Exact mesoscopic correlation functions of the Richardson pairing model

Faribault, Alexandre; Calabrese, Pasquale; Caux, Jean-Sébastien

doi:10.1103/physrevb.77.064503

Cited by 59 publications

(103 citation statements)

References 62 publications

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“…If we set µ = 0 in Eqs. (32,33), we find that this coincides with g −1 = 1 − 2ρ. This transition line has been identified in previous works as the Read-Green line 14,18 .…”

Section: Derivatives Of the Energy Densitymentioning

confidence: 72%

“…(32,33) we see that g −1 and ρ are continuous functions of µ and ∆. Hence, µ and ∆ are continuous functions of ρ and g, and therefore the derivatives of ε with respect to ρ and g are continuous functions of ρ and g. We conclude that there is no first order QPT in this model.…”

Section: Derivatives Of the Energy Densitymentioning

confidence: 80%

“…A special point that one observes in Eqs. (32,33) corresponds to µ = ∆ 2 /2, which leads to g −1 = 1 − ρ. This is the Moore-Read line we discussed in Sec.…”

Section: Derivatives Of the Energy Densitymentioning

confidence: 99%

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Quantum phase diagram of the integrablepx+ipyfermionic superfluid

2010

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We determine the zero temperature quantum phase diagram of a px + ipy pairing model based on the exactly solvable hyperbolic Richardson-Gaudin model. We present analytical and large-scale numerical results for this model. In the continuum limit, the exact solution exhibits a third-order quantum phase transition, separating a strong-pairing from a weak-pairing phase. The mean field solution allows to connect these results to other models with px + ipy pairing order. We define an experimentally accessible characteristic length scale, associated with the size of the Cooper pairs, that diverges at the transition point, indicating that the phase transition is of a confinementdeconfinement type without local order parameter. We show that this phase transition is not limited to the px + ipy pairing model, but can be found in any representation of the hyperbolic RichardsonGaudin model and is related to a symmetry that is absent in the rational Richardson-Gaudin model.

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“…If we set µ = 0 in Eqs. (32,33), we find that this coincides with g −1 = 1 − 2ρ. This transition line has been identified in previous works as the Read-Green line 14,18 .…”

Section: Derivatives Of the Energy Densitymentioning

confidence: 72%

Section: Derivatives Of the Energy Densitymentioning

confidence: 80%

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Quantum phase diagram of the integrablepx+ipyfermionic superfluid

2010

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“…A "canonical pairing parameter" has been proposed by von Delft et al [26] and adopted in other studies [27,28],…”

Section: Order Parametermentioning

confidence: 99%

“…The matrix elements C μν can be expressed as sums of certain determinants which depend explicitly on the rapidities λ i [28] and are not simple functions of the quantities ν . Nevertheless it turns out to be advantageous to solve first the quadratic equations for ν and then use the procedure outlined in Ref.…”

Section: Order Parametermentioning

confidence: 99%

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

Araby

Baeriswyl

2014

Phys. Rev. B

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The exact ground state of the reduced BCS Hamiltonian is investigated numerically for large system sizes and compared with the BCS ansatz. A "canonical" order parameter is found to be equal to the largest eigenvalue of Yang's reduced density matrix in the thermodynamic limit. Moreover, the limiting values of the exact analysis agree with those obtained for the BCS ground state. Exact results for the ground-state energy, level occupations, and a pseudospin-pseudospin correlation function are also found to converge to the BCS values already for relatively small system sizes. However, discrepancies persist for a pair-pair correlation function, for interlevel correlations of occupancies and for the fidelity susceptibility, even for large system sizes where these quantities have visibly converged to well-defined limits. Our results indicate that there exist nonperturbative corrections to the BCS predictions in the thermodynamic limit.

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Bethe Ansatz approach to the pairing fluctuations in the mesoscopic regime

Amico

Osterloh

2012

Annalen der Physik

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Dedicated to Ulrich Eckern on the occasion of his 60th birthday.We review the exact treatment of the pairing correlation functions in the canonical ensemble. The key for the calculations has been provided by relating the discrete BCS model to known integrable theories corresponding to the so called Gaudin magnets with suitable boundary terms. In the present case the correlation functions can be accessed beyond the formal level, allowing the description of the cross-over from few electrons to the thermodynamic limit. In particular, we summarize the results on the finite size scaling behavior of the canonical pairing clarifying some puzzles emerged in the past. Some recent developments and applications are outlined.

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Exact mesoscopic correlation functions of the Richardson pairing model

Cited by 59 publications

References 62 publications

Quantum phase diagram of the integrablepx+ipyfermionic superfluid

Quantum phase diagram of the integrablepx+ipyfermionic superfluid

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

Bethe Ansatz approach to the pairing fluctuations in the mesoscopic regime

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