We construct quasilocal conserved charges in the gapless ( |Δ|≤1 ) regime of the Heisenberg XXZ spin-1/2 chain, using semicyclic irreducible representations of Uq(sl2) . 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.

Slovenia

Lenart Zadnik

Marko Medenjak

Tomaž Prosen

Quasilocal conservation laws from semicyclic irreducible representations of Uq(sl2) in XXZ spin-1/2 chains

A continuous family of quasilocal exact conservation laws is constructed in the anisotropic Heisenberg ( XXZ ) spin-1/2 chain for periodic (or twisted) boundary conditions and for a set of commensurate anisotropies densely covering the entire easy plane interaction regime. All local conserved operators follow from the standard ( Hermitian ) transfer operator in fundamental representation (with auxiliary spin s=1/2 ), and are all even with respect to a spin flip operation. However, the quasilocal family is generated by differentiation of a non-Hermitian highest weight transfer operator with respect to a complex auxiliary spin representation parameter s and includes also operators of odd parity. For a finite chain with open boundaries the time derivatives of quasilocal operators are not strictly vanishing but result in operators localized near the boundaries of the chain. We show that a simple modification of the non-Hermitian transfer operator results in exactly conserved, but still quasilocal operators for periodic or generally twisted boundary conditions. As an application, we demonstrate that implementing the new exactly conserved operator family for estimating the high-temperature spin Drude weight results, in the thermodynamic limit, in exactly the same lower bound as for almost conserved family and open boundaries. Under the assumption that the bound is saturating (suggested by agreement with previous thermodynamic Bethe ansatz calculations) we propose a simple explicit construction of infinite time averages of local operators such as the spin current.

Quasilocal conservation laws in XXZ spin-1/2 chains: Open, periodic and twisted boundary conditions

We present an explicit construction of a family of steady state density matrices for an open integrable spin-1 chain with bilinear and biquadratic interactions, also known as the Lai–Sutherland model, driven far from equilibrium by means of two oppositely polarizing Markovian dissipation channels localized at the boundary. The steady state solution exhibits n+1 fold degeneracy, for a chain of length n , due to existence of (strong) Liouvillian U(1) symmetry. The latter can be exploited to introduce a chemical potential and define a grand canonical nonequilibrium steady state ensemble. The matrix product form of the solution entails an infinitely-dimensional representation of a non-trivial Lie algebra (semidirect product of sl2 and a non-nilpotent radical) and hints to a novel Yang–Baxter integrability structure.