Implementing global Abelian symmetries in projected entangled-pair state algorithms

TL;DR

This paper introduces a formalism for implementing Abelian symmetries in two-dimensional tensor network states, enhancing the efficiency of simulations for strongly entangled systems, with validated benchmark results.

Contribution

It presents a new formalism to incorporate Abelian symmetries into 2D tensor network algorithms, reducing computational costs and improving simulation accuracy.

Findings

Formalism successfully implements Abelian symmetries in 2D tensor networks.

Benchmark results confirm the validity of the approach.

Method improves efficiency for strongly entangled, gapless systems.

Abstract

Due to the unfavorable scaling of tensor network methods with the refinement parameter M, new approaches are necessary to improve the efficiency of numerical simulations based on such states in particular for gapless, strongly entangled systems. In one-dimensional DMRG, the use of Abelian symmetries has lead to large computational gain. In higher-dimensional tensor networks, this is associated with significant technical efforts and additional approximations. We explain a formalism to implement such symmetries in two-dimensional tensor network states and present benchmark results that confirm the validity of these approximations in the context of projected entangled-pair state algorithms.