Calvin Pozderac, The Ohio State University

Exact solution for the thermalization transition in a model fracton system

In fracton systems, the dynamics is constrained by higher-order conservation laws, such as the conservation of both charge and dipole moment. In certain situations, these constraints prevent the system from thermalizing by causing a “fragmentation” of the Hilbert space into many dynamically disconnected sectors. In this work we consider a simple one-dimensional lattice of charges that evolve under the influence of random local operators that conserve both charge and dipole moment. This system exhibits a thermalization transition as a function of the total charge, such that only systems with sufficiently large charge density are able to thermalize. We construct an exact solution for this transition by mapping the dynamics to two different problems in combinatorics. Our solution allows us to identify the critical charge density as a function of the gate size, as well as the critical scaling and certain critical exponents.