Quantum-critical properties of the long-range transverse-field Ising model from quantum Monte Carlo simulations

TL;DR

This study uses quantum Monte Carlo simulations to analyze the quantum-critical behavior of the long-range transverse-field Ising model, revealing how critical exponents vary with interaction range and confirming universality classes.

Contribution

It provides a comprehensive numerical analysis of the critical exponents and universality classes of the long-range transverse-field Ising model across different dimensions and interaction regimes.

Findings

Critical exponents vary with decay exponent of interactions.

Universality classes range from nearest-neighbor to Gaussian regimes.

Results are consistent with nearest-neighbor Ising universality across regimes.

Abstract

The quantum-critical properties of the transverse-field Ising model with algebraically decaying interactions are investigated by means of stochastic series expansion quantum Monte Carlo, on both the one-dimensional linear chain and the two-dimensional square lattice. We extract the critical exponents $\nu$ and $\beta$ as a function of the decay exponent of the long-range interactions. For ferromagnetic Ising interactions, we resolve the limiting regimes known from field theory, ranging from the nearest-neighbor Ising to the long-range Gaussian universality classes, as well as the intermediate regime with continuously varying critical exponents. In the long-range Gaussian regime, we treat the effect of dangerous irrelevant variables on finite-size scaling forms. For antiferromagnetic and therefore competing Ising interactions, the stochastic series expansion algorithm displays growing auto-correlation times leading to a reduced performance. Nevertheless, our results are consistent with the nearest-neighbor Ising universality for all investigated interaction ranges both on the linear chain and the square lattice.