New numerical transfer-matrix results for a quantum spin chain corresponding to (C6H11NH3) CuBr3(CHAB)

1988 ◽  
Vol 37 (16) ◽  
pp. 9879-9881 ◽  
Author(s):  
Thomas Delica
Keyword(s):  
Transfer Matrix ◽  
Spin Chain ◽  
Quantum Spin ◽  
Quantum Spin Chain

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.

scholarly journals Spin chains with boundary inhomogeneities

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Rafael I. Nepomechie ◽  
Ana L. Retore
Keyword(s):  
Quantum Group ◽  
Bethe Ansatz ◽  
Transfer Matrix ◽  
Spin Chain ◽  
Quantum Spin ◽  
Spin Chains ◽  
Group Symmetry ◽  
Quantum Spin Chain ◽  
Open Quantum ◽  
Bethe Ansatz Solution

Abstract We investigate the effect of introducing a boundary inhomogeneity in the transfer matrix of an integrable open quantum spin chain. We find that it is possible to construct a local Hamiltonian, and to have quantum group symmetry. The boundary inhomogeneity has a profound effect on the Bethe ansatz solution.

SPECTRUM OF THE TRANSFER MATRIX FOR THE Uq(Bn)-INVARIANT $A_{2n}^{(2)}$ OPEN SPIN CHAIN

1995 ◽  
Vol 10 (13) ◽  
pp. 1937-1952 ◽  
Author(s):  
SIMONE ARTZ ◽  
LUCA MEZINCESCU ◽  
RAFAEL I. NEPOMECHIE
Keyword(s):  
Asymptotic Behavior ◽  
Transfer Matrix ◽  
Spin Chain ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Quantum Spin ◽  
Quantum Spin Chain ◽  
Fundamental Representation ◽  
Closed Chain ◽  
Matrix Eigenvalues

We propose an expression for the eigenvalues of the transfer matrix for the Uq(Bn)-invariant open quantum spin chain associated with the fundamental representation of [Formula: see text] By assumption, the Bethe ansatz equations are “doubled” with respect to those of the corresponding closed chain with periodic boundary conditions. We verify that the transfer matrix eigenvalues have the correct analyticity properties and asymptotic behavior. We also briefly discuss the structure of the eigenstates of the transfer matrix.

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

A Note on the Symmetry Algebra of An Asymmetric XXZ Quantum Spin Chain

1997 ◽  
Vol 11 (01) ◽  
pp. 17-24
Author(s):  
M. A. Rego-Monteiro
Keyword(s):  
Spin Chain ◽  
Symmetry Algebra ◽  
Quantum Spin ◽  
Quantum Spin Chain ◽  
Deformation Parameters ◽  
Surface Fields

We show that an interesting open asymmetric XXZ quantum spin chain with surface fields is invariant under a two-parametric generalization of the slq(2) algebra with deformation parameters being a particular root of unit.

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