Theory of the Kagome Lattice Ising Antiferromagnet in Weak Transverse Field

TL;DR

This paper investigates the quantum Ising antiferromagnet on the Kagome lattice under weak transverse fields, revealing a disordered phase connected to strong field phases via a gauge theory approach, consistent with Monte Carlo results.

Contribution

It introduces an analytical mapping to a U(1) gauge theory that explains the disordered phase in the Kagome lattice Ising antiferromagnet at weak transverse fields.

Findings

Disordered phase exists at weak transverse fields on Kagome lattice.

Mapping to U(1) gauge theory explains phase behavior.

Ordered phases are possible in principle at weak fields.

Abstract

We study the quantum Ising antiferromagnet on the Kagome lattice, with weak transverse field dynamics and other local perturbations. We analytically demonstrate the possibility of a disordered zero-temperature phase that is smoothly connected to the phase at strong transverse fields. This is done by means of an appropriate mapping to a compact U(1) gauge theory on the honeycomb lattice that is coupled to a charge-1 matter field. Our results are consistent with existing Monte-Carlo calculations. The differences with other commonly studied lattices (in which such disordered phases do not obtain at weak transverse fields) is explained. Ordered phases are also shown to be possible in principle in the weak transverse field limit, and are briefly studied.