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

by Claudius Hubig

Submission summary

As Contributors: Claudius Hubig
Arxiv Link: (pdf)
Date accepted: 2018-11-07
Date submitted: 2018-10-17 02:00
Submitted by: Hubig, Claudius
Submitted to: SciPost Physics
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Quantum Physics
Approach: Computational


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.

Ontology / Topics

See full Ontology or Topics database.

Abelian symmetries Heisenberg model Infinite projected entangled pair states (iPEPS) Non-abelian symmetries Spontaneous symmetry breaking

Published as SciPost Phys. 5, 047 (2018)

Author comments upon resubmission

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

Additionally, minor changes include:

- 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

Reports on this Submission

Anonymous Report 1 on 2018-10-20 (Invited 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

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