Algorithms for finite Projected Entangled Pair States

TL;DR

This paper analyzes and improves algorithms for Projected Entangled Pair States (PEPS), enhancing their efficiency and accuracy for simulating two-dimensional quantum many-body systems, with benchmarking on large lattice models.

Contribution

It provides a detailed analysis of PEPS contraction accuracy, introduces algorithmic improvements for tensor updates, and benchmarks the state-of-the-art code on large-scale models.

Findings

Correlation length affects contraction accuracy.

Purifications improve approximate contraction.

Enhanced algorithms significantly boost efficiency.

Abstract

Projected Entangled Pair States (PEPS) are a promising ansatz for the study of strongly correlated quantum many-body systems in two dimensions. But due to their high computational cost, developing and improving PEPS algorithms is necessary to make the ansatz widely usable in practice. Here we analyze several algorithmic aspects of the method. On the one hand, we quantify the connection between the correlation length of the PEPS and the accuracy of its approximate contraction, and discuss how purifications can be used in the latter. On the other, we present algorithmic improvements for the update of the tensor that introduce drastic gains in the numerical conditioning and the efficiency of the algorithms. Finally, the state-of-the-art general PEPS code is benchmarked with the Heisenberg and quantum Ising models on lattices of up to $21 \times 21$ sites.