Recent progress in understanding non-Fermi liquid compressible phases and gauge-gravity duality insights.

Abstract

I present a selective survey of the phases of quantum matter with varieties of many-particle quantum entanglement. I classify the phases as gapped, conformal, or compressible quantum matter. Gapped quantum matter is illustrated by a simple discussion of the Z_2 spin liquid, and connections are made to topological field theories. I discuss how conformal matter is realized at quantum critical points of realistic lattice models, and make connections to a number of experimental systems. Recent progress in our understanding of compressible quantum phases which are not Fermi liquids is summarized. Finally, I discuss how the strongly-coupled phases of quantum matter may be described by gauge-gravity duality. The structure of the large N limit of SU(N) gauge theory, coupled to adjoint fermion matter at non-zero density, suggests aspects of gravitational duals of compressible quantum matter.