# Ergodic and localized regions in quantum spin glasses on the Bethe lattice

## TL;DR

This paper investigates the quantum dynamics of a transverse field Ising spin glass on the Bethe lattice, identifying a many-body localized phase at low transverse fields within the spin glass region, with implications for quantum algorithms.

## Contribution

It reveals the existence of a many-body localized phase within the spin glass phase on the Bethe lattice and discusses its impact on quantum adiabatic algorithms.

## Key findings

- Existence of a many-body localized region at low transverse fields.
- Quantum dynamics split into localized and delocalized regions within the spin glass phase.
- Implications for the performance of quantum adiabatic algorithms.

## Abstract

By considering the quantum dynamics of a transverse field Ising spin glass on the Bethe lattice we find the existence of a many body localized region at small transverse field and low temperature. The region is located within the thermodynamic spin glass phase. Accordingly, we conjecture that quantum dynamics inside the glassy region is split in a small MBL and a large delocalized (but not necessarily ergodic) region. This has implications for the analysis of the performance of quantum adiabatic algorithms.