# Glassy quantum dynamics in translation invariant fracton models

## TL;DR

This paper reveals that translation invariant fracton models exhibit glassy quantum dynamics, including suppressed charge mobility and logarithmic relaxation, resembling disordered systems but without quenched disorder.

## Contribution

It demonstrates that fracton models inherently display glassy dynamics and subdiffusive behavior, expanding understanding of quantum relaxation in disorder-free systems.

## Key findings

- Charge mobility is exponentially suppressed at low temperatures.
- Relaxation to equilibrium follows a logarithmic time dependence.
- Type II fracton models show super-exponential divergence of relaxation times.

## Abstract

We investigate relaxation in the recently discovered "fracton" models and discover that these models naturally host glassy quantum dynamics in the absence of quenched disorder. We begin with a discussion of "type I" fracton models, in the taxonomy of Vijay, Haah, and Fu. We demonstrate that in these systems, the mobility of charges is suppressed exponentially in the inverse temperature. We further demonstrate that when a zero temperature type I fracton model is placed in contact with a finite temperature heat bath, the approach to equilibrium is a logarithmic function of time over an exponentially wide window of time scales. Generalizing to the more complex "type II" fracton models, we find that the charges exhibit subdiffusion upto a relaxation time that diverges at low temperatures as a super-exponential function of inverse temperature. This behaviour is reminiscent of "nearly localized" disordered systems, but occurs with a translation invariant three-dimensional Hamiltonian. We also conjecture that fracton models with conserved charge may support a phase which is a thermal metal but a charge insulator.