Intertwining relations, asymmetric face model, and algebraic Bethe ansatz forSU p,q (2) invariant spin chain

1996 ◽  
Vol 35 (8) ◽  
pp. 1699-1708
Author(s):  
A. Ghose Choudhury ◽  
A. Roy Chowdhury
Keyword(s):  
Bethe Ansatz ◽  
Spin Chain ◽  
Face Model ◽  
Algebraic Bethe Ansatz

scholarly journals Aspects of Integrable Models

2018 ◽  
Author(s):  
Pranav Diwakar
Keyword(s):  
Bethe Ansatz ◽  
Spin Chain ◽  
Bound States ◽  
Body Problem ◽  
Scattering Matrix ◽  
Baxter Equation ◽  
Chain Model ◽  
Two Body Problem ◽  
Algebraic Bethe Ansatz ◽  
Spin Chain Model

The objective of this thesis is to study the isotropic XXX-1/2 spin chain model using the Algebraic Bethe Ansatz. To this end, we discuss the concept of integrability as well as the Lax operator and R-matrix, which help generate as many commuting operators in involution as there are degrees of freedom. We establish that the spin chain Hamiltonian belongs to this set and provide a definition of a state vector whose parameters, the Bethe roots, are constrained by a set of equations called the Bethe Ansatz Equations. We show that there is a one-to-one correspondence between the Bethe roots and the eigenfunctions of the system. Next, we proceed to study the nature of the low-lying excitations of both the ferromagnetic and antiferromagnetic model in the thermodynamic limit N → ∞ and show that the Bethe roots can be grouped into complexes or strings, which behave like bound states. We see that integrability is directly related to diffractionless scattering, which is obeyed by systems whose scattering matrices satisfy the Yang-Baxter Equation. In order to provide a more physical interpretation, we calculate the scattering matrix of the two-body problem for a system that satisfies the Yang-Baxter Equation and obtain exchange relations that are identical to those obtained using the Algebraic Bethe Ansatz for the XXX-1/2 spin chain model. Finally, we calculate the scattering matrix for a two-body problem interacting with a delta potential and show that this is the same as what we derived using the Coordinate Bethe Ansatz.

scholarly journals A SPIN CHAIN PRIMER

1999 ◽  
Vol 13 (24n25) ◽  
pp. 2973-2985 ◽  
Author(s):  
RAFAEL I. NEPOMECHIE
Keyword(s):  
Bethe Ansatz ◽  
Spin Chain ◽  
Quantum Spin ◽  
Baxter Equation ◽  
Quantum Spin Chain ◽  
Algebraic Bethe Ansatz ◽  
Chain Primer

This is a very elementary introduction to the Heisenberg (XXX) quantum spin chain, the Yang–Baxter equation, and the algebraic Bethe Ansatz.

scholarly journals Form Factors of the Heisenberg Spin Chain in the Thermodynamic Limit: Dealing with Complex Bethe Roots

2021 ◽  
Author(s):  
Nikolai Kitanine ◽  
◽  
Giridhar Kulkarni ◽  
◽  
◽  
...  
Keyword(s):  
Bethe Ansatz ◽  
Thermodynamic Limit ◽  
Spin Chain ◽  
Form Factors ◽  
Heisenberg Spin ◽  
Heisenberg Spin Chain ◽  
Algebraic Bethe Ansatz ◽  
Bethe Equations ◽  
Treat All ◽  
Ansatz Approach

In this article we study the thermodynamic limit of the form factors of the XXX Heisenberg spin chain using the algebraic Bethe ansatz approach. Our main goal is to express the form factors for the low-lying excited states as determinants of matrices that remain finite dimensional in the thermodynamic limit. We show how to treat all types of the complex roots of the Bethe equations within this framework. In particular we demonstrate that the Gaudin determinant for the higher level Bethe equations arises naturally from the algebraic Bethe ansatz.

scholarly journals Factorization identities and algebraic Bethe ansatz for $$ {D}_2^{(2)} $$ models

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Rafael I. Nepomechie ◽  
Ana L. Retore
Keyword(s):  
Bethe Ansatz ◽  
Spin Chain ◽  
Spin Chains ◽  
Transfer Matrices ◽  
Algebraic Bethe Ansatz ◽  
Continuous Parameter

Abstract We express $$ {D}_2^{(2)} $$ D 2 2 transfer matrices as products of $$ {A}_1^{(1)} $$ A 1 1 transfer matrices, for both closed and open spin chains. We use these relations, which we call factorization identities, to solve the models by algebraic Bethe ansatz. We also formulate and solve a new integrable XXZ-like open spin chain with an even number of sites that depends on a continuous parameter, which we interpret as the rapidity of the boundary.

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