“Exact solution for the filling-induced thermalization transition in a 1D fracton system” by Brian S

arxiv.org/abs/...
Authors: Calvin Pozderac, Steven Speck, Xiaozhou Feng, David A. Huse, Brian Skinner
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 $
u = 2$. We confirm our theoretical results with numer