Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm

TL;DR

This paper develops a novel critical theory for quantum phase transitions in two-dimensional antiferromagnets and bosonic systems, emphasizing fractionalized excitations and topological conservation laws beyond traditional Landau-Ginzburg-Wilson frameworks.

Contribution

It introduces a new paradigm for quantum criticality involving fractionalized degrees of freedom and emergent gauge fields, extending understanding beyond classical symmetry-breaking theories.

Findings

Identifies a second order quantum phase transition between Neel and valence bond solid states.

Shows the critical theory involves fractionalized excitations and topological conservation laws.

Applies the theory to superfluid-insulator and Z_2 spin liquid transitions.

Abstract

We present the critical theory of a number of zero temperature phase transitions of quantum antiferromagnets and interacting boson systems in two dimensions. The most important example is the transition of the S = 1/2 square lattice antiferromagnet between the Neel state (which breaks spin rotation invariance) and the paramagnetic valence bond solid (which preserves spin rotation invariance but breaks lattice symmetries). We show that these two states are separated by a second order quantum phase transition. The critical theory is not expressed in terms of the order parameters characterizing either state (as would be the case in Landau-Ginzburg-Wilson theory) but involves fractionalized degrees of freedom and an emergent, topological, global conservation law. A closely related theory describes the superfluid-insulator transition of bosons at half-filling on a square lattice, in which the insulator has a bond density wave order. Similar considerations are shown to apply to transitions of antiferromagnets between the valence bond solid and the Z_2 spin liquid: the critical theory has deconfined excitations interacting with an emergent U(1) gauge force. We comment on the broader implications of our results for the study of quantum criticality in correlated electron systems.