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arXiv · 2508.16286

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

Hao Zhu·Ding-Zu Wang·Shi-Ju Ran·Guo-Feng Zhang
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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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Hao Zhu, Ding-Zu Wang, Shi-Ju Ran, Guo-Feng Zhang. 2025-08-22. Statistics-encoded tensor network approach in disordered quantum many-body spin chains. https://doi.org/10.1103/vb4b-m5h6

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