Phase structure of $Z_2$ gauge theories for frustrated antiferromagnets in two dimensions

TL;DR

This study explores the phase diagram of $Z_2$ lattice gauge theories in two-dimensional frustrated antiferromagnets, revealing three distinct phases through Monte Carlo simulations, including spiral order, dimer, and spin liquid states.

Contribution

It provides a detailed analysis of the phase structure of $Z_2$ gauge theories in 2D frustrated antiferromagnets using Monte Carlo methods, highlighting the existence of three different phases.

Findings

Existence of three phases: spiral order, dimer state, and spin liquid.

Monte Carlo simulations reveal phase transitions depend on model details.

Deconfined spinons are present in the spin liquid phase.

Abstract

In this paper, we study phase structure of $Z_2$ lattice gauge theories that appear as an effective field theory describing low-energy properties of frustrated antiferromagnets in two dimensions. Spin operators are expressed in terms of Schwinger bosons, and an emergent U(1) gauge symmetry reduces to a $Z_2$ gauge symmetry as a result of condensation of a bilinear operator of the Schwinger boson describing a short-range spiral order. We investigated the phase structure of the gauge theories by means of the Monte-Carlo simulations, and found that there exist three phases, phase with a long-range spiral order, a dimer state, and a spin liquid with deconfined spinons. Detailed phase structure and properties of phase transitions depend on details of the models.