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An introduction to infinite projected entangled-pair state methods for variational ground state simulations using automatic differentiation
by Jan Naumann, Erik Lennart Weerda, Matteo Rizzi, Jens Eisert, Philipp Schmoll
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Jan Naumann · Philipp Schmoll |
| Submission information | |
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| Preprint Link: | scipost_202405_00004v2 (pdf) |
| Code repository: | https://github.com/variPEPS/ |
| Date accepted: | 2024-08-28 |
| Date submitted: | 2024-08-20 14:50 |
| Submitted by: | Naumann, Jan |
| Submitted to: | SciPost Physics Lecture Notes |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Computational |
Abstract
Tensor networks capture large classes of ground states of phases of quantum matter faithfully and efficiently. Their manipulation and contraction has remained a challenge over the years, however. For most of the history, ground state simulations of two-dimensional quantum lattice systems using (infinite) projected entangled pair states have relied on what is called a time-evolving block decimation. In recent years, multiple proposals for the variational optimization of the quantum state have been put forward, overcoming accuracy and convergence problems of previously known methods. The incorporation of automatic differentiation in tensor networks algorithms has ultimately enabled a new, flexible way for variational simulation of ground states and excited states. In this work we review the state-of-the-art of the variational iPEPS framework, providing a detailed introduction to automatic differentiation, a description of a general foundation into which various two-dimensional lattices can be conveniently incorporated, and demonstrative benchmarking results.
Author comments upon resubmission
We want to thank the referee for their valuable comments and the detailed report on our manuscript. We have revised the draft by incorporating the suggestions made in the report by adding a paragraph discussing alternative methods for contractions as well as a new section about the extension of the framework to include physical symmetries in the ansatz.
For your convenience, we have highlighted the changes in red colour in the resubmitted manuscript.
Yours sincerely,
The authors
List of changes
- In the introduction of Chapter 2, we have added a paragraph discussing alternative methods for contractions. We point the reader to the relevant literature, particularly with the focus on alternative methods incorporating a variational ansatz. (Lines 152-160).
- We have added Section 2.7 focusing on the ability of tensor network ansätze to incorporate physical symmetries exactly. We mention the relevant methodology and point the reader to software implementations in this field. (Lines 538 - 560).
Published as SciPost Phys. Lect. Notes 86 (2024)