Abelian and non-abelian symmetries in infinite projected entangled pair states

TL;DR

This paper details the implementation of abelian and non-abelian symmetries in infinite projected entangled pair states, significantly improving computational efficiency and enabling better detection of symmetry breaking in 2D lattice models.

Contribution

It introduces a method for incorporating symmetries into iPEPS, achieving faster computations and maintaining or improving accuracy in ground-state energy calculations.

Findings

Large computational speed-up with symmetry implementation

Unbroken symmetries do not reduce the expressive power of the states

Symmetry implementation aids in detecting spontaneous symmetry breaking

Abstract

We explore in detail the implementation of arbitrary abelian and non-abelian symmetries in the setting of infinite projected entangled pair states on the two-dimensional square lattice. We observe a large computational speed-up; easily allowing bond dimensions $D = 10$ in the square lattice Heisenberg model at computational effort comparable to calculations at $D = 6$ without symmetries. We also find that implementing an unbroken symmetry does not negatively affect the representative power of the state and leads to identical or improved ground-state energies. Finally, we point out how to use symmetry implementations to detect spontaneous symmetry breaking.