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

• URL: http://arxiv.org/abs/2210.02469v1
• Date: Wed, 5 Oct 2022 18:00:02 GMT
• Title: Exact solution for the filling-induced thermalization transition in a 1D fracton system
• Authors: Calvin Pozderac, Steven Speck, Xiaozhou Feng, David A. Huse, and Brian Skinner
• Abstract summary: We study a random circuit model of constrained fracton dynamics in which particles undergo random local motion. We identify an exact solution for the critical density $n_c$. We show that there is a universal value of the correlation length exponent $nu = 2$ near the transition.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $z_c \gtrsim 6$.

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