Quantum Group Random Walks in Strongly Correlated $2+1$ $D$ Spin Systems

TL;DR

This paper explores the evolution of strongly correlated 2+1D spin systems using quantum-group diffusion equations, revealing polynomial solutions at roots of unity, which advances understanding of quantum symmetries in such systems.

Contribution

It introduces a novel approach to analyze 2+1D spin systems via quantum-group diffusion equations with polynomial solutions at roots of unity.

Findings

Quantum-group diffusion equations have polynomial solutions at roots of unity.

Eigenvalues of Wilson operators serve as key variables.

Provides new insights into quantum symmetries in correlated spin systems.

Abstract

We consider the temporal evolution of strong correlated degrees of freedom in $2+1$~$D$ spin systems using the Wilson operator eigenvalues as variables. It is shown that the quantum-group diffusion equation at deformation parameter $q$ being the $k$-th root of unity has the polynomial solution of degree $k$.