Stochastic parameter optimization analysis of dynamical quantum critical phenomena in long-range transverse-field Ising chain

TL;DR

This paper combines quantum Monte Carlo and stochastic parameter optimization to analyze quantum phase transitions in a long-range transverse-field Ising chain, automatically determining critical parameters and studying their dependence on interaction decay.

Contribution

It introduces an automated method for parameter tuning in quantum Monte Carlo simulations to analyze critical phenomena without prior knowledge of critical points.

Findings

Identified the universality boundary at $\sigma=7/4$ between different regimes.

Precisely determined critical exponents across various interaction decay regimes.

Demonstrated the effectiveness of automatic parameter optimization in quantum critical analysis.

Abstract

The quantum phase transition of the one-dimensional long-range transverse-field Ising model is explored by combining the quantum Monte Carlo method and stochastic parameter optimization, specifically achieved by tuning correlation ratios so that space and imaginary time are isotropic. In our simulations, the simulator automatically determines the parameters to sample from, even without prior knowledge of the critical point and universality class. The leading-order finite-size corrections are eliminated by comparing two systems with different sizes; this procedure is also performed automatically. Varying the decay exponent of the long-range interaction, $\sigma$, we investigate $\sigma$-dependence of the dynamical exponent and the other critical exponents precisely in the mean-field, non-universal, and two-dimensional classical Ising universality regimes. We successfully obtained numerical evidence supporting $\sigma = 7/4$ as the universality boundary between the latter two.