Geometric phases and competing orders in two dimensions

TL;DR

This paper explores how geometric phases influence quantum disordered states in two-dimensional systems, revealing their impact on electron bilinears and connections to topological terms in Dirac spectra.

Contribution

It introduces a framework linking geometric phases to quantum disordered states and topological effects in two-dimensional lattices with arbitrary electronic structures.

Findings

Electron bilinears respond to skyrmion density via geometric phases

Topological terms emerge in systems with Dirac electronic spectra

Characterization of quantum disordered ground states in 2D lattices

Abstract

We discuss the problem of characterizing "quantum disordered" ground states, obtained upon loss of antiferromagnetic order on general lattices in two spatial dimensions, with arbitrary electronic band structure. A key result is the response in electron bilinears to the skyrmion density in the local antiferromagnetic order, induced by geometric phases. We also discuss the connection to topological terms obtained under situations where the electronic spectrum has a Dirac form.