scholarly journals Integrable quenches in nested spin chains II: fusion of boundary transfer matrices

2019 ◽  
Vol 2019 (6) ◽  
pp. 063104 ◽  
Author(s):  
Lorenzo Piroli ◽  
Eric Vernier ◽  
Pasquale Calabrese ◽  
Balázs Pozsgay
Keyword(s):  
Spin Chains ◽  
Transfer Matrices

scholarly journals QQ-system and Weyl-type transfer matrices in integrable SO(2r) spin chains

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Gwenäel Ferrando ◽  
Rouven Frassek ◽  
Vladimir Kazakov
Keyword(s):  
Lie Algebra ◽  
Finite Length ◽  
Spin Chains ◽  
Transfer Matrices ◽  
Full System ◽  
Functional Relations ◽  
Integrable Spin ◽  
Integrable Spin Chains

Abstract We propose the full system of Baxter Q-functions (QQ-system) for the integrable spin chains with the symmetry of the Dr Lie algebra. We use this QQ-system to derive new Weyl-type formulas expressing transfer matrices in all symmetric and antisymmetric (fundamental) representations through r + 1 basic Q-functions. Our functional relations are consistent with the Q-operators proposed recently by one of the authors and verified explicitly on the level of operators at small finite length.

scholarly journals Multiparameter Statistical Models from Braid Matrices: Explicit Eigenvalues of Transfer Matrices , Spin Chains, Factorizable Scatterings for All

2012 ◽  
Vol 2012 ◽  
pp. 1-21
Author(s):  
B. Abdesselam ◽  
A. Chakrabarti
Keyword(s):  
Statistical Models ◽  
Linear Equations ◽  
Spin Chains ◽  
Transfer Matrices ◽  
Circular Permutations ◽  
Constant Coefficients ◽  
Free Parameters ◽  
Class Of Matrices ◽  
Zero Sum

For a class of multiparameter statistical models based on braid matrices, the eigenvalues of the transfer matrix are obtained explicitly for all . Our formalism yields them as solutions of sets of linear equations with simple constant coefficients. The role of zero-sum multiplets constituted in terms of roots of unity is pointed out, and their origin is traced to circular permutations of the indices in the tensor products of basis states induced by our class of matrices. The role of free parameters, increasing as withN, is emphasized throughout. Spin chain Hamiltonians are constructed and studied for allN. Inverse Cayley transforms of the Yang-Baxter matrices corresponding to our braid matrices are obtained for allN. They provide potentials for factorizableS-matrices. Main results are summarized, and perspectives are indicated in the concluding remarks.

QUANTUM ALGEBRA STRUCTURE OF EXACTLY SOLUBLE QUANTUM SPIN CHAINS

1991 ◽  
Vol 06 (27) ◽  
pp. 2497-2508 ◽  
Author(s):  
LUCA MEZINCESCU ◽  
RAFAEL I. NEPOMECHIE
Keyword(s):  
Large Class ◽  
Quantum Algebra ◽  
Quantum Spin ◽  
Spin Chains ◽  
Algebra Structure ◽  
Quantum Spin Chains ◽  
Transfer Matrices ◽  
Highest Weight

We consider a large class of quantum spin chains, whose Hamiltonians commute with generators of a quantum algebra and which are integrable. We argue that the corresponding transfer matrices also commute with the quantum algebra. For the spin [Formula: see text] chain, we show that the Bethe states are highest weight states of Uq[ su (2)].

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.

Set of open-loop block-diagonalizers of transfer matrices

1989 ◽  
Vol 49 (1) ◽  
pp. 161-168
Author(s):  
A. Bülent Özgü Ler ◽  
Vasfi Eldem
Keyword(s):  
Open Loop ◽  
Transfer Matrices
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