Abstract
We generalize the previous study on the application of variational autoencoders to the two-dimensional Ising model to a system with anisotropy. Due to the self-duality property of the system, the critical points can be located exactly for the entire range of anisotropic coupling. This presents an excellent test bed for the validity of using a variational autoencoder to characterize an anisotropic classical model. We reproduce the phase diagram for a wide range of anisotropic couplings and temperatures via a variational autoencoder without the explicit construction of an order parameter. Considering that the partition function of (d+1)-dimensional anisotropic models can be mapped to that of the d-dimensional quantum spin models, the present study provides numerical evidence that a variational autoencoder can be applied to analyze quantum systems via the quantum Monte Carlo method.
| Original language | English |
|---|---|
| Article number | 045301 |
| Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |
| Volume | 107 |
| Issue number | 4 |
| DOIs | |
| State | Published - Apr 2023 |
| Externally published | Yes |
Funding
A.B. and N.W. are supported by NSF Grant No. DMR-1728457. J.M. and K.-M.T. are supported by the U.S. Department of Energy, Office of Science and Office of Basic Energy Sciences, under Award No. DE-SC0017861. This work used high-performance computational resources provided by the Louisiana Optical Network Initiative and HPC@LSU computing.