Stochastic Sampling of Operator Growth Dynamics

TL;DR

This paper introduces a sign-problem-free Monte Carlo method to study operator growth in quantum many-body systems, revealing rapid thermalization, exponential decay of response functions, and subtle corrections in 1D and 2D quantum Ising models.

Contribution

The authors develop a novel Monte Carlo algorithm that enables unbiased, exact sampling of operator growth dynamics without the sign problem, applicable to complex quantum spin systems.

Findings

Demonstrated rapid thermalization in high-frequency dynamics

Detected logarithmic corrections to operator growth hypothesis in 1D

Uncovered a dynamical crossover in 2D quantum Ising model

Abstract

We put forward a Monte Carlo algorithm that samples the Euclidean time operator growth dynamics at infinite temperature. Crucially, our approach is free from the numerical sign problem for a broad family of quantum many-body spin systems, allowing for numerically exact and unbiased calculations. We apply this methodological headway to study the high-frequency dynamics of the mixed-field quantum Ising model (QIM) in one and two dimensions. The resulting quantum dynamics display rapid thermalization, supporting the recently proposed operator growth hypothesis. Physically, our findings correspond to an exponential fall-off of generic response functions of local correlators at large frequencies. Remarkably, our calculations are sufficiently sensitive to detect subtle logarithmic corrections of the hypothesis in one dimension. In addition, in two dimensions, we uncover a non-trivial dynamical crossover between two large frequency decay rates. Lastly, we reveal spatio-temporal scaling laws associated with operator growth, which are found to be strongly affected by boundary contributions.