Quantum spin pump in S=1/2 antiferromagnetic chains -: Holonomy of phase operators in sine-Gordon theory

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 2 pi t/T, cos 2 pi t/T) and travel along the loop Gamma(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(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 Yb4As3 is also discussed.