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

TL;DR

This paper constructs a family of quasilocal conservation laws in the XXZ spin-1/2 chain for various boundary conditions, revealing new operators that help estimate transport properties like the spin Drude weight.

Contribution

It introduces a novel method to generate exactly conserved quasilocal operators using a non-Hermitian transfer operator differentiation, applicable to different boundary conditions.

Findings

Constructed quasilocal conservation laws for periodic and twisted boundaries.

Demonstrated the operators' role in estimating the spin Drude weight.

Proposed explicit construction of infinite time averages of local operators.

Abstract

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.