Quantum phases and phase transitions of Mott insulators

TL;DR

This paper reviews the theoretical understanding of quantum phases and phase transitions in antiferromagnetic Mott insulators, highlighting recent theories on topological order, fractionalization, and the breakdown of traditional paradigms at critical points.

Contribution

It provides a comprehensive overview of the quantum phases of Mott insulators, including new insights into topological order and emergent gauge fields at quantum critical points.

Findings

Bond operator method accurately describes spin gaps in even spin systems

Conditions for bond order and topological order in odd spin systems are identified

Quantum critical points exhibit emergent gauge excitations and non-Landau behavior

Abstract

This article contains a theoretical overview of the physical properties of antiferromagnetic Mott insulators in spatial dimensions greater than one. Many such materials have been experimentally studied in the past decade and a half, and we make contact with these studies. The simplest class of Mott insulators have an even number of S=1/2 spins per unit cell, and these can be described with quantitative accuracy by the bond operator method: we discuss their spin gap and magnetically ordered states, and the transitions between them driven by pressure or an applied magnetic field. The case of an odd number of S=1/2 spins per unit cell is more subtle: here the spin gap state can spontaneously develop bond order (so the ground state again has an even number of S=1/2 spins per unit cell), and/or acquire topological order and fractionalized excitations. We describe the conditions under which such spin gap states can form, and survey recent theories (T. Senthil et al., cond-mat/0312617) of the quantum phase transitions among these states and magnetically ordered states. We describe the breakdown of the Landau-Ginzburg-Wilson paradigm at these quantum critical points, accompanied by the appearance of emergent gauge excitations.