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

TL;DR

This paper introduces the statistics-encoded tensor network (SeTN), a novel method for simulating disordered quantum many-body systems by encoding disorder and enabling efficient averaging, revealing new insights into their dynamical behavior.

Contribution

The paper presents SeTN, a new tensor network approach that encodes disorder into an auxiliary layer, restoring translational invariance and enabling transfer matrix analysis for disordered quantum systems.

Findings

SeTN effectively captures spectral properties of disordered models.

The universal criterion links discretization, disorder strength, and evolution time.

SeTN reveals the dominant eigenvalue governs spectral form factor.

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.