Monte Carlo Simulation of Operator Dynamics and Entanglement in Dual-Unitary Circuits

TL;DR

This paper introduces a Monte Carlo simulation approach for studying operator dynamics and entanglement growth in dual-unitary circuits, revealing exponential convergence to steady states, volume-law entanglement scaling, and a critical transition in entanglement growth.

Contribution

It develops a scalable Monte Carlo method to analyze long-time operator evolution and entanglement in dual-unitary circuits, with analytical and numerical insights into phase transitions.

Findings

Operator density converges exponentially to a steady state.

Operator entanglement exhibits volume-law scaling.

Identifies a critical transition in entanglement growth governed by circuit parameters.

Abstract

We investigate operator dynamics and entanglement growth in dual-unitary circuits, a class of locally scrambled quantum systems that enables efficient simulation beyond the exponential complexity of the Hilbert space. By mapping the operator evolution to a classical Markov process,we perform Monte Carlo simulations to access the time evolution of local operator density and entanglement with polynomial computational cost. Our results reveal that the operator density converges exponentially to a steady-state value, with analytical bounds that match our simulations. Additionally, we observe a volume-law scaling of operator entanglement across different subregions,and identify a critical transition from maximal to sub-maximal entanglement growth, governed by the circuit's gate parameter. This transition, confirmed by both mean-field theory and Monte Carlo simulations, provides new insights into operator entanglement dynamics in quantum many-body systems. Our work offers a scalable computational framework for studying long-time operator evolution and entanglement, paving the way for deeper exploration of quantum information dynamics.