Quantum Spin Pump in S=1/2 antiferromagnetic chains -Holonomy of phase operators in sine-Gordon theory-

TL;DR

This paper demonstrates a theoretical mechanism for quantum spin pumping in S=1/2 antiferromagnetic chains using sine-Gordon theory, showing how cyclic electromagnetic fields induce quantized spin transport via phase holonomy.

Contribution

It introduces a novel theoretical framework linking phase holonomy in sine-Gordon models to quantized spin pumping in antiferromagnetic chains.

Findings

Phase operator acquires 2π holonomy during cyclic fields.

Quantized spin current is transported through the bulk.

Relevance to real materials like Cu-benzoate and Yb4As3.

Abstract

In this paper, we propose the quantum spin pumping in quantum spin systems where an applied electric field ($E$) and magnetic field ($H$) cause a finite spin gap to its critical ground state. When these systems are subject to alternating electromangetic fields; $(E,H)=(\sin\frac{2\pi t}{T},\cos\frac{2\pi t}{T})$ and travel along the {\it{loop}} $\Gamma_{\rm{loop}}$ which encloses their critical ground state in this $E$-$H$ phase diagram, the locking potential in the sine-Gordon model slides and changes its minimum. As a result, the phase operator acquires $2\pi$ holonomy during one cycle along $\Gamma_{\rm{loop}}$, which means that the quantized spin current has been transported through the bulk systems during this adiabatic process. The relevance to real systems such as Cu-benzoate and ${\rm{Yb}}_4{\rm{As}}_3$ is also discussed.