Quantum effects in rotationally invariant spin glass models

Fuente: arXiv
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Autores principales: Hara, Yoshinori, Kabashima, Yoshiyuki
Formato: Preprint
Publicado: 2025
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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