The Anisotropic Heisenberg Quantum Spin Chain

2019 ◽  
pp. 491-501
Author(s):  
Hans-Peter Eckle
Keyword(s):  
Magnetic Materials ◽  
Spin Chain ◽  
Heisenberg Model ◽  
Magnetic Moments ◽  
Quantum Spin ◽  
Quantum Spin Chain ◽  
Good Picture ◽  
One Dimensional ◽  
Dimensional Version ◽  
The One

This chapter introduces the Heisenberg model, a fully quantum mechanical model that describes the magnetism of localized magnetic moments. The one-dimensional version of the Heisenberg model, the Heisenberg quantum spin chain, provides a good picture of magnetic materials that belong to a class of insulating magnetic materials where the interaction of the magnetic moments in one particular direction is much larger than in the perpendicular directions, and which can be described with high accuracy as quasi- one-dimensional magnets. A detailed description of the Heisenberg quantum spin chain is followed by a discussion of its various special cases, in particular the special case of the anisotropic Heisenberg quantum spin chain, the so-called XXZ quantum spin chain. It considers the solution of eigenvalue problem of this quantum spin and leads to Bethe’s conjecture for the wave function.

Magnetic field induced ferroelectric transition of quasi one-dimensional frustrated quantum spin chain system Rb2Cu2Mo3O12

2013 ◽  
Vol 113 (17) ◽  
pp. 17D910 ◽  
Author(s):  
Yukio Yasui ◽  
Yudai Yanagisawa ◽  
Ryuji Okazaki ◽  
Ichiro Terasaki ◽  
Yasuhiro Yamaguchi ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Spin Chain ◽  
Quantum Spin ◽  
Quantum Spin Chain ◽  
Ferroelectric Transition ◽  
One Dimensional ◽  
Chain System

Six-Vertex Model

2019 ◽  
pp. 454-473
Author(s):  
Hans-Peter Eckle
Keyword(s):  
Bethe Ansatz ◽  
Transfer Matrix ◽  
Spin Chain ◽  
Quantum Spin ◽  
Square Lattice ◽  
Vertex Model ◽  
Quantum Spin Chain ◽  
Special Value ◽  
Quantum Operators ◽  
The One

This chapter considers the special case of the six-vertex model on a square lattice using a trigonometric parameterization of the vertex weights. It demonstrates how, by exploiting the Yang-Baxter relations, the six-vertex model is diagonalized and the Bethe ansatz equations are derived. The Hamiltonian of the Heisenberg quantum spin chain is obtained from the transfer matrix for a special value of the spectral parameter together with an infinite set of further conserved quantum operators. By the diagonalization of the transfer matrix the exact solution of the one-dimensional quantum spin chain Hamiltonian has automatically also been obtained, which is given by the same Bethe ansatz equations.

New polarization effect and collective excitation in S = 1/2 quasi-one-dimensional antiferromagnetic quantum spin chain

JETP Letters ◽  
2006 ◽  
Vol 84 (5) ◽  
pp. 249-253
Author(s):  
S. V. Demishev ◽  
A. V. Semeno ◽  
H. Ohta ◽  
S. Okubo ◽  
I. E. Tarasenko ◽  
...  
Keyword(s):  
Spin Chain ◽  
Polarization Effect ◽  
Collective Excitation ◽  
Quantum Spin ◽  
Quantum Spin Chain ◽  
One Dimensional

scholarly journals T − W relation and free energy of the Heisenberg chain at a finite temperature

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Pengcheng Lu ◽  
Yi Qiao ◽  
Junpeng Cao ◽  
Wen-Li Yang ◽  
Kang jie Shi ◽  
...  
Keyword(s):  
Free Energy ◽  
Spin Chain ◽  
Quantum Spin ◽  
Heisenberg Chain ◽  
Quantum Spin Chain ◽  
Heisenberg Spin ◽  
Heisenberg Spin Chain ◽  
Lattice Quantum ◽  
Quantum Integrable Models ◽  
Invariant Quantum

Abstract A new nonlinear integral equation (NLIE) describing the thermodynamics of the Heisenberg spin chain is derived based on the t − W relation of the quantum transfer matrices. The free energy of the system in a magnetic field is thus obtained by solving the NLIE. This method can be generalized to other lattice quantum integrable models. Taking the SU(3)-invariant quantum spin chain as an example, we construct the corre- sponding NLIEs and compute the free energy. The present results coincide exactly with those obtained via other methods previously.

scholarly journals Quantum spin chain dissipative mean-field dynamics

2018 ◽  
Vol 51 (32) ◽  
pp. 325001 ◽  
Author(s):  
F Benatti ◽  
F Carollo ◽  
R Floreanini ◽  
H Narnhofer
Keyword(s):  
Spin Chain ◽  
Mean Field ◽  
Quantum Spin ◽  
Quantum Spin Chain

scholarly journals Toeplitz algebras and spectral results for the one-dimensional Heisenberg model

2006 ◽  
Vol 47 (8) ◽  
pp. 082107 ◽  
Author(s):  
Mondher Damak ◽  
Marius Măntoiu ◽  
Rafael Tiedra de Aldecoa
Keyword(s):  
Heisenberg Model ◽  
One Dimensional ◽  
The One
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