Spatial structure of the pair wave function and the density correlation functions throughout the BEC-BCS crossover

Obeso-Jureidini, J. C.; Romero-Rochı́n, Vı́ctor

doi:10.1103/physreva.101.033619

Cited by 5 publications

(15 citation statements)

References 70 publications

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“…12, these plots reflect the same behavior reported in Ref. [34] across the BCS-BEC crossover, albeit at zero temperature only.…”

Section: Appendix A: Analytic Results For the Fermionic One-particle ...supporting

confidence: 85%

“…[33] both at T = 0 and T → T − c but only in the BCS (weakcoupling) limit, and more recently in Ref. [34] throughout the BCS-BEC crossover but only at T = 0.…”

Section: Normal Contribution To Hmentioning

confidence: 56%

“…[33] at any temperature but in the weak-coupling (BCS) limit only, on the one hand, and in Ref. [34] throughