TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.18.1.011
TI  - Universal performance gap of neural quantum states applied to the Hofstadter-Bose-Hubbard model
PY  - 2025/01/10
UR  - https://scipost.org/SciPostPhys.18.1.011
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 18
IS  - 1
SP  - 011
A1  - Ledinauskas, Eimantas
AU  - Anisimovas, Egidijus
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.18.1.011,
	title={{Universal performance gap of neural quantum states applied to the Hofstadter-Bose-Hubbard model}},
	author={Eimantas Ledinauskas and Egidijus Anisimovas},
	journal={SciPost Phys.},
	volume={18},
	pages={011},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.18.1.011},
	url={https://scipost.org/10.21468/SciPostPhys.18.1.011},
}