New quantum Monte Carlo study of quantum critical phenomena with Trotter-number-dependent finite-size scaling and non-equilibrium relaxation

TL;DR

This paper introduces a new quantum Monte Carlo method combining finite-size scaling and non-equilibrium relaxation to efficiently study quantum critical phenomena, validated on a one-dimensional XY model.

Contribution

It develops a generalized scheme that simplifies quantum critical point estimation using Trotter number and system size, improving accuracy and efficiency.

Findings

Accurate estimation of the critical point and exponents for the 1D XY model.

Transition point and critical exponents agree with exact solutions.

Dynamical critical exponent matches that of the 2D Ising model.

Abstract

We propose a new efficient scheme for the quantum Monte Carlo study of quantum critical phenomena in quantum spin systems. Rieger and Young's Trotter-number-dependent finite-size scaling in quantum spin systems and Ito {\it et al.}'s evaluation of the transition point with the non-equilibrium relaxation in classical spin systems are combined and generalized. That is, only one Trotter number and one inverse temperature proportional to system sizes are taken for each system size, and the transition point of the transformed classical spin model is estimated as the point at which the order parameter shows power-law decay. The present scheme is confirmed by the determination of the critical phenomenon of the one-dimensional $S=1/2$ asymmetric XY model in the ground state. The estimates of the transition point and the critical exponents $\beta$, $\gamma$ and $\nu$ are in good agreement with the exact solutions. The dynamical critical exponent is also estimated as ${\mit \Delta}=2.14(I4(Jpm 0.06$, which is consistent with that of the two-dimensional Ising model.