Reentrance of the Disordered Phase in the Antiferromagnetic Ising Model on a Square Lattice with Longitudinal and Transverse Magnetic Fields

TL;DR

This paper maps the ground-state phase diagram of the antiferromagnetic Ising model with magnetic fields, revealing reentrant transitions and providing benchmarks for quantum simulation with Rydberg atoms.

Contribution

It presents the first detailed quantum Monte Carlo phase diagram showing reentrant transitions in this model with implications for quantum simulation.

Findings

Reentrant transitions between disordered and antiferromagnetic phases.

Nearly constant transition longitudinal field for small transverse fields.

Phase diagram serves as a benchmark for Rydberg atom quantum simulations.

Abstract

Motivated by recent experiments with Rydberg atoms in an optical tweezer array, we accurately map out the ground-state phase diagram of the antiferromagnetic Ising model on a square lattice with longitudinal and transverse magnetic fields using the quantum Monte Carlo method. For a small but nonzero transverse field, the transition longitudinal field is found to remain nearly constant. By scrutinizing the phase diagram, we uncover a narrow region where the system exhibits reentrant transitions between the disordered and antiferromagnetic phases with increasing transverse field. Our phase diagram provides a useful benchmark for quantum simulation of a Rydberg atom system.