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arXiv:cond-mat/0312668 · Journal of the Physical Society of Japan

Quantum Spin Pump in S=1/2 Antiferromagnetic Chains –Holonomy of Phase Operators in sine-Gordon Theory–

Ryuichi Shindou

Published Apr 1, 2005• 46 citations

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.

DOI: 10.1143/jpsj.74.1214

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arXiv:1208.4914•Aug 24, 2012•4 citations

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.

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 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.

Abstract A spin-1/2 Heisenberg antiferromagnetic chain is one of the most important paradigmatic models in quantum magnetism. Its ground state is a spin singlet, while the excitation spectrum is formed by gapless fractional excitations, spinons. The presence of alternating g-tensors and/or the staggered Dzyaloshinskii-Moriya interaction results in opening the energy gap

\varDelta \propto H^{2/3}

Δ ∝ H 2 / 3 , once the magnetic field H is applied. A fairly good understanding of this phenomenon was achieved in the framework of the sine-Gordon quantum-field theory, taking into account the effective transverse staggered field induced by the applied uniform field. The theory predicts solitons and antisolitons as elementary excitations, as well as their bound states, breathers. Here, I review recent high-field electron spin resonance spectroscopy studies of such systems, focusing on peculiarities of their spin dynamics in the sine-Gordon regime and beyond.

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.

We study the spin transport on a S=1/2 antiferromagnetic chain with external fields which provids a phase angle. The equation of motion becomes the sine-Gordon equation after Jordan-Wigner transformation and bosonization. Soliton solutions of the sine-Gordon equations for a system of finite length are found and the quantum fluctuations are calculated. The spin is transported as the soliton solutions evolves with the adiabatical variation of the phase angle in the phase space. We observe that the spin is transported by ΔS=1, as the phase angle changes by the period of 2π when the quantum fluctuation enables the system makes transition between two solutions. This quantum spin transport is not affected by disturbance of environment.