Order parameter, correlation functions, and fidelity susceptibility for the BCS model in the thermodynamic limit

Araby, Omar El; Baeriswyl, D.

doi:10.1103/physrevb.89.134521

Cited by 6 publications

(11 citation statements)

References 33 publications

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“…Such an investigation has been carried out for the reduced BCS Hamiltonian by El Araby and Baeriswyl [48], who compared exact results for large system sizes with the BCS ansatz. Again, it would be worthwhile to compare the results rigorously with the results from BCS mean-field theory [4].…”

Section: Discussionmentioning

confidence: 99%

Eigenvalue-based method and form-factor determinant representations for integrable XXZ Richardson-Gaudin models

et al. 2015

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We propose an extension of the numerical approach for integrable Richardson-Gaudin models based on a new set of eigenvalue-based variables [A. Faribault et al., Phys. Rev. B 83, 235124 (2011); O. El Araby et al., ibid. 85, 115130 (2012)]. 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 nonintegrable. 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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Section: Discussionmentioning

confidence: 99%

Eigenvalue-based method and form-factor determinant representations for integrable XXZ Richardson-Gaudin models

et al. 2015

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“…While many efforts have been made over time to deal with these equations directly [13][14][15][16], the rewriting of the Bethe equations as an ensemble of N quadratic equations [7,17,18] has recently greatly simplified the numerical treatment of such systems [19][20][21][22]. It has indeed been shown that the Bethe equations for models with…”

Section: ( )S ( ) S ( )S ( ) 2s ( )S ( ) mentioning

confidence: 99%

Algebraic Bethe ansätze and eigenvalue-based determinants for Dicke–Jaynes–Cummings–Gaudin quantum integrable models

Tschirhart¹,

Faribault²

2014

J. Phys. A: Math. Theor.

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In this work, we construct an alternative formulation to the traditional algebraic Bethe ansätze for quantum integrable models derived from a generalized rational Gaudin algebra realized in terms of a collection of spins 1/2 coupled to a single bosonic mode. The ensemble of resulting models which we call Dicke-Jaynes-Cummings-Gaudin models are particularly relevant for the description of light-matter interaction in the context of quantum optics. Having two distinct ways to write any eigenstate of these models we then combine them in order to write overlaps and form factors of local operators in terms of partition functions with domain wall boundary conditions. We also demonstrate that they can all be written in terms of determinants of matrices whose entries only depend on the eigenvalues of the conserved charges. Since these eigenvalues obey a much simpler set of quadratic Bethe equations, the resulting expressions could then offer important simplifications for the numerical treatment of these models.

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“…The Bethe ansatz also allows for exact theoretical and numerical studies in system sizes beyond the reach of exact diagonalization [24,29,30,[67][68][69][70][71], providing different avenues for the study of nonequilibrium dynamics in central spin models.…”

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confidence: 99%

Integrability and dark states in an anisotropic central spin model

Villazon

Chandran

Claeys

2020

Phys. Rev. Research

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Central spin models describe a variety of quantum systems in which a spin-1 2 qubit interacts with a bath of surrounding spins, as realized in quantum dots and defect centers in diamond. We show that the fully anisotropic central spin Hamiltonian with (XX) Heisenberg interactions is integrable. Building on the class of integrable Richardson-Gaudin models, we derive an extensive set of conserved quantities and obtain the exact eigenstates using the Bethe ansatz. These states divide into two exponentially large classes: bright states, where the qubit is entangled with the bath, and dark states, where it is not. We discuss how dark states limit qubit-assisted spin bath polarization and provide a robust long-lived quantum memory for qubit states.

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Order parameter, correlation functions, and fidelity susceptibility for the BCS model in the thermodynamic limit

Cited by 6 publications

References 33 publications

Eigenvalue-based method and form-factor determinant representations for integrable XXZ Richardson-Gaudin models

Eigenvalue-based method and form-factor determinant representations for integrable XXZ Richardson-Gaudin models

Algebraic Bethe ansätze and eigenvalue-based determinants for Dicke–Jaynes–Cummings–Gaudin quantum integrable models

Integrability and dark states in an anisotropic central spin model

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