Tree tensor networks for many-body localization in two dimensions

TL;DR

This paper demonstrates that optimized tree tensor networks effectively simulate two-dimensional many-body localization, capturing complex entanglement patterns more efficiently than traditional methods.

Contribution

The authors introduce a physics-informed structural optimization of TTNs, enabling more accurate and efficient simulation of 2D many-body localization dynamics.

Findings

TTNs outperform MPS in capturing 2D entanglement patterns.

Optimized tree structures reduce bond dimensions needed for accurate results.

The method achieves better accuracy across different regimes with similar computational cost.

Abstract

We investigate the disordered spin-$\frac12$Heisenberg model in two dimensions and employ tree tensor networks (TTNs) with a physics-informed structural optimization of the tree layout, to simulate dynamics in the many-body localization problem. We find that TTNs are able to capture two-dimensional entanglement patterns more effectively than matrix product states (MPS) while being more efficient to contract than projected entangled pair states (PEPS) to probe larger systems and longer times. Structural optimization of the trees based on time evolution of the entanglement in the system allows to keep the necessary bond dimensions low and to maximally exploit the increased expressiveness of TTNs over MPS. In this way, we achieve more accurate results in all considered parameter regimes both below and above the ergodicity-to-localization crossover at a comparable compute-time cost.