Quasilocal charges in integrable lattice systems

TL;DR

This paper reviews recent advances in understanding quasilocal conserved quantities in integrable quantum lattice systems, highlighting their construction, classification, and implications for transport and non-thermal states.

Contribution

It introduces systematic methods to construct and classify quasilocal conserved operators in the XXZ spin chain, emphasizing their physical significance.

Findings

Quasilocal conserved charges are crucial for anomalous transport.

Construction methods based on quantum transfer matrices are detailed.

Quasilocal charges influence relaxation and steady states in quantum quenches.

Abstract

We review recent progress in understanding the notion of locality in integrable quantum lattice systems. The central concept are the so-called quasilocal conserved quantities, which go beyond the standard perception of locality. Two systematic procedures to rigorously construct families of quasilocal conserved operators based on quantum transfer matrices are outlined, specializing on anisotropic Heisenberg XXZ spin-1/2 chain. Quasilocal conserved operators stem from two distinct classes of representations of the auxiliary space algebra, comprised of unitary (compact) representations, which can be naturally linked to the fusion algebra and quasiparticle content of the model, and non-unitary (non-compact) representations giving rise to charges, manifestly orthogonal to the unitary ones. Various condensed matter applications in which quasilocal conservation laws play an essential role are presented, with special emphasis on their implications for anomalous transport properties (finite Drude weight) and relaxation to non-thermal steady states in the quantum quench scenario.