Time evolution of projected entangled pair states in the single layer picture

TL;DR

This paper introduces an efficient single-layer tensor network algorithm for simulating two-dimensional quantum many-body systems, reducing computational costs and enabling larger Hilbert space exploration.

Contribution

It proposes a novel environment approximation method using a single-layer tensor network for time evolution in PEPS, improving efficiency and scalability.

Findings

Method shows stability on Heisenberg model

Achieves good agreement with accurate results

Enables larger submanifold simulations

Abstract

We propose an efficient algorithm for simulating quantum many-body systems in two spatial dimensions using projected entangled pair states. This is done by approximating the environment, arising in the context of updating tensors in the process of time evolution, using a single-layered tensor network structure. This significantly reduces the computational costs and allows simulations in a larger submanifold of the Hilbert space as bounded by the bond dimension of the tensor network. We present numerical evidence for stability of the method on an antiferromagnetic isotropic Heisenberg model where good agreement is found with the available accurate results.