Chinese Physics Letters

Spin Transport Properties of the One-Dimensional Heisenberg Chain: Bethe-Ansatz Solution with Twist Boundary Conditions

Zhang Qiu-Lan, Shi-Jian Gu

Published May 1, 2007• 5 citations

Abstract

Based on the Bethe-Ansatz solution of the one-dimensional Heisenberg model under twist boundary conditions, we study the spectra of the persistent current carried by the low-lying excited states. It is shown that though the energy spectra of spin-singlet and spin-triplet excitations are degenerate, their persistent current spectra are quite different.

DOI: 10.1088/0256-307x/24/5/063

Related papers

Spin Transport Properties of the One-Dimensional Heisenberg Chain： Bethe-Ansatz Solution with Twist Boundary Conditions

张秋兰, 顾世建

基于一个维的海森堡 modelunder 扭曲边界条件的 Bethe-Ansatz 答案，我们学习带由的坚持的电流的系列 thelow 躺激动的状态。尽管纺纱汗衫 andspin 三位字节刺激的精力系列是退化的，他们的坚持的当前的系列是相当不同的，这被显示出。

Chinese Physics LettersJan 1, 20070 citations

Charge and spin transport in the one-dimensional Hubbard model

Shi-Jian Gu, Nuno M. R. Peres, J. M. P. Carmelo

arXiv:0710.4444Journal of Physics Condensed MatterNov 19, 200712 citations

Ground state and excitations of a spin chain with orbital degeneracy

You‐Quan Li, Michael Ma, Daning Shi +1 more

arXiv:cond-mat/9902269Physical review. B, Condensed matterNov 1, 199940 citations

Spin transport properties in Heisenberg antiferromagnetic spin chains: Spin current induced by twisted boundary magnetic fields

Wei Zhuo, Xiaoqun Wang, Yupeng Wang

arXiv:cond-mat/0501693Physical Review BJun 19, 20066 citations

Excitation Spectra of the Singlet Bound States in the Antiferromagnetic Spin 1/2 Chain

K. Hashimoto

Excited singlet spectra in the antiferromagnetic Heisenberg chain of spin 1/2 are obtained by solving Bethe's equations containing a pair of complex wave numbers. The lowest spectrum is found to become degenerate with that of the triplet states derived by des Cloizeaux and Pearson in the limit of infinite number of spins.

Progress of Theoretical PhysicsOct 1, 198213 citations

Introduction to the Bethe Ansatz II

Michael Karbach, Kun Hu, Gerhard Müller

arXiv:cond-mat/9809163Computers in PhysicsNov 1, 1998115 citations

Chinese Physics Letters

Spin Transport Properties of the One-Dimensional Heisenberg Chain: Bethe-Ansatz Solution with Twist Boundary Conditions

Zhang Qiu-Lan, Shi-Jian Gu

Published May 1, 2007• 5 citations

Publisher

Abstract

DOI: 10.1088/0256-307x/24/5/063

Related papers

Spin Transport Properties of the One-Dimensional Heisenberg Chain： Bethe-Ansatz Solution with Twist Boundary Conditions

张秋兰, 顾世建

Chinese Physics LettersJan 1, 20070 citations

Charge and spin transport in the one-dimensional Hubbard model

Shi-Jian Gu, Nuno M. R. Peres, J. M. P. Carmelo

In this paper we study the charge and spin currents transported by the elementary excitations of the one-dimensional Hubbard model. The corresponding current spectra are obtained by both analytic methods and numerical solution of the Bethe-ansatz equations. For the case of half-filling, we find that the spin-triplet excitations carry spin but no charge, while charge $η$ -spin triplet excitations carry charge but no spin, and both spin-singlet and charge $η$ -spin-singlet excitations carry neither spin nor charge currents.In this paper we study the charge and spin currents transported by the elementary excitations of the one-dimensional Hubbard model. The corresponding current spectra are obtained by both analytic methods and numerical solution of the Bethe-ansatz equations. For the case of half-filling, we find that the spin-triplet excitations carry spin but no charge, while charge $η$-spin triplet excitations carry charge but no spin, and both spin-singlet and charge $η$-spin-singlet excitations carry neither spin nor charge currents.

arXiv:0710.4444Journal of Physics Condensed MatterNov 19, 200712 citations

Ground state and excitations of a spin chain with orbital degeneracy

You‐Quan Li, Michael Ma, Daning Shi +1 more

The one-dimensional Heisenberg model in the presence of orbital degeneracy is studied at the $\mathrm{SU}(4)$ symmetric point by means of Bethe ansatz. Following Sutherland's previous work on an equivalent model, we discuss the ground state and the low-lying excitations more extensively in connection to the spin systems with orbital degeneracy. We show explicitly that the ground state is a $\mathrm{SU}(4)$ singlet. We study the degeneracies of the elementary excitations and the spectra of the generalized magnons consisting of these excitations. We also discuss the complex 2-strings in the context of the Bethe ansatz solutions.The one-dimensional Heisenberg model in the presence of orbital degeneracy is studied at the $\mathrm{SU}(4)$ symmetric point by means of Bethe ansatz. Following Sutherland's previous work on an equivalent model, we discuss the ground state and the low-lying excitations more extensively in connection to the spin systems with orbital degeneracy. We show explicitly that the ground state is a $\mathrm{SU}(4)$ singlet. We study the degeneracies of the elementary excitations and the spectra of the generalized magnons consisting of these excitations. We also discuss the complex 2-strings in the context of the Bethe ansatz solutions.

