Kinetically constrained freezing transition in a dipole-conserving system

Abstract

We study a stochastic lattice gas of particles in one dimension with strictly finite-range interactions that respect the fracton-like conservation laws of total charge and dipole moment. As the charge density is varied, the connectivity of the system's charge configurations under the dynamics changes qualitatively. We find two distinct phases: Near half filling the system thermalizes subdiffusively, with almost all configurations belonging to a single dynamically connected sector. As the charge density is tuned away from half filling there is a phase transition to a frozen phase where locally active finite bubbles cannot exchange particles and the system fails to thermalize. The two phases exemplify what has recently been referred to as weak and strong Hilbert space fragmentation, respectively. We study the static and dynamic scaling properties of this weak-to-strong fragmentation phase transition in a kinetically-constrained classical Markov circuit model, obtaining some conjectured exact critical exponents.

Hydrodynamics in lattice models with continuous non-Abelian symmetries

“…We first describe fluids with a conserved U(1) charge and dipole moment, whose hydrodynamics was recently formulated in [43]; see also [44][45][46][47]. An instructive cartoon is to start by supposing that there is a local conserved density ρ corresponding to charge, and s i corresponding to local dipole density orthogonal to x i ρ: namely, the total conserved dipole moment can be written as…”

Holographic subdiffusion

“…A significant challenge with studying the dynamics of a many-body system with constraints is that, essentially by definition, there is not an obvious quasiparticle description -after all, if individual excitations cannot move in space, the only possible way for dynamics to proceed is through the interactions of multiple excitations. Many of the systems which have been amenable to study in the past are models of random unitary circuits (with constraints), yet typically the models studied amount to classical Markov chains [22][23][24][25][26], which should be sufficiently generic to capture hydrodynamic phenomena, but may not capture quantum transport phenomena and the crossover away from hydrodynamics at shorter time and length scales.…”