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

Ryuichi Shindou
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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; $(E,H)=(\sin\frac{2πt}{T},\cos\frac{2πt}{T})$ and travel along the {\it{loop}} $Γ_{\rm{loop}}$ 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 $2π$ holonomy during one cycle along $Γ_{\rm{loop}}$, 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.

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Ryuichi Shindou. 2005-01-28. Quantum Spin Pump in S=1/2 antiferromagnetic chains -Holonomy of phase operators in sine-Gordon theory-. https://doi.org/10.1143/jpsj.74.1214

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