Time evolution of the quantum Ising model in two dimensions using Tree Tensor Networks

TL;DR

This paper explores the use of Tree Tensor Networks to simulate the non-equilibrium dynamics of the 2D quantum Ising model, demonstrating accuracy in certain regimes and analyzing computational limitations and optimizations.

Contribution

It introduces TTNs for 2D quantum Ising dynamics, benchmarks GPU acceleration, and discusses entanglement growth challenges in non-equilibrium simulations.

Findings

TTNs accurately reproduce known results in the perturbative regime.

GPU acceleration significantly improves computational performance.

Entanglement growth limits the simulation of long-time dynamics.

Abstract

The numerical simulation of two-dimensional quantum many-body systems away from equilibrium constitutes a major challenge for all known computational methods. We investigate the utility of Tree Tensor Network (TTN) states to solve the dynamics of the quantum Ising model in two dimensions. Within the perturbative regime of small transverse fields, TTNs faithfully reproduce analytically known, but non-trivial and physically interesting results, for lattices up to $16 \times 16$ sites. Limitations of the method related to the rapid growth of entanglement entropy are explored within more general, paradigmatic quench settings. We provide and discuss comprehensive benchmarks regarding the benefit of \emph{GPU} acceleration and the impact of using local operator sums on the performance.