Quasilocal conservation laws from semicyclic irreducible representations of $U_q(\mathfrak{sl}_2)$ in $XXZ$ spin-$1/2$ chains

TL;DR

This paper constructs new quasilocal conserved charges for the gapless Heisenberg XXZ spin-1/2 chain using semicyclic representations of quantum algebra, which break magnetization symmetry and could impact relaxation dynamics.

Contribution

It introduces a novel method to generate quasilocal conserved charges that break $U(1)$ symmetry using semicyclic irreducible representations of $U_q(rak{sl}_2)$ in the XXZ model.

Findings

Constructed quasilocal conserved charges that do not preserve magnetization.

Demonstrated application potential in $U(1)$-breaking quantum quenches.

Extended the algebraic framework for integrability in spin chains.

Abstract

We construct quasilocal conserved charges in the gapless ($|\Delta| \le 1$) regime of the Heisenberg $XXZ$ spin-$1/2$ chain, using semicyclic irreducible representations of $U_q(\mathfrak{sl}_2)$. These representations are characterized by a periodic action of ladder operators, which act as generators of the aforementioned algebra. Unlike previously constructed conserved charges, the new ones do not preserve magnetization, i.e. they do not possess the $U(1)$ symmetry of the Hamiltonian. The possibility of application in relaxation dynamics resulting from $U(1)$-breaking quantum quenches is discussed.