An eigenvalue-based method and determinant representations for general integrable XXZ Richardson-Gaudin models

Abstract

We propose an extension of the numerical approach for integrable Richardson-Gaudin models based on a new set of eigenvalue-based variables. Starting solely from the Gaudin algebra, the approach is generalized towards the full class of XXZ Richardson-Gaudin models. This allows for a fast and robust numerical determination of the spectral properties of these models, avoiding the singularities usually arising at the so-called singular points. We also provide different determinant expressions for the normalization of the Bethe Ansatz states and form factors of local spin operators, opening up possibilities for the study of larger systems, both integrable and non-integrable. These expressions can be written in terms of the new set of variables and generalize the results previously obtained for rational Richardson-Gaudin models and Dicke-Jaynes-Cummings-Gaudin models. Remarkably, these results are independent of the explicit parametrization of the Gaudin algebra, exposing a universality in the properties of Richardson-Gaudin integrable systems deeply linked to the underlying algebraic structure.

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Cited by in corpus (8)

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• Combining symmetry breaking and restoration with configuration interaction: a highly accurate many-body scheme applied to the pairing Hamiltonian
• Exact dynamics of the homogeneous two-qubit $XXZ$ central spin model with the spin bath prepared in superpositions of symmetric Dicke states
• A variational method for integrability-breaking Richardson-Gaudin models
• Ground-state energy of a Richardson-Gaudin integrable BCS model
• Particle-hole duality, integrability, and Russian doll BCS model
• Near-exact treatment of seniority-zero ground and excited states with a Richardson-Gaudin mean-field
• Transition density matrices of Richardson-Gaudin states