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Tensor network variational optimizations for real-time dynamics: application to the time-evolution of spin liquids
by Ravi Teja Ponnaganti, Matthieu Mambrini, Didier Poilblanc
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Submission summary
| Authors (as registered SciPost users): | Matthieu Mambrini · Didier Poilblanc · Ravi Teja Ponnaganti |
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| Preprint Link: | https://arxiv.org/abs/2304.13184v3 (pdf) |
| Date accepted: | 2023-09-13 |
| Date submitted: | 2023-07-25 11:17 |
| Submitted by: | Ponnaganti, Ravi Teja |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Within the Projected Entangled Pair State (PEPS) tensor network formalism, a simple update (SU) method has been used to investigate the time evolution of a two-dimensional U(1) critical spin-1/2 spin liquid under Hamiltonian quench [Phys. Rev. B 106, 195132 (2022)]. Here we introduce two different variational frameworks to describe the time dynamics of SU(2)-symmetric translationally-invariant PEPS, aiming to improve the accuracy. In one approach, after using a Trotter-Suzuki decomposition of the time evolution operator in term of two-site elementary gates, one considers a single bond embedded in an environment approximated by a Corner Transfer Matrix Renormalization Group (CTMRG). A variational update of the two tensors on the bond is performed under the application of the elementary gate and then, after symmetrization of the site tensors, the environment is updated. In the second approach, a cluster optimization is performed on a finite (periodic) cluster, maximizing the overlap of the exact time-evolved state with a symmetric finite-size PEPS ansatz. Observables are then computed on the infinite lattice contracting the infinite-PEPS (iPEPS) by CTMRG. We show that the variational schemes outperform the SU method and remain accurate over a significant time interval before hitting the entanglement barrier. Studying the spectrum of the transfer matrix, we find that the asymptotic correlations are very well preserved under time evolution, including the critical nature of the singlet correlations, as expected from the Lieb-Robinson (LR) bound theorem. Consistently, the system (asymptotic) boundary is found to be described by the same Conformal Field Theory of central charge c = 1 during time evolution. We also compute the time-evolution of the short distance spin-spin correlations and estimate the LR velocity.
Author comments upon resubmission
List of changes
1) Figures 4 and 9 have been revised following recommendations.
2) Results on the central charge have been added to the abstract and the conclusion, as recommended.
3)"highly" in "highly entangled" has been removed, "small entanglement" has been defined.
4) Z2 gauge operator has been introduced at the end of page 4.
5) Fig. 1 moved to sec. 2.2.1
6) on page 9, "again" has been removed and "as in the EBVO method" has been added, to improve clarity.
7) "r>>1" has been removed, a quantitative definition of 'long-distance' has been discussed in the following subsection.
8) Fig. 5 and Fig. 6 captions have been revised, providing a short analysis of the data.
9) The mentioned typos have been corrected.
Published as SciPost Phys. 15, 158 (2023)
Reports on this Submission
Anonymous Report 1 on 2023-9-4 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2304.13184v3, delivered 2023-09-04, doi: 10.21468/SciPost.Report.7758
Report
The authors have sufficiently addressed all referee's comments. I believe the article is now ready to be published.
Understanding non-equilibrium quench dynamics is an often considered problem. Despite that, results in two-dimensional systems are scarce due to the notorious difficulty of addressing setups. Among the numerical methods, iPEPS is one of the very few approaches that can offer some hope to faithfully capture evolution dynamics, even if only for short times. The article makes steps to incorporate full symmetries of the problem (SU(2) and lattice translational and rotational invariance) in the algorithm. While the overall research direction is natural (given the author's expertise), the outcome of such effort was unclear and it required committed studies performed in this article. I see a potential for the application of the particular methodology developed in this work (following a general trend where symmetries are used to stabilize the results of iPEPS simulations) to numerous setups, warranting a body of follow-up works. As such would like to recommend publication in SciPost Physics. On top of building physical understanding, such results should also become useful in crosschecking results produced by fast-approaching quantum simulators.