Revisiting Many-body Localization with Random Networks of Tensors

TL;DR

This paper explores many-body localization through a novel approach using random tensor networks, linking tensor fluctuations to localization phenomena via holographic principles and quantum channel analysis.

Contribution

It introduces a new perspective by interpreting matrix product states as particle systems and maps localization problems across different dimensions using holography.

Findings

Localization can be understood through spectral properties of quantum channels

Mapping between different spacetime dimensions provides new insights into MBL

Holographic principles connect tensor network fluctuations to localization phenomena

Abstract

We argue first that translational invariant Matrix Product can be interpreted as a stationary sea of particles. Next, rather than starting from some local Hamiltonian with random potentials, we consider fluctuations of the local tensors of a continuous one-parameter family of Matrix Product States. This leads to a mapping from 1+1+0 to 0+1+1, being time-space-$\lambda$. We argue that both pictures are equivalent. Finally, the holography principle and an operational argumentation is used to map the problem onto 1+0+1. Localization in 1-dimension, can be understood from a simple study spectral and mixing properties of finite dimensional quantum channels.