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QSpace - An Open-Source Tensor Library for Abelian and non-Abelian Symmetries
by Andreas Weichselbaum
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Andreas Weichselbaum |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202405_00027v2 (pdf) |
| Code repository: | https://bitbucket.org/qspace4u/qspace-v4-pub/ |
| Code version: | v4.0 |
| Code license: | Apache 2.0 |
| Date accepted: | 2024-07-22 |
| Date submitted: | 2024-07-04 03:23 |
| Submitted by: | Weichselbaum, Andreas |
| Submitted to: | SciPost Physics Codebases |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Computational |
Abstract
This is the documentation for the tensor library QSpace (v4.0), a toolbox to exploit `quantum symmetry spaces' in tensor network states in the quantum many-body context. QSpace permits arbitrary combinations of symmetries including the abelian symmetries $\mathbb{Z}_n$ and $U(1)$, as well as all non-abelian symmetries based on the semisimple classical Lie algebras: $A_n$, $B_n$, $C_n$, and $D_n$, or respectively, the special unitary group SU($n$), the odd orthogonal group SO($2n+1$), the symplectic group Sp($2n$), and the even orthogonal group SO($2n$). The code (C++ embedded via the MEX interface into Matlab) is available \href{https://bitbucket.org/qspace4u/}{open-source as of QSpace v4.0 on bitbucket} under the Apache 2.0 license. QSpace is designed as a bottom-up approach for non-abelian symmetries. It starts from the defining representation and the respective Lie algebra. By explicitly computing and tabulating generalized Clebsch-Gordan coefficient tensors, QSpace is versatile in its operations across all symmetries. At the level of an application, much of the symmetry-related details are hidden within the QSpace C++ core libraries. Hence when developing tensor network algorithms with QSpace, these can be coded (nearly) as if there are no symmetries at all, despite being able to fully exploit general non-abelian symmetries.
Author comments upon resubmission
I posted the reply to the questions concerning DMRG and PEPS with iterative power methods online with the report. The remaining reply and changes are listed below.
List of changes
The acronyms irops and ireps are now introduced the first time they are used.
The referee suggested fusion of indices for higher-rank tensors
to avoid a growing number of individual symmetry block.
I added a paragraph addressing this point at the end of
Sec. 2.11 (page 22).
On showing trailing singleton dimensions with RMTs only:
To motivate the shown behavior, I extended the second
paragraph in Sec. 3.2 QSpace display on page 35.
The inconsistent use of "j symbols" and "j-symbols"
is fixed (hyphens removed throughout).
The format of the symmetry rank from r -> mathfrak{r}
around Eq. (12) is fixed: this needed to read mathfrak{r}, indeed,
for consistency.
The typo on page 56 concerning q_2 is also fixed.
Published as SciPost Phys. Codebases 40-r4.0 (2024) , SciPost Phys. Codebases 40 (2024)