Absorbing state transitions with long-range annihilation

TL;DR

This paper introduces a family of classical stochastic models with long-range annihilation, analyzing their phase transitions and universality classes, relevant for classical and quantum systems with non-local interactions.

Contribution

It develops a comprehensive analysis of long-range annihilation processes, revealing a continuum of universality classes connecting directed-percolation and parity-conserving types.

Findings

Identification of a line of universality classes with continuously varying critical exponents.

Analytical and numerical characterization of absorbing phase transitions.

Connection of classical long-range processes to quantum dynamics and error correction.

Abstract

We introduce a family of classical stochastic processes describing diffusive particles undergoing branching and long-range annihilation in the presence of a parity constraint. The probability for a pair-annihilation event decays as a power-law in the distance between particles, with a tunable exponent. Such long-range processes arise naturally in various classical settings, such as chemical reactions involving reagents with long-range electromagnetic interactions. They also increasingly play a role in the study of quantum dynamics, in which certain quantum protocols can be mapped to classical stochastic processes with long-range interactions: for example, state preparation or error correction processes aim to prepare ordered ground states, which requires removing point-like excitations in pairs via non-local feedback operations conditioned on a global set of measurement outcomes. We analytically and numerically describe features of absorbing phases and phase transitions in this family of classical models as pairwise annihilation is performed at larger and larger distances. Notably, we find that the two canonical absorbing-state universality classes -- directed-percolation and parity-conserving -- are endpoints of a line of universality classes with continuously interpolating critical exponents.