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

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 >> α²t², linking discretization n, disorder strength α, 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, over the numerically accessible time window, 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.