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Abelian and non-abelian symmetries in infinite projected entangled pair states
by Claudius Hubig
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Claudius Hubig |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/1808.10804v2 (pdf) |
| Date accepted: | Nov. 7, 2018 |
| Date submitted: | Oct. 17, 2018, 2 a.m. |
| Submitted by: | Hubig, Claudius |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Computational |
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.
Author comments upon resubmission
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
Published as SciPost Phys. 5, 047 (2018)