Exact solution for the filling-induced thermalization transition in a 1D fracton system

TL;DR

This paper provides an exact solution for the critical density in a 1D fracton system with charge and dipole conservation, revealing a phase transition with universal critical behavior and subdiffusive dynamics.

Contribution

It derives an exact critical density for the phase transition in a constrained fracton model and characterizes the universal critical scaling and dynamical exponents.

Findings

Exact critical density $n_c = 1/( extell - 2)$ for the phase transition.

Universal correlation length exponent $ u=2$.

Subdiffusive dynamics with $z=4$ in the thermal phase and $z_c extgreater 6$ at criticality.

Abstract

We study a random circuit model of constrained fracton dynamics, in which particles on a one-dimensional lattice undergo random local motion subject to both charge and dipole moment conservation. The configuration space of this system exhibits a continuous phase transition between a weakly fragmented ("thermalizing") phase and a strongly fragmented ("nonthermalizing") phase as a function of the number density of particles. Here, by mapping to two different problems in combinatorics, we identify an exact solution for the critical density $n_c$. Specifically, when evolution proceeds by operators that act on $\ell$ contiguous sites, the critical density is given by $n_c = 1/(\ell -2)$. We identify the critical scaling near the transition, and we show that there is a universal value of the correlation length exponent $\nu = 2$. We confirm our theoretical results with numeric simulations. In the thermalizing phase the dynamical exponent is subdiffusive: $z=4$, while at the critical point it increases to $z_c \gtrsim 6$.