SciPost Submission Page
Universal Performance Gap of Neural Quantum States Applied to the Hofstadter-Bose-Hubbard Model
by Eimantas Ledinauskas, Egidijus Anisimovas
Submission summary
| Authors (as registered SciPost users): | Eimantas Ledinauskas |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2405.01981v3 (pdf) |
| Date submitted: | 2024-10-14 06:57 |
| Submitted by: | Ledinauskas, Eimantas |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approaches: | Theoretical, Computational |
Abstract
Neural Quantum States (NQS) have demonstrated significant potential in approximating ground states of many-body quantum systems, though their performance can be inconsistent across different models. This study investigates the performance of NQS in approximating the ground state of the Hofstadter-Bose-Hubbard (HBH) model, an interacting boson system on a two-dimensional square lattice with a perpendicular magnetic field. Our results indicate that increasing magnetic flux leads to a substantial increase in energy error, up to three orders of magnitude. Importantly, this decline in NQS performance is consistent across different optimization methods, neural network architectures, and physical model parameters, suggesting a significant challenge intrinsic to the model. Despite investigating potential causes such as wave function phase structure, quantum entanglement, fractional quantum Hall effect, and the variational loss landscape, the precise reasons for this degradation remain elusive. The HBH model thus proves to be an effective testing ground for exploring the capabilities and limitations of NQS. Our study highlights the need for advanced theoretical frameworks to better understand the expressive power of NQS which would allow a systematic development of methods that could potentially overcome these challenges.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
List of changes
- Text below Eq. 10: We have added comments and a reference for more details on the differences between the SR and SITE methods, as suggested by Referee 2.
- Sec. 3.3.3: We moved Eq. 11 to this section, following the suggestion of Referee 2.
- Section 4.1, Fig. 1: As recommended by Referee 2, we have included data points for DMRG with a larger virtual bond dimension and added corresponding comments in the text discussing this figure.
- Last paragraph of section 4.1 and Fig. 2: We provided a more detailed analysis of the NQS energy accuracy as a function of the number of parameters and magnetic flux, as suggested by Referee 1.