# Dynamical scar states in driven fracton systems

## TL;DR

This paper uncovers dynamical scar states in driven one-dimensional fracton systems, showing how certain initial states avoid thermalization due to fracton conservation laws, with implications for nonergodic quantum dynamics.

## Contribution

It demonstrates the existence of dynamical scar states in a driven fracton system, linking scars to conservation laws and providing a mechanism for nonthermal behavior in Floquet systems.

## Key findings

- Most states thermalize to infinite temperature
- A small subset of states remains localized as scars
- Scar states are robust and related to fracton conservation laws

## Abstract

One-dimensional fracton systems can exhibit perfect localization, failing to reach thermal equilibrium under arbitrary local unitary time evolution. We investigate how this nonergodic behavior manifests in the dynamics of a driven fracton system, specifically a one-dimensional Floquet quantum circuit model featuring conservation of a U(1) charge and its dipole moment. For a typical basis of initial conditions, a majority of states heat up to a thermal state at near-infinite temperature. In contrast, a small number of states flow to a localized steady state under the Floquet time evolution. We refer to these athermal steady states as ``dynamical scars," in analogy with the scar states observed in the spectra of certain many-body Hamiltonians. Despite their small number, these dynamical scars are experimentally relevant due to their high overlap with easily-prepared product states. Each scar state displays a single agglomerated fracton peak, in agreement with the steady-state configurations of fractonic random circuits. The details of these scars are insensitive to the precise form of the Floquet operator, which is constructed from random unitary matrices. Rather, dynamical scar states arise directly from fracton conservation laws, providing a concrete mechanism for the appearance of scars in systems with constrained quantum dynamics.