Simulation of three-dimensional quantum systems with projected entangled-pair states

TL;DR

This paper advances the simulation of 3D quantum systems by developing and benchmarking two tensor network contraction methods for infinite projected entangled-pair states, enabling more effective analysis of complex 3D models.

Contribution

It introduces two novel contraction algorithms for 3D iPEPS and benchmarks their performance on key quantum models, expanding the applicability of tensor networks to three-dimensional systems.

Findings

Both algorithms produce competitive results for 3D models.

The methods effectively handle the contraction complexity of 3D tensor networks.

iPEPS shows promise as a tool for challenging 3D quantum problems.

Abstract

Tensor network algorithms have proven to be very powerful tools for studying one- and two-dimensional quantum many-body systems. However, their application to three-dimensional (3D) quantum systems has so far been limited, mostly because the efficient contraction of a 3D tensor network is very challenging. In this paper we develop and benchmark two contraction approaches for infinite projected entangled-pair states (iPEPS) in 3D. The first approach is based on a contraction of a finite cluster of tensors including an effective environment to approximate the full 3D network. The second approach performs a full contraction of the network by first iteratively contracting layers of the network with a boundary iPEPS, followed by a contraction of the resulting quasi-2D network using the corner transfer matrix renormalization group. Benchmark data for the Heisenberg and Bose-Hubbard models on the cubic lattice show that the algorithms provide competitive results compared to other approaches, making iPEPS a promising tool to study challenging open problems in 3D.