Stochastic Model and Equivalent Ferromagnetic Spin Chain with Alternation

TL;DR

This paper explores a non-equilibrium reaction-diffusion model and its equivalent ferromagnetic spin chain with alternating couplings, analyzing their spectra and correlations using fermionization and distribution functions.

Contribution

It provides an exact analysis of the energy spectrum and correlations in a non-uniform spin chain, revealing translational invariance emergence over time.

Findings

Exact energy spectrum obtained

Translational invariance recovered at long times

Scaling relations for concentration and correlations

Abstract

We investigate a non-equilibrium reaction-diffusion model and equivalent ferromagnetic spin 1/2 XY spin chain with alternating coupling constant. The exact energy spectrum and the n-point hole correlations are considered with the help of the Jordan-Wigner fermionization and the inter-particle distribution function method. Although the Hamiltonian has no explicit translational symmetry, the translational invariance is recovered after long time due to the diffusion. We see the scaling relations for the concentration and the two-point function in finite size analysis.