Quantum Chains with U_q(SL(2)) Symmetry and Unrestricted Representations

TL;DR

This paper investigates quantum spin chains with U_q(SL(2)) symmetry, analyzing conditions for Hermitian Hamiltonians using various unrestricted representations, including periodic, semi-periodic, and nilpotent cases.

Contribution

It identifies necessary conditions for constructing Hermitian Hamiltonians in quantum chains with unrestricted U_q(SL(2)) representations, expanding understanding of their symmetry and representation types.

Findings

Hermitian Hamiltonian conditions depend on representation type

Unrestricted representations include periodic, semi-periodic, and nilpotent cases

Results guide the design of quantum chains with specific symmetry properties

Abstract

We consider two-state (q^2=-1) and three-state (q^3=1) one-dimensional quantum spin chains with U_q(SL(2)) symmetry. Taking unrestricted representations (periodic, semi-periodic and nilpotent), we show which are the necessary conditions to obtain a Hermitian Hamiltonian.