Exact solution for the filling-induced thermalization transition in a one-dimensional fracton system
Calvin Pozderac, Steven Speck, Xiaozhou Feng, David A. Huse, Brian Skinner
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 $\ensuremath{\ell}$ contiguous sites, the critical density is given by ${n}_{c}=1/(\ensuremath{\ell}\ensuremath{-}2)$. We identify the critical scaling near the transition, and we show that there is a universal value of the correlation length exponent $\ensuremath{\nu}=2$. 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 ${z}_{c}\ensuremath{\gtrsim}6$.