© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

International Journal of Modern Physics C

PERMUTATION GROUP APPROACH TO THE ONE-DIMENSIONAL XXX HEISENBERG OPEN SPIN-1/2 CHAINS

Feng Pan, L. R. Dai, Dan Zhang, Jerry Paul Draayer

Published Feb 1, 2004• 0 citations

Abstract

Permutation group approach to the one-dimensional XXX Heisenberg open spin-1/2 chain with nearest neighbor interaction is proposed, which is formulated not only for half-filling excitations, but also for general case. Regularity of energy matrices and the corresponding wavefunctions are made up by using an induction method, which makes it possible to study the eigenvalue problem systematically. A Mathematica package for generating the energy matrices is implemented according to this procedure.

DOI: 10.1142/s0129183104005668

Related papers

Regular Fractal Structure of the Energy Matrix in One-dimensional Heisenberg Open Spin-1/2 Chains

Feng Pan

A permutation group approach to a one dimensional Heisenberg open spin 12 chain with nearest neighbor interactions is studied.Regular fractal structures appear in matrices of the Hamiltonian constructed under the outer product basis of the permutation group, which enables one to solve the eigenvalue problem in a systematic manner.

Journal of Liaoning Normal University•Jan 1, 2002•0 citations

Regular fractal structure of the energy matrix in ID Heisenberg open spin- 1 2 chains

Feng Pan, J. P. Draayer, L -R Dai +1 more

A permutation group approach to a one-dimensional Heisenberg open spin-j chain with nearest neighbor interactions is studied. Regular fractal structures appear in matrices of the Hamiltonian constructed under the outer-product basis of the permutation group, which enables one to solve the eigenvalue problem in a systematic manner.

CRC Press eBooks•Nov 30, 2003•0 citations

Integrable Multi-impurity Open XXZ Chain with Next-Nearest-Neighbor Interaction

Lai Yun-zhong, Ai-zhen Zhang, Zhan-Ning Hu +2 more

The Hamiltonian of one-dimensional integrable multi-impurity XXZ spin chain with open boundary cases is constructed by using the method of adding parameters to the vertical matrices. This is the first approach to add multi-impurity and next-nearest-neighbor interaction to the integrable anisotropic Heisenberg spin chain. It is found that all of the impurity parameters in the bulk must be pure imaginary numbers if the cross parameter is real for getting the hermitian Hamiltonian, or vice versa, when the next-nearest-neighbor interactions are introduced. The Hamiltonian can be also applied to describe the many body systems with two kinds of particles if all of the impurity parameters are equal.

Chinese Physics Letters•Jun 1, 1999•0 citations

A NEW METHOD TO SOLVE THE S = l/2 HEISENBERG SPIN CHAIN

Nian Lin, Zurong Yu, 同济大学物理系,上海200092

We present a new approach which is completely based on the permutation group theory to solve the eigenvalue problem of the S = 1/2 Heisenberg finite-chain with free-ends boundary. All of the eigenvalues and the corresponding eigenstates are obtained. The properties of the ground state and the low-lying excited states of the antiferromagnetic chain are examined.

Acta Physica Sinica•Jan 1, 1993•2 citations

Spin chain under next nearest neighbor interaction

L. C. Kwek, Y Takahashi, Keng Wah Choo

We perform a numerical study on the concurrence of the ground state Heisenberg XXX with next-nearest-neighbor interaction with open and periodic boundary condition.

Journal of Physics Conference Series•Jan 7, 2009•16 citations

A NEW METHOD TO SOLVE THE S = l/2 HEISENBERG SPIN CHAIN

Ian Yu

We present a new approach which is completely based on the permutation group theory to solve the eigenvalue problem of the S = 1/2 Heisenberg finite-chain with free-ends boundary. All of the eigenvalues and the corresponding eigenstates are obtained. The properties of the ground state and the low-lying excited states of the antiferromagnetic chain are examined.

Acta Physica Sinica•Jan 1, 1993•0 citations

Permutation group approach to the one-dimensional XXX Heisenberg open spin-1/2 chain with nearest neighbor interaction is proposed, which is formulated not only for half-filling excitations, but also for general case. Regularity of energy matrices and the corresponding wavefunctions are made up by using an induction method, which makes it possible to study the eigenvalue problem systematically. A Mathematica package for generating the energy matrices is implemented according to this procedure.

The Hamiltonian of one-dimensional integrable multi-impurity XXZ spin chain with open boundary cases is constructed by using the method of adding parameters to the vertical matrices. This is the first approach to add multi-impurity and next-nearest-neighbor interaction to the integrable anisotropic Heisenberg spin chain. It is found that all of the impurity parameters in the bulk must be pure imaginary numbers if the cross parameter is real for getting the hermitian Hamiltonian, or vice versa, when the next-nearest-neighbor interactions are introduced. The Hamiltonian can be also applied to describe the many body systems with two kinds of particles if all of the impurity parameters are equal.