Algebraic Bethe Ansatz for U(1) Invariant Integrable Models: The Method and General Results

Abstract

In this work we have developed the essential tools for the algebraic Bethe ansatz solution of integrable vertex models invariant by a unique U(1) charge symmetry. The formulation is valid for arbitrary statistical weights and respective number $N$ of edge states. We show that the fundamental commutation rules between the monodromy matrix elements are derived by solving linear systems of equations. This makes possible the construction of the transfer matrix eigenstates by means of a new recurrence relation depending on $N-1$ distinct types of creation fields. The necessary identities to solve the eigenvalue problem are obtained exploring the unitarity property and the Yang-Baxter equation satisfied by the $R$-matrix. The on-shell and off-shell properties of the algebraic Bethe ansatz are explicitly presented in terms of the arbitrary $R$-matrix elements. This includes the transfer matrix eigenvalues, the Bethe ansatz equations and the structure of the vectors not parallel to the eigenstates.

90 pages

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Cited by in corpus (13)

• Finite size properties of staggered $U_q[sl(2|1)]$ superspin chains
• Correlation functions of the integrable higher-spin XXX and XXZ spin chains through the fusion method
• Form factors of integrable higher-spin XXZ chains and the affine quantum-group symmetry
• The Yang-Baxter equation for PT invariant nineteen vertex models
• Integrable three-state vertex models with weights lying on genus five curves
• Coordinate Bethe Ansatz for Spin s XXX Model
• Algebraic Bethe ansatz for U(1) Invariant Integrable Models: Compact and non-Compact Applications
• Thermodynamics of quantum spin chains with competing interactions
• The monodromy matrix in the F-basis for arbitrary six-vertex models
• Scalar product of Bethe vectors from functional equations
• General scalar products in the arbitrary six-vertex model
• Algebraic Bethe ansatz for Q-operators of the open XXX Heisenberg chain with arbitrary spin
• The spectrum of a vertex model and related spin one chain sitting in a genus five curve