The nested Bethe ansatz for ‘all’ open spin chains with diagonal boundary conditions

The nested Bethe ansatz is generalized to open and independent boundary conditions depending on two continuous and two discrete free parameters. This is used to find the exact eigenvectors and eigenvalues of the An−1 vertex models and SU (n) spin chains with such boundary conditions. The solution is found for all diagonal families of solutions to the reflection equations in all possible combinations. The Bethe ansatz equations are used to find the first order finite size correction.

Download Full-text

Nested Bethe ansatz for the vertex model with open boundary conditions

Nuclear Physics B ◽

10.1016/j.nuclphysb.2004.06.054 ◽

2004 ◽

Vol 696 (3) ◽

pp. 381-412 ◽

Cited By ~ 6

Author(s):

Guang-Liang Li ◽

Kang-Jie Shi ◽

Rui-Hong Yue

Keyword(s):

Boundary Conditions ◽

Bethe Ansatz ◽

Open Boundary ◽

Vertex Model ◽

Open Boundary Conditions ◽

Nested Bethe Ansatz

Download Full-text

Nested Bethe Ansatz for Spin Ladder Model with Open Boundary Conditions

Communications in Theoretical Physics ◽

10.1088/0253-6102/43/4/022 ◽

2005 ◽

Vol 43 (4) ◽

pp. 687-694 ◽

Cited By ~ 1

Author(s):

Wu Jun-Fang ◽

Zhang Chun-Min ◽

Yue Rui-Hong ◽

Li Run-Ling

Keyword(s):

Boundary Conditions ◽

Bethe Ansatz ◽

Open Boundary ◽

Spin Ladder ◽

Open Boundary Conditions ◽

Ladder Model ◽

Nested Bethe Ansatz

Download Full-text

ANALYTICAL BETHE ANSATZ FOR OPEN SPIN CHAINS WITH SOLITON NONPRESERVING BOUNDARY CONDITIONS

International Journal of Modern Physics A ◽

10.1142/s0217751x06029077 ◽

2006 ◽

Vol 21 (07) ◽

pp. 1537-1554 ◽

Cited By ~ 9

Author(s):

D. ARNAUDON ◽

A. DOIKOU ◽

L. FRAPPAT ◽

É. RAGOUCY ◽

N. CRAMPÉ

Keyword(s):

Boundary Conditions ◽

Bethe Ansatz ◽

Spin Chains ◽

Full Generality ◽

Finite Dimensional ◽

Algebraic Treatment ◽

Algebraic Framework ◽

Matrix Eigenvalues ◽

Bethe Equations

We present an "algebraic treatment" of the analytical Bethe ansatz for open spin chains with soliton nonpreserving (SNP) boundary conditions. For this purpose, we introduce abstract monodromy and transfer matrices which provide an algebraic framework for the analytical Bethe ansatz. It allows us to deal with a generic [Formula: see text] open SNP spin chain possessing on each site an arbitrary representation. As a result, we obtain the Bethe equations in their full generality. The classification of finite dimensional irreducible representations for the twisted Yangians are directly linked to the calculation of the transfer matrix eigenvalues.

Download Full-text

BETHE ANSATZ SOLUTIONS FOR TEMPERLEY–LIEB QUANTUM SPIN CHAINS

International Journal of Modern Physics A ◽

10.1142/s0217751x00001245 ◽

2000 ◽

Vol 15 (21) ◽

pp. 3395-3425 ◽

Cited By ~ 2

Author(s):

R. C. T. GHIOTTO ◽

A. L. MALVEZZI

Keyword(s):

Free Boundary ◽

Boundary Conditions ◽

Quantum Group ◽

Bethe Ansatz ◽

Periodic Boundary ◽

Periodic Boundary Conditions ◽

Quantum Spin ◽

Spin Chains ◽

Quantum Spin Chains ◽

Free Boundary Conditions

We solve the spectrum of quantum spin chains based on representations of the Temperley–Lieb algebra associated with the quantum groups [Formula: see text] for Xn=A1, Bn, Cn and Dn. The tool is a modified version of the coordinate Bethe ansatz through a suitable choice of the Bethe states which give to all models the same status relative to their diagonalization. All these models have equivalent spectra up to degeneracies and the spectra of the lower-dimensional representations are contained in the higher-dimensional ones. Periodic boundary conditions, free boundary conditions and closed nonlocal boundary conditions are considered. Periodic boundary conditions, unlike free boundary conditions, break quantum group invariance. For closed nonlocal cases the models are quantum group invariant as well as periodic in a certain sense.

Download Full-text