Classical and quantum facilitated exclusion processes

TL;DR

This paper explores the parallels between classical and quantum facilitated exclusion processes, revealing phase transitions, entanglement dynamics, and non-equilibrium behaviors that unify these two areas of many-body physics.

Contribution

It introduces a quantum analogue of classical facilitated exclusion processes, demonstrating phase transitions and entanglement phenomena that connect classical and quantum non-equilibrium systems.

Findings

Quantum system exhibits an absorbing transition with entanglement development.

A special density $ ho^*=1/3$ separates different steady-state regimes.

Non-monotonic entanglement features observed in the quantum model.

Abstract

We demonstrate exciting similarities between classical and quantum many body systems whose microscopic dynamics are composed of non-reciprocal three-site facilitated exclusion processes. We show that the quantum analogue of the classical facilitated process engineers an interesting $quantum$ $absorbing$ $transition$ where the quantum particles transit from an unentangled direct-product absorbing phase to an entangled steady state with a finite current at density $\rho=1/2$. In the generalised classical facilitated exclusion process, which includes independent hopping of particles with rate $p$, our analytical and Monte-Carlo results establish emergence of a special density $\rho^*=1/3$ that demarcates two regimes in the steady state, based on the competition between two current carrying modes (facilitated and independent). The corresponding quantum system also displays similar qualitative behaviours with striking non-monotonic features in the bipartite entanglement. Our work ties the two sub-fields of classically interacting exclusion processes, and interacting non-Hermitian quantum Hamiltonians to show common themes in the non-equilibrium phases they realise.