A DMRG study of the q-symmetric Heisenberg chain

TL;DR

This paper uses density-matrix renormalization to analyze the q-symmetric Heisenberg chain, calculating energies and correlations for different q values, revealing insights into related statistical models and diffusion processes.

Contribution

It provides the first detailed DMRG analysis of the q-symmetric Heisenberg chain, including non-hermitian and real q cases, linking to Ising, Potts, and diffusion models.

Findings

Calculated ground-state energies and correlation functions for non-hermitian q

Determined bulk and surface exponents for fermionic correlations

Analytical treatment of the real q case related to diffusion

Abstract

The spin one-half Heisenberg chain with $U_q[SU(2)]$ symmetry is studied via density-matrix renormalization. Ground-state energy and $q$-symmetric correlation functions are calculated for the non-hermitian case $q=\exp(i\pi/(r+1))$ with integer $r$. This gives bulk and surface exponents for (para)fermionic correlations in the related Ising and Potts models. The case of real $q$ corresponding to a diffusion problem is treated analytically.