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

References in corpus (8)

• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Complete Generalized Gibbs Ensemble in an interacting Theory
• Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble Predictions
• Correlations after quantum quenches in the XXZ spin chain: Failure of the Generalized Gibbs Ensemble
• Thermal conductivity via magnetic excitations in spin-chain materials
• Quasilocal conservation laws in XXZ spin-1/2 chains: open, periodic and twisted boundary conditions
• Breakdown of the generalized Gibbs ensemble for current-generating quenches
• Exact solutions of open integrable quantum spin chains

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