Antiperiodic XXZ chains with arbitrary spins: Complete eigenstate construction by functional equations in separation of variables

Abstract

Generic inhomogeneous integrable XXZ chains with arbitrary spins are studied by means of the quantum separation of variables (SOV) method. Within this framework, a complete description of the spectrum (eigenvalues and eigenstates) of the antiperiodic transfer matrix is derived in terms of discrete systems of equations involving the inhomogeneity parameters of the model. We show here that one can reformulate this discrete SOV characterization of the spectrum in terms of functional T-Q equations of Baxter's type, hence proving the completeness of the solutions to the associated systems of Bethe-type equations. More precisely, we consider here two such reformulations. The first one is given in terms of Q-solutions, in the form of trigonometric polynomials of a given degree $N_s$, of a one-parameter family of T-Q functional equations with an extra inhomogeneous term. The second one is given in terms of Q-solutions, again in the form of trigonometric polynomials of degree $N_s$ but with double period, of Baxter's usual (i.e. without extra term) T-Q functional equation. In both cases, we prove the precise equivalence of the discrete SOV characterization of the transfer matrix spectrum with the characterization following from the consideration of the particular class of Q-solutions of the functional T-Q equation: to each transfer matrix eigenvalue corresponds exactly one such Q-solution and vice versa, and this Q-solution can be used to construct the corresponding eigenstate.

38 pages

References in corpus (10)

• The dynamical spin structure factor for the anisotropic spin-1/2 Heisenberg chain
• A Shortcut to the Q-Operator
• Antiperiodic spin-1/2 XXZ quantum chains by separation of variables: Complete spectrum and form factors
• Functional relations from the Yang-Baxter algebra: Eigenvalues of the XXZ model with non-diagonal twisted and open boundary conditions
• Correlation functions of the open XXZ chain I
• Completeness of Bethe Ansatz by Sklyanin SOV for Cyclic Representations of Integrable Quantum Models
• The XXZ model with anti-periodic twisted boundary conditions
• Form factors of integrable Heisenberg (higher) spin chains
• Q-operators in the six-vertex model
• On the evaluation of form factors and correlation functions for the integrable spin-s XXZ chains via the fusion method