# Abelian Tensor Models on the Lattice

## TL;DR

This paper studies a chain of Abelian fermionic tensor models with nearest-neighbor interactions, analyzing their spectrum for small chains and providing evidence of quasi-many body localization through spectral statistics.

## Contribution

It introduces Abelian tensor models on a lattice and characterizes their gauge-singlet spectrum, revealing localization phenomena not previously explored in such models.

## Key findings

- Spectral statistics suggest quasi-many body localization.
- Spectrum characterized for small chain lengths (L=2,3,4,5).
- Evidence of localization phenomena in Abelian tensor models.

## Abstract

We consider a chain of Abelian Klebanov-Tarnopolsky fermionic tensor models coupled through quartic nearest-neighbor interactions. We characterize the gauge-singlet spectrum for small chains ($L=2,3,4,5$) and observe that the spectral statistics exhibits strong evidences in favor of quasi-many body localization.