arXiv:cond-mat/9902269Physical review. B, Condensed matterNov 1, 199940 citations

Spin transport properties in Heisenberg antiferromagnetic spin chains: Spin current induced by twisted boundary magnetic fields

Wei Zhuo, Xiaoqun Wang, Yupeng Wang

Spin transport properties of the one-dimensional Heisenberg antiferromagnetic spin systems for both $S=1∕2$ and $S=1$ are studied by applying twisted boundary magnetic field. The spin current displays significantly different behavior of the spin transport properties between $S=1∕2$ and $S=1$ cases. For the spin-half case, a London equation for the current and the detection of an alternating electric field are proposed for the linear response regime. The correlation functions reveal the spiral nature of spin configuration for both ground state and the spinon excitations. For the spin-one chain otherwise, a kink generated in the ground state for the size is larger than the correlation length, leading to an exponential dependence of spin current with respect to the chains length. The midgap state emerges from the degenerate ground state even for small boundary fields.Spin transport properties of the one-dimensional Heisenberg antiferromagnetic spin systems for both $S=1∕2$ and $S=1$ are studied by applying twisted boundary magnetic field. The spin current displays significantly different behavior of the spin transport properties between $S=1∕2$ and $S=1$ cases. For the spin-half case, a London equation for the current and the detection of an alternating electric field are proposed for the linear response regime. The correlation functions reveal the spiral nature of spin configuration for both ground state and the spinon excitations. For the spin-one chain otherwise, a kink generated in the ground state for the size is larger than the correlation length, leading to an exponential dependence of spin current with respect to the chains length. The midgap state emerges from the degenerate ground state even for small boundary fields.

arXiv:cond-mat/0501693Physical Review BJun 19, 20066 citations

Excitation Spectra of the Singlet Bound States in the Antiferromagnetic Spin 1/2 Chain

K. Hashimoto

Progress of Theoretical PhysicsOct 1, 198213 citations

Introduction to the Bethe Ansatz II

Michael Karbach, Kun Hu, Gerhard Müller

Building on the fundamentals introduced in part I, we employ the Bethe ansatz to study some ground-state properties (energy, magnetization, susceptibility) of the one-dimensional s=1/2 Heisenberg antiferromagnet in zero and nonzero magnetic field. The 2-spinon triplet and singlet excitations from the zero-field ground state are discussed in detail, and their energies are calculated for finite and infinite chains. Procedures for the numerical calculation of real and complex solutions of the Bethe ansatz equations are discussed and applied. The paper is designed as a tutorial for beginning graduate students. It includes 10 problems for further study.Building on the fundamentals introduced in part I, we employ the Bethe ansatz to study some ground-state properties (energy, magnetization, susceptibility) of the one-dimensional s=1/2 Heisenberg antiferromagnet in zero and nonzero magnetic field. The 2-spinon triplet and singlet excitations from the zero-field ground state are discussed in detail, and their energies are calculated for finite and infinite chains. Procedures for the numerical calculation of real and complex solutions of the Bethe ansatz equations are discussed and applied. The paper is designed as a tutorial for beginning graduate students. It includes 10 problems for further study.

arXiv:cond-mat/9809163Computers in PhysicsNov 1, 1998115 citations

η

-spin triplet excitations carry charge but no spin, and both spin-singlet and charge

η

-spin-singlet excitations carry neither spin nor charge currents.

The one-dimensional Heisenberg model in the presence of orbital degeneracy is studied at the

\mathrm{SU}(4)

symmetric point by means of Bethe ansatz. Following Sutherland's previous work on an equivalent model, we discuss the ground state and the low-lying excitations more extensively in connection to the spin systems with orbital degeneracy. We show explicitly that the ground state is a

\mathrm{SU}(4)

singlet. We study the degeneracies of the elementary excitations and the spectra of the generalized magnons consisting of these excitations. We also discuss the complex 2-strings in the context of the Bethe ansatz solutions.

Spin transport properties of the one-dimensional Heisenberg antiferromagnetic spin systems for both

S=1∕2

and

S=1

are studied by applying twisted boundary magnetic field. The spin current displays significantly different behavior of the spin transport properties between

S=1∕2

and

S=1

cases. For the spin-half case, a London equation for the current and the detection of an alternating electric field are proposed for the linear response regime. The correlation functions reveal the spiral nature of spin configuration for both ground state and the spinon excitations. For the spin-one chain otherwise, a kink generated in the ground state for the size is larger than the correlation length, leading to an exponential dependence of spin current with respect to the chains length. The midgap state emerges from the degenerate ground state even for small boundary fields.