Quantum hydrodynamics of spin winding

TL;DR

This paper develops a hydrodynamic theory for quantum spin chain winding transport, incorporating phase slips and damping, and proposes a device to measure winding conductivity as a key property of quantum magnets.

Contribution

It introduces a hydrodynamic framework for quantum spin winding, including phase slips and vorticity effects, and proposes a device to measure winding conductivity.

Findings

Winding transport can be described by a modified continuity equation with source terms.

A linear-response formalism relates winding flow to vorticity flow via Kubo response.

Winding conductivity is proposed as a measurable property characterizing quantum magnet dynamics.

Abstract

An easy-plane spin winding in a quantum spin chain can be treated as a transport quantity, which propagates along the chain but has a finite lifetime due to phase slips. In a hydrodynamic formulation for the winding dynamics, the quantum continuity equation acquires a source term due to the transverse vorticity flow. The latter reflects the phase slips and generally compromises the global conservation law. A linear-response formalism for the nonlocal winding transport then reduces to a Kubo response for the winding flow along the spin chain, in conjunction with the parasitic vorticity flow transverse to it. One-dimensional topological hydrodynamics can be recovered when the vorticity flow is asymptotically small. Starting with a microscopic spin-chain formulation, we focus on the asymptotic behavior of the winding transport based on the renormalized sine-Gordon equation, incorporating phase slips as well as Gilbert damping. A generic electrical device is proposed to manifest this physics. We thus suggest winding conductivity as a tangible concept that can characterize low-energy dynamics in a broad class of quantum magnets.