An integrable case of the<i>p</i>+ i<i>p</i>pairing Hamiltonian interacting with its environment

Lukyanenko, Inna; Isaac, Phillip S.; Links, Jon

doi:10.1088/1751-8113/49/8/084001

Cited by 25 publications

(58 citation statements)

References 39 publications

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“…The additional terms are responsible for the breaking of the u(1)-symmetry associated to the total particle number, and are interpreted as interaction with the system's environment. The Hamiltonian (1) is a generalisation of the open p + ip Hamiltonian [10]. By setting λ = 0 and β x = β y ⇐⇒ β = 0, we recover the conserved operators underlying the open p + ip model.…”

Section: The Hamiltonianmentioning

confidence: 99%

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Ground-state energy of a Richardson-Gaudin integrable BCS model

2020

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We investigate the ground-state energy of a Richardson-Gaudin integrable BCS model, generalizing the closed and open p+ip models. The Hamiltonian supports a family of mutually commuting conserved operators satisfying quadratic relations. From the eigenvalues of the conserved operators we derive, in the continuum limit, an integral equation for which a solution corresponding to the ground state is established. The energy expression from this solution agrees with the BCS mean-field result.

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Section: The Hamiltonianmentioning

confidence: 99%

“…Integrability of the open model was established in [10] through use of the boundary Quantum Inverse Scattering Method. An alternative derivation, which is less technical, was later provided in [11].…”

Section: Introductionmentioning

confidence: 99%

Ground-state energy of a Richardson-Gaudin integrable BCS model

2020

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“…Note that the boundary parameters α, β enter here in the combination ξ = α − β, so effectively there is only one boundary parameter in the Gaudin limit instead of two. More general Gaudin models with boundary are discussed in [15] and [16].…”

Section: Gaudin Model With Boundarymentioning

confidence: 99%

Quantum-classical duality for Gaudin magnets with boundary

2020

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We establish a remarkable relationship between the quantum Gaudin models with boundary and the classical many-body integrable systems of Calogero-Moser type associated with the root systems of classical Lie algebras (B, C and D). We show that under identification of spectra of the Gaudin Hamiltonians H G j with particles velocitiesq j of the classical model all integrals of motion of the latter take zero values. This is the generalization of the quantum-classical duality observed earlier for Gaudin models with periodic boundary conditions and Calogero-Moser models associated with the root system of the type A.

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“…As in the case of ∆ = 1, this integrability holds for any value of S, including the classical limit S → ∞. The integrability of the model at ∆ = 0 is connected to the existence of a non-standard class of Gaudin models [39][40][41][42][43][44][45][46].…”

Section: Overview Of the Phase Diagrammentioning

confidence: 99%

Integrable and Chaotic Dynamics of Spins Coupled to an Optical Cavity

et al. 2019

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We show that a class of random all-to-all spin models, realizable in systems of atoms coupled to an optical cavity, gives rise to a rich dynamical phase diagram due to the pairwise separable nature of the couplings. By controlling the experimental parameters, one can tune between integrable and chaotic dynamics on the one hand, and between classical and quantum regimes on the other hand. For two special values of a spin-anisotropy parameter, the model exhibits rational-Gaudin type integrability and it is characterized by an extensive set of spin-bilinear integrals of motion, independent of the spin size. More generically, we find a novel integrable structure with conserved charges that are not purely bilinear. Instead, they develop "dressing tails" of higher-body terms, reminiscent of the dressed local integrals of motion found in Many-Body Localized phases. Surprisingly, this new type of integrable dynamics found in finite-size spin-1/2 systems disappears in the large-S limit, giving way to classical chaos. We identify parameter regimes for characterizing these different dynamical behaviors in realistic experiments, in view of the limitations set by cavity dissipation. arXiv:1904.10966v3 [cond-mat.stat-mech]

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An integrable case of thep+ ippairing Hamiltonian interacting with its environment

Cited by 25 publications

References 39 publications

Ground-state energy of a Richardson-Gaudin integrable BCS model

Ground-state energy of a Richardson-Gaudin integrable BCS model

Quantum-classical duality for Gaudin magnets with boundary

Integrable and Chaotic Dynamics of Spins Coupled to an Optical Cavity

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