Competing orders, non-linear sigma models, and topological terms in quantum magnets

TL;DR

This paper explores how topological terms in field theories can explain the failure of traditional Landau-Ginzburg-Wilson paradigms in describing complex phase transitions in two-dimensional quantum magnets, proposing alternative models.

Contribution

It introduces field theoretic descriptions with topological terms as alternatives to gauge theories for non-LGW quantum magnet behaviors.

Findings

Topological terms are crucial for accurate field descriptions of quantum magnets.

Anisotropic O(4) sigma model with a theta term captures key properties of these systems.

Potential sigma model descriptions for fermionic algebraic spin liquids are suggested.

Abstract

A number of examples have demonstrated the failure of the Landau-Ginzburg-Wilson(LGW) paradigm in describing the competing phases and phase transitions of two dimensional quantum magnets. In this paper we argue that such magnets possess field theoretic descriptions in terms of their slow fluctuating orders provided certain topological terms are included in the action. These topological terms may thus be viewed as what goes wrong within the conventional LGW thinking. The field theoretic descriptions we develop are possible alternates to the popular gauge theories of such non-LGW behavior. Examples that are studied include weakly coupled quasi-one dimensional spin chains, deconfined critical points in fully two dimensional magnets, and two component massless $QED_3$. A prominent role is played by an anisotropic O(4) non-linear sigma model in three space-time dimensions with a topological theta term. Some properties of this model are discussed. We suggest that similar sigma model descriptions might exist for fermionic algebraic spin liquid phases.