Probing universal imaginary-time relaxation critical dynamics with infinite projected entangled pair states

TL;DR

This paper uses infinite projected entangled pair states (iPEPS) to study imaginary-time relaxation dynamics of the 2D transverse-field Ising model, revealing universal critical behavior and demonstrating the method's effectiveness in probing quantum criticality.

Contribution

The study introduces a scalable iPEPS-based approach to analyze dynamical critical phenomena in 2D quantum systems via imaginary-time evolution.

Findings

Power law scaling of magnetization near critical point.

Determination of critical point and exponents with high accuracy.

Universal initial-slip exponent consistent with quantum Monte Carlo results.

Abstract

We investigate the imaginary-time relaxation critical dynamics of the two-dimensional transverse-field Ising model using infinite projected entangled pair states (iPEPS) with the full-update strategy. Simulating directly in the thermodynamic limit, we explore the relaxation process near the critical point with two types of initial states: a fully polarized state and a product state with a small magnetization. For the fully polarized state, the magnetization shows a power law scaling $M\propto \tau^{-\beta/(\nu z)}$ in the imaginary-time evolution, from which both the critical point and critical exponent can be determined with high accuracy. For the nearly paramagnetic state, the relaxation process exhibits a behavior of $M\propto \tau^\theta$ with $\theta=0.1958$ being the critical initial-slip exponent, which is in good agreement with that obtained from the dynamic scaling of the self-correlation in quantum Monte Carlo method. These universal features emerge well before the system converges to the ground state, demonstrating the efficiency of imaginary-time evolution for probing quantum criticality. Our results demonstrate that iPEPS can serve as a robust and scalable method for studying dynamical critical phenomena in two-dimensional quantum many-body systems.