Exotic quantum phases and phase transitions in correlated matter

TL;DR

This paper provides an overview of recent theoretical advances in understanding exotic quantum phases and phase transitions in strongly correlated condensed matter systems, emphasizing topological and critical spin liquids and their experimental relevance.

Contribution

It introduces gauge theory descriptions of topological and critical spin liquids and discusses recent developments in deconfined quantum critical points, with an expository focus.

Findings

Description of topological and critical spin liquids without long-range order

Use of gauge theories to explain fractionalization and deconfinement

Connections to experimental probes of exotic quantum phases

Abstract

We present a pedagogical overview of recent theoretical work on unconventional quantum phases and quantum phase transitions in condensed matter systems. Strong correlations between electrons can lead to a breakdown of two traditional paradigms of solid state physics: Landau's theories of Fermi liquids and phase transitions. We discuss two resulting "exotic" states of matter: topological and critical spin liquids. These two quantum phases do not display any long-range order even at zero temperature. In each case, we show how a gauge theory description is useful to describe the new concepts of topological order, fractionalization and deconfinement of excitations which can be present in such spin liquids. We make brief connections, when possible, to experiments in which the corresponding physics can be probed. Finally, we review recent work on deconfined quantum critical points. The tone of these lecture notes is expository: focus is on gaining a physical picture and understanding, with technical details kept to a minimum.