Quantum effects in rotationally invariant spin glass models
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866908582805504000 |
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| author | Hara, Yoshinori Kabashima, Yoshiyuki |
| author_facet | Hara, Yoshinori Kabashima, Yoshiyuki |
| contents | This study investigates the quantum effects in transverse-field Ising spin glass models with rotationally invariant random interactions. The primary aim is to evaluate the validity of a quasi-static approximation that captures the imaginary-time dependence of the order parameters beyond the conventional static approximation. Using the replica method combined with the Suzuki--Trotter decomposition, we established a stability condition for the replica symmetric solution, which is analogous to the de Almeida--Thouless criterion. Numerical analysis of the Sherrington--Kirkpatrick model estimates a value of the critical transverse field, $Γ_\mathrm{c}$, which agrees with previous Monte Carlo-based estimations. For the Hopfield model, it provides an estimate of $Γ_\mathrm{c}$, which has not been previously evaluated. For the random orthogonal model, our analysis suggests that quantum effects alter the random first-order transition scenario in the low-temperature limit. This study supports a quasi-static treatment for analyzing quantum spin glasses and may offer useful insights into the analysis of quantum optimization algorithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_18034 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum effects in rotationally invariant spin glass models Hara, Yoshinori Kabashima, Yoshiyuki Disordered Systems and Neural Networks Statistical Mechanics Quantum Physics This study investigates the quantum effects in transverse-field Ising spin glass models with rotationally invariant random interactions. The primary aim is to evaluate the validity of a quasi-static approximation that captures the imaginary-time dependence of the order parameters beyond the conventional static approximation. Using the replica method combined with the Suzuki--Trotter decomposition, we established a stability condition for the replica symmetric solution, which is analogous to the de Almeida--Thouless criterion. Numerical analysis of the Sherrington--Kirkpatrick model estimates a value of the critical transverse field, $Γ_\mathrm{c}$, which agrees with previous Monte Carlo-based estimations. For the Hopfield model, it provides an estimate of $Γ_\mathrm{c}$, which has not been previously evaluated. For the random orthogonal model, our analysis suggests that quantum effects alter the random first-order transition scenario in the low-temperature limit. This study supports a quasi-static treatment for analyzing quantum spin glasses and may offer useful insights into the analysis of quantum optimization algorithms. |
| title | Quantum effects in rotationally invariant spin glass models |
| topic | Disordered Systems and Neural Networks Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2504.18034 |