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arXiv:0803.2951 · Physical Review B

Quantum spin pumping at a fractionally quantized magnetization state for a system with competing exchange interactions

Sujit Sarkar, Chong Der Hu

Published Feb 12, 2008• 4 citations
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Abstract

We study the quantum spin pumping of an antiferromagnetic spin-$1∕2$ chain with competing exchange interactions. We show that spatially periodic potential modulated in space and time acts as a quantum spin pump. In our model system, an applied electric field causes a spin gap to its critical ground state by introducing bond-alternation exchange interactions. We study quantum spin pumping at different quantized magnetization states and also explain physically the presence and absence of quantum spin pumping at different fractionally quantized magnetization states.

DOI
10.1103/physrevb.77.064413

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In this paper, we propose the quantum spin pumping in quantum spin systems where an applied electric field (EEE) and magnetic field (HHH) cause a finite spin gap to its critical ground state. When these systems are subject to alternating electromangetic fields; (E,H)=(sin⁡2πtT,cos⁡2πtT)(E,H)=(\sin\frac{2πt}{T},\cos\frac{2πt}{T})(E,H)=(sinT2πt​,cosT2πt​) and travel along the {\it{loop}} ΓloopΓ_{\rm{loop}}Γloop​ which encloses their critical ground state in this EEE-HHH phase diagram, the locking potential in the sine-Gordon model slides and changes its minimum. As a result, the phase operator acquires 2π2π2π holonomy during one cycle along ΓloopΓ_{\rm{loop}}Γloop​, 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{\rm{Yb}}_4{\rm{As}}_3Yb4​As3​ is also discussed.
We studied the possibility of the spin pump in a S=1/2 antiferromagnetic chain. The spin chain is mapped into a fermion system and bosonization is utilized to transform the equation of motion to a sine-Gordon equation. The sine-Gordon equation on a finite chain with different boundary conditions is solved. Among numerous solutions, the static soliton is compatible with the original physical system. By varying adiabatically a angle in the phase space composed of applied electric and magnetic fields, the spin states change between the Neel state and dimer state and a quantized spin is transported by the bulk state from one end of the system to the other.
We study a system with spin-Peierls dimerization in next-nearest-neighbor (NNN) interaction and also the presence of nearest-neighbor (NN) interaction under a magnetic field. We predict the existence of different fractionally quantized magnetization plateaus with many interesting physical properties. The effect of the frustrating NNN interaction and the role of quantum fluctuations are also explored for different magnetization plateaus. We explain more physically the gapless state of spin spectrum for small values of the frustrating NNN interaction. The transition from commensurate gapped phase to incommensurate Luttinger liquid phase is of Mott-δ type.
We propose an exactly solvable quantum spin model, in which the alternation of the exchange interactions between neighboring spins is accompanied by the multiple spin exchange. The model permits us to obtain exactly thermodynamic characteristics of the considered quantum spin chain. In the ground state, depending on the strength of the three-spin coupling, the model manifests either the spin-gapped behavior of low-lying excitations at low magnetic fields, or the ferrimagnetic ordering with the spontaneous magnetization and with gapless low-lying excitations. The system undergoes second order or first order quantum phase transitions, governed by an external magnetic field and the multiple spin exchange coupling strength. Our exactly solvable quantum spin model demonstrates that multispin interactions in a dimerized quantum spin chain can produce a spontaneous magnetization. On the other hand, for quantum spin chains with a spontaneous magnetization, caused by multispin couplings, the alternation of nearest neighbor exchange interactions can be the reason for destroying of that magnetization and the onset of a spin gap for low-lying excitations.
We studied the possibility of the spin pump in an S =1/2 antiferromagnetic chain. The spin chain is mapped into a fermion system and bosonization is utilized to transform the equation of motion to a sine-Gordon equation. The solutions of the sine-Gordon equation on a finite chain with different boundary conditions are analyzed. Among numerous solutions, the static soliton is compatible with the original physical system. By varying adiabatically an angle φ in the phase space composed of applied electric and magnetic fields, the spin states change between the Néel state and dimer state and a quantized spin S =1 is transported by the bulk state from one end of the system to the other.