The spectrum and the phase transition of models solvable through the full interval method

TL;DR

This paper analyzes one-dimensional exclusion reaction-diffusion models solvable via the full interval method, revealing their spectral properties and phase transition behavior based on reaction rates.

Contribution

It introduces a generating function approach to solve for full interval probabilities and characterizes the spectral and phase transition properties of these models.

Findings

Identification of the spectrum of the Hamiltonian

Existence of dynamical phase transitions

Explicit stationary probabilities

Abstract

The most general exclusion single species reaction-diffusion models with nearest-neighbor interactions one a one dimensional lattice are investigated, for which the evolution of full intervals are closed. Using a generating function method, the probability that n consecutive sites be full is investigated. The stationary values of these probabilities, as well as the spectrum of the time translation generator (Hamiltonian) of these are obtained. It is shown that depending on the reaction rates the model could exhibit a dynamical phase transition.