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

### Submission summary

 As Contributors: Claudius Hubig Arxiv Link: https://arxiv.org/abs/1808.10804v2 Date accepted: 2018-11-07 Date submitted: 2018-10-17 Submitted by: Hubig, Claudius Submitted to: SciPost Physics Domain(s): Computational Subject area: Condensed Matter Physics - Theory

### 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.

###### Current status:

I would like to thank the editor and the referees for their work and careful reading of the manuscript. All the comments have been incorporated (see below), in particular the description of Clebsch-Gordan tensors was extended with an example and the discussion of the Kagomé Heisenberg model results with and without SU(2) symmetry reworked.

### List of changes

The following primary changes have been incorporated:

- the aim of the paper was clarified to explore the implementation of global symmetries in the context of iPEPS
- an example was added to the description of the Clebsch-Gordan tensors
- the discussion of results for the SU(2)-invariant spin-½ Kagomé results was reworked

- clarification of d, D, χ and X for the reduced/total state and reduced/total environment bond dimensions respectively
- definition of "CTM" (corner transfer matrix) and "FFU" (fast full update) at first use
- clarification that the focus of the Kagomé section is on the benchmarking of symmetry implementations, a study of the physics of the model and in particular its gap is outside the scope of the current work
- references to existing work on the spin-1 Kagomé lattice with SU(2)-iPEPS, the J1-J2 Heisenberg lattice with U(1)-iPEPS and the physics of the spin-½ Kagomé lattice were included and the relation of these results to those found here clarified
- larger symbol sizes in Fig. 5 to avoid confusion
- Writing "iPEPS" instead of "IPEPS", as the former appears to be more common
- clearer definition of the remover tensor and its initialisation and update

### Submission & Refereeing History

Resubmission 1808.10804v2 (17 October 2018)
Submission 1808.10804v1 (3 September 2018)

## Invited Reports on this Submission

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### Report

The author has updated the manuscript according to the wishes of the reviewers. I believe the modifications and additions have sufficiently clarified the methods that are described.

• validity: good
• significance: good
• originality: good
• clarity: good
• formatting: good
• grammar: excellent