Quantum many-body dynamics in two dimensions with artificial neural networks

TL;DR

This paper introduces a neural network-based method for simulating the real-time dynamics of two-dimensional quantum many-body systems, overcoming previous limitations and matching the capabilities of advanced tensor network techniques.

Contribution

The authors develop a neural network encoding approach that enables efficient simulation of 2D quantum dynamics, addressing key challenges in large system and long-time evolution modeling.

Findings

Successfully simulated 2D transverse field Ising model dynamics

Observed collapse and revival oscillations of ferromagnetic order

Achieved time scales comparable to tensor network methods

Abstract

The efficient numerical simulation of nonequilibrium real-time evolution in isolated quantum matter constitutes a key challenge for current computational methods. This holds in particular in the regime of two spatial dimensions, whose experimental exploration is currently pursued with strong efforts in quantum simulators. In this work we present a versatile and efficient machine learning inspired approach based on a recently introduced artificial neural network encoding of quantum many-body wave functions. We identify and resolve some key challenges for the simulation of time evolution, which previously imposed significant limitations on the accurate description of large systems and long-time dynamics. As a concrete example, we study the dynamics of the paradigmatic two-dimensional transverse field Ising model, as recently also realized experimentally in systems of Rydberg atoms. Calculating the nonequilibrium real-time evolution across a broad range of parameters, we, for instance, observe collapse and revival oscillations of ferromagnetic order and demonstrate that the reached time scales are comparable to or exceed the capabilities of state-of-the-art tensor network methods.