Zero-temperature Monte Carlo simulations of two-dimensional quantum spin glasses guided by neural network states
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912164703371264 |
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| author | Brodoloni, L. Pilati, S. |
| author_facet | Brodoloni, L. Pilati, S. |
| contents | A continuous-time projection quantum Monte Carlo algorithm is employed to simulate the ground state of a short-range quantum spin-glass model, namely, the two-dimensional Edwards-Anderson Hamiltonian with transverse field, featuring Gaussian nearest-neighbor couplings. We numerically demonstrate that guiding wave functions based on self-learned neural networks suppress the population control bias below modest statistical uncertainties, at least up to a hundred spins. By projecting a two-fold replicated Hamiltonian, the spin overlap is determined. A finite-size scaling analysis is performed to estimate the critical transverse field where the spin-glass transition occurs, as well as the critical exponents of the correlation length and the spin-glass susceptibility. For the latter two, good agreement is found with recent estimates from the literature for different random couplings. We also address the spin-overlap distribution within the spin-glass phase, finding that, for the workable system sizes, it displays a non-trivial double-peak shape with large weight at zero overlap. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05978 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Zero-temperature Monte Carlo simulations of two-dimensional quantum spin glasses guided by neural network states Brodoloni, L. Pilati, S. Disordered Systems and Neural Networks Statistical Mechanics Computational Physics A continuous-time projection quantum Monte Carlo algorithm is employed to simulate the ground state of a short-range quantum spin-glass model, namely, the two-dimensional Edwards-Anderson Hamiltonian with transverse field, featuring Gaussian nearest-neighbor couplings. We numerically demonstrate that guiding wave functions based on self-learned neural networks suppress the population control bias below modest statistical uncertainties, at least up to a hundred spins. By projecting a two-fold replicated Hamiltonian, the spin overlap is determined. A finite-size scaling analysis is performed to estimate the critical transverse field where the spin-glass transition occurs, as well as the critical exponents of the correlation length and the spin-glass susceptibility. For the latter two, good agreement is found with recent estimates from the literature for different random couplings. We also address the spin-overlap distribution within the spin-glass phase, finding that, for the workable system sizes, it displays a non-trivial double-peak shape with large weight at zero overlap. |
| title | Zero-temperature Monte Carlo simulations of two-dimensional quantum spin glasses guided by neural network states |
| topic | Disordered Systems and Neural Networks Statistical Mechanics Computational Physics |
| url | https://arxiv.org/abs/2407.05978 |