Statistics-encoded tensor network approach in disordered quantum many-body spin chains

• URL: http://arxiv.org/abs/2508.16286v1
• Date: Fri, 22 Aug 2025 10:50:27 GMT
• Title: Statistics-encoded tensor network approach in disordered quantum many-body spin chains
• Authors: Hao Zhu, Ding-Zu Wang, Shi-Ju Ran, Guo-Feng Zhang,
• Abstract summary: We propose a general approach -- the statistics-encoded tensor network (SeTN) -- to study quantum many-body systems with disorder.<n>We derive a universal criterion, $n gg alpha2 t2$, linking discretization $n$, disorder strength $alpha$, and evolution duration $t$.<n>SeTN provides a novel framework for probing the disorder-driven dynamical phenomena in many-body quantum systems.
• Score: 7.016643488761326
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Simulating the dynamics of quantum many-body systems with disorder is a fundamental challenge. In this work, we propose a general approach -- the statistics-encoded tensor network (SeTN) -- to study such systems. By encoding disorder into an auxiliary layer and averaging separately, SeTN restores translational invariance, enabling a well-defined transfer matrix formulation. We derive a universal criterion, $n \gg \alpha^2 t^2$, linking discretization $n$, disorder strength $\alpha$, and evolution duration $t$. This sets the resolution required for faithful disorder averaging and shows that encoding is most efficient in the weak-disorder, typically chaotic regime. Applied to the disordered transverse-field Ising model, SeTN shows that the spectral form factor is governed by the leading transfer-matrix eigenvalue, in contrast to the kicked Ising model. SeTN thus provides a novel framework for probing the disorder-driven dynamical phenomena in many-body quantum systems.

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