Determinant representation of the domain-wall boundary condition partition function of a Richardson–Gaudin model containing one arbitrary spin

Faribault, Alexandre; Tschirhart, Hugo; Müller, Nicolás

doi:10.1088/1751-8113/49/18/185202

Cited by 7 publications

(9 citation statements)

References 31 publications

(76 reference statements)

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“…A common approach, known as the eigenvaluebased method, maps the Richardson-Gaudin equations (3) to an equivalent set of equations for the variables 13,14,25,52,[93][94][95][96][97][98][99]…”

Section: Numericsmentioning

confidence: 99%

Variational method for integrability-breaking Richardson-Gaudin models

et al. 2017

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We present a variational method for approximating the ground state of spin models close to (Richardson-Gaudin) integrability. This is done by variationally optimizing eigenstates of integrable Richardson-Gaudin models, where the toolbox of integrability allows for an efficient evaluation and minimization of the energy functional. The method is shown to return exact results for integrable models and improve substantially on perturbation theory for models close to integrability. For large integrability-breaking interactions, it is shown how (avoided) level crossings necessitate the use of excited states of integrable Hamiltonians in order to accurately describe the ground states of general non-integrable models.

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Section: Numericsmentioning

confidence: 99%

Variational method for integrability-breaking Richardson-Gaudin models

et al. 2017

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“…However, the BAE recovered for the extended Hamiltonian in the Supplemental Material are a great deal more involved than those for the canonical Hamiltonian, which are already notoriously difficult to solve generally. Instead of solving these equations directly, we will generalize a recent method pioneered by Faribault et al [34][35][36][37][38] and later extended by us [24,39]. In this method, an algebraic relationship is obtained for the conserved operators in the integrable system, which are then converted to non-linear equations for their eigenvalues.…”

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confidence: 99%

Read-Green resonances in a topological superconductor coupled to a bath

2016

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We study a topological superconductor capable of exchanging particles with an environment. This additional interaction breaks particle-number symmetry and can be modelled by means of an integrable Hamiltonian, building on the class of Richardson-Gaudin pairing models. The isolated system supports zero-energy modes at a topological phase transition, which disappear when allowing for particle exchange with an environment. However, it is shown from the exact solution that these still play an important role in system-environment particle exchange, which can be observed through resonances in low-energy and -momentum level occupations. These fluctuations signal topologically protected Read-Green points and cannot be observed within traditional mean-field theory.Comment: 7 pages, 4 figure

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“…as noted in [14]. Because of the known structure of the inverse of a Cauchy matrix, these matrices can be explicitly calculated as…”

Section: Properties Of Cauchy Matricesmentioning

confidence: 99%

“…Such determinant expressions provide a basic building block for the calculation of correlation coefficients from the Bethe states, which has allowed for massive simplifications in the calculations of correlation coefficients in these models [6][7][8][9][10]. Such inner products can also be interpreted as domain wall boundary partition functions (DWPF), which can similarly be expressed as determinants [11][12][13][14].…”

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confidence: 99%

Inner products in integrable Richardson-Gaudin models

2017

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We present the inner products of eigenstates in integrable Richardson-Gaudin models from two different perspectives and derive two classes of Gaudin-like determinant expressions for such inner products. The requirement that one of the states is on-shell arises naturally by demanding that a state has a dual representation. By implicitly combining these different representations, inner products can be recast as domain wall boundary partition functions. The structure of all involved matrices in terms of Cauchy matrices is made explicit and used to show how one of the classes returns the Slavnov determinant formula.Furthermore, this framework provides a further connection between two different approaches for integrable models, one in which everything is expressed in terms of rapidities satisfying Bethe equations, and one in which everything is expressed in terms of the eigenvalues of conserved charges, satisfying quadratic equations.

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Determinant representation of the domain-wall boundary condition partition function of a Richardson–Gaudin model containing one arbitrary spin

Cited by 7 publications

References 31 publications

Variational method for integrability-breaking Richardson-Gaudin models

Variational method for integrability-breaking Richardson-Gaudin models

Read-Green resonances in a topological superconductor coupled to a bath

Inner products in integrable Richardson-Gaudin models

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