First- and second-order quantum phase transitions in the long-range unfrustrated antiferromagnetic Ising chain

TL;DR

This paper investigates the phase transitions in a long-range unfrustrated antiferromagnetic Ising chain, revealing a tricritical point where the transition switches from first to second order, with the transition range depending on interaction length.

Contribution

It provides an analytical solution in the long-range limit and numerically explores the transition behavior across interaction ranges using neural-network-based variational methods.

Findings

Mean-field treatment is exact in the long-range limit.

A tricritical point separates first- and second-order phase transitions.

First-order transition shrinks as interaction range decreases.

Abstract

We study the ground-state phase diagram of an unfrustrated antiferromagnetic Ising chain with longitudinal and transverse fields in the full range of interactions: from all-to-all to nearest-neighbors. First, we solve the model analytically in the strong long-range regime, confirming in the process that a mean-field treatment is exact for this model. We compute the order parameter and the correlations and show that the model exhibits a tricritical point where the phase transition changes from first to second order. This is in contrast with the nearest-neighbor limit where the phase transition is known to be second order. To understand how the order of the phase transition changes from one limit to the other, we tackle the analytically-intractable interaction ranges numerically, using a variational quantum Monte Carlo method with a neural-network-based ansatz, the visual transformer. We show how the first-order phase transition shrinks with decreasing interaction range and establish approximate boundaries in the interaction range for which the first-order phase transition is present. Finally, we establish that the key ingredient to stabilize a first-order phase transition and a tricritical point is the presence of ferromagnetic interactions between spins of the same sublattice on top of antiferromagnetic interactions between spins of different sublattices. Tunable-range unfrustrated antiferromagnetic interactions are just one way to implement such staggered interactions.