Finite-temperature critical behavior of long-range quantum Ising models

TL;DR

This study explores the phase transitions and critical behavior of long-range quantum Ising chains at finite temperatures using Monte Carlo simulations, revealing how interaction range influences universality classes and transition properties.

Contribution

It provides the first comprehensive analysis of both ground-state and finite-temperature critical behavior in long-range quantum Ising models, especially for the challenging regime where the decay exponent is less than one.

Findings

Phase boundary of ferromagnetic phase identified.

Accurate estimates of transition temperatures obtained.

Critical exponents largely agree with existing predictions, with small deviations.

Abstract

We study the phase diagram and critical properties of quantum Ising chains with long-range ferromagnetic interactions decaying in a power-law fashion with exponent $\alpha$, in regimes of direct interest for current trapped ion experiments. Using large-scale path integral Monte Carlo simulations, we investigate both the ground-state and the nonzero-temperature regimes. We identify the phase boundary of the ferromagnetic phase and obtain accurate estimates for the ferromagnetic-paramagnetic transition temperatures. We further determine the critical exponents of the respective transitions. Our results are in agreement with existing predictions for interaction exponents $\alpha > 1$ up to small deviations in some critical exponents. We also address the elusive regime $\alpha < 1$, where we find that the universality class of both the ground-state and nonzero-temperature transition is consistent with the mean-field limit at $\alpha = 0$. Our work not only contributes to the understanding of the equilibrium properties of long-range interacting quantum Ising models, but can also be important for addressing fundamental dynamical aspects, such as issues concerning the open question of thermalization in such models.