Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Progress of Theoretical Physics

One-Dimensional Heisenberg Model. I: Exact Spin Eigenstates

T. Kebukawa

Published Jul 1, 1985• 1 citation
Publisher

Abstract

In a system of N spins ordered on a linear chain, an eigenvalue problem for the square and z-component of a total spin operator is solved exactly by using the Bethe ansatz. It is shown that the eigenstates are given by the solutions of coupled equations. For a given eigenvalue of the square of the total spin, the eigenstates for various eigenvalues of the z-component are expressed in a systematic and compact form.

DOI
10.1143/ptp.74.1

Related papers

One-Dimensional Heisenberg Model. I: Exact Spin Eigenstates

T. Kebukawa

Dans un systeme de N spins ordonnes dans une chaine lineaire, on resout exactement un probleme aux valeurs propres pour le carre et la composante Z d'un operateur de spin total a l'aide de l'hypothese de Bethe. On montre que les etats propres sont donnes par les solutions d'equations couplees. Pour une valeur propre donnee du carre du spin total, on exprime les etats propres pour diverses valeurs propres de la composante Z dans une forme systematique et compacte

Progress of Theoretical Physics•Mar 1, 1986•0 citations

One-Dimensional Many-Fermion System. I: Exact Solution in a Field Theoretical Framework

T. Kebukawa

The eigenvalue problem in a one-dimensional system of many fermions interacting via a delta-function potential is solved exactly in a field theoretical framework. Simultaneous eigenstates of spin and energy are represented in a systematic and compact form, that is, in such a form that the orbital and spin eigenfunctions are unified in harmony without the aid of Young’s tableau. The eigenstate and energy eigenvalue are specified by two sets of quantum numbers, particle momenta and spin momenta, besides two eigenvalues of a total spin angular momentum and its z-component. It is shown that for given particle momenta and spin momenta the energy eigenvalue is given by the solutions of coupled equations.

Progress of Theoretical Physics•May 1, 1985•3 citations

One-Dimensional Many-Fermion System. II: Spin Eigenstates and Their Structure

T. Kebukawa

For a given eigenvalue of the square of the total spin operator, the spin eigenvectors with various eigenvalues of the z-component are obtained systematically by successive operations of the spin lowering operator on the eigenvector proposed in a previous paper for a one-dimensional many-fermion system with delta-function potential. The property of the spin eigenvector under the operation of the spin raising operator is investigated to clarify the mechanism how it has the given eigenvalue of the square of the total spin operator. It is shown that the spin eigenvector can be modified in various forms under some condition presented in the previous paper.

Progress of Theoretical Physics•Mar 1, 1986•3 citations

Elementary Bethe Ansatz solution of two lattice spin models

Paul Bracken

A simple detailed derivation is given of the Bethe Ansatz solution and the raising operator condition on the amplitudes of the wave function that demands that this state be a highest weight state for the one-dimensional Heisenberg model. This is extended to the case of a single spin impurity on the lattice. The equivalent form of the Ansatz is derived, and several properties of the associated eigenvalue problem are developed. R´ esum´

Canadian Journal of Physics•Jan 1, 1997•0 citations

Some results of exact solutions for the two-spin-flip number problem of the spin-1 Heisenberg chain

Yangdong Zheng

The eigenvalues and eigenvectors of the spin-1 Heisenberg chain are not exactly soluble by using of the Bethe Ansatz method. As an attempt, we propose a new format of the basic states and derive the exact solutions for the two-spin-flip number problem of the spin-1 Heisenberg chain. We discuss qualitatively some basic features of the above model for different types of wave number values.

Journal of Physics Conference Series•Jul 1, 2018•0 citations

New exact integrable spin-1 quantum chains

Francisco Castilho Alcaraz, R. Z. Bariev

New exactly integrable quantum spin-1 chains are derived. These new quantum Hamiltonians, like the XXZ chain, have a free parameter (anisotropy) and commute with the z -component of the total magnetization. The eigenvalues and eigenvectors are obtained directly by imposing a generalized coordinate Bethe ansatz. The derived Bethe ansatz equations have an unusual form and the associated R -matrix, has a dependence with the spectral parameter that is not of difference form, like the Hubbard quantum chain.

Journal of Physics A Mathematical and General•Aug 10, 2001•9 citations
In a system of N spins ordered on a linear chain, an eigenvalue problem for the square and z-component of a total spin operator is solved exactly by using the Bethe ansatz. It is shown that the eigenstates are given by the solutions of coupled equations. For a given eigenvalue of the square of the total spin, the eigenstates for various eigenvalues of the z-component are expressed in a systematic and compact form.
The eigenvalue problem in a one-dimensional system of many fermions interacting via a delta-function potential is solved exactly in a field theoretical framework. Simultaneous eigenstates of spin and energy are represented in a systematic and compact form, that is, in such a form that the orbital and spin eigenfunctions are unified in harmony without the aid of Young’s tableau. The eigenstate and energy eigenvalue are specified by two sets of quantum numbers, particle momenta and spin momenta, besides two eigenvalues of a total spin angular momentum and its z-component. It is shown that for given particle momenta and spin momenta the energy eigenvalue is given by the solutions of coupled equations.
For a given eigenvalue of the square of the total spin operator, the spin eigenvectors with various eigenvalues of the z-component are obtained systematically by successive operations of the spin lowering operator on the eigenvector proposed in a previous paper for a one-dimensional many-fermion system with delta-function potential. The property of the spin eigenvector under the operation of the spin raising operator is investigated to clarify the mechanism how it has the given eigenvalue of the square of the total spin operator. It is shown that the spin eigenvector can be modified in various forms under some condition presented in the previous paper.
New exactly integrable quantum spin-1 chains are derived. These new quantum Hamiltonians, like the XXZ chain, have a free parameter (anisotropy) and commute with the z -component of the total magnetization. The eigenvalues and eigenvectors are obtained directly by imposing a generalized coordinate Bethe ansatz. The derived Bethe ansatz equations have an unusual form and the associated R -matrix, has a dependence with the spectral parameter that is not of difference form, like the Hubbard quantum chain.