On U_q(SU(2))-symmetric Driven Diffusion

TL;DR

This paper analytically investigates a U_q(SU(2))-symmetric driven diffusion model, deriving exact correlation functions and analyzing the system's density and correlation dynamics influenced by asymmetry.

Contribution

It provides exact expressions for correlation functions in a U_q(SU(2))-symmetric driven diffusion model, linking dynamics to energy gaps and asymmetry effects.

Findings

Correlation length and time depend on asymmetry for large systems.

For small asymmetry, correlation time scales quadratically with correlation length.

Dynamical exponent z=2 for symmetric diffusion.

Abstract

We study analytically a model where particles with a hard-core repulsion diffuse on a finite one-dimensional lattice with space-dependent, asymmetric hopping rates. The system dynamics are given by the \mbox{U$_{q}$[SU(2)]}-symmetric Hamiltonian of a generalized anisotropic Heisenberg antiferromagnet. Exploiting this symmetry we derive exact expressions for various correlation functions. We discuss the density profile and the two-point function and compute the correlation length $\xi_s$ as well as the correlation time $\xi_t$. The dynamics of the density and the correlations are shown to be governed by the energy gaps of a one-particle system. For large systems $\xi_s$ and $\xi_t$ depend only on the asymmetry. For small asymmetry one finds $\xi_t \sim \xi_s^2$ indicating a dynamical exponent $z=2$ as for symmetric diffusion.