# Beyond many-body localized states in a spin-disordered Hubbard model with pseudo-spin symmetry

## TL;DR

This paper investigates a spin-disordered Hubbard model revealing a coexistence of area-law and log-law entangled eigenstates, indicating a phase that is neither fully ergodic nor many-body localized, through analytic and numerical methods.

## Contribution

It introduces a microscopic Hamiltonian exhibiting both area-law and log-law eigenstates, expanding understanding of non-ergodic, non-MBL phases.

## Key findings

- Presence of both area-law and log-law eigenstates in the model
- Analytic and numerical methods confirm the coexistence of different entanglement scaling
- Dynamic simulations can distinguish between eigenstate types

## Abstract

A prime characterization of many-body localized (MBL) systems is the entanglement of their eigenstates; in contrast to the typical ergodic phase whose eigenstates are volume law, MBL eigenstates obey an area law. In this work, we show that a spin-disordered Hubbard model has both a large number of area-law eigenstates as well as a large number of eigenstates whose entanglement scales logarithmically with system size (log-law). This model, then, is a microscopic Hamiltonian which is neither ergodic nor many-body localized. We establish these results through a combination of analytic arguments based on the eta-pairing operators combined with a numerical analysis of eigenstates. In addition, we describe and simulate a dynamic time evolution approach starting from product states through which one can separately probe the area law and log-law eigenstates in this system.