Evidence of columnar order in the fully frustrated transverse field Ising model on the square lattice

TL;DR

This paper uses Monte Carlo simulations to reveal that the fully frustrated transverse field Ising model on a square lattice exhibits columnar order at low fields, with a large length scale and an effective U(1) symmetry at intermediate scales.

Contribution

It demonstrates the emergence of columnar order in the model and clarifies the nature of phase transitions, connecting quantum fluctuations to order types.

Findings

Columnar order develops in the low-field phase.

An effective U(1) symmetry exists at intermediate scales.

Transition from plaquette to columnar order is driven by quantum fluctuations.

Abstract

Using extensive classical and quantum Monte Carlo simulations, we investigate the ground-state phase diagram of the fully frustrated transverse field Ising model on the square lattice. We show that pure columnar order develops in the low-field phase above a surprisingly large length scale, below which an effective U(1) symmetry is present. The same conclusion applies to the Quantum Dimer Model with purely kinetic energy, to which the model reduces in the zero-field limit, as well as to the stacked classical version of the model. By contrast, the 2D classical version of the model is shown to develop plaquette order. Semiclassical arguments show that the transition from plaquette to columnar order is a consequence of quantum fluctuations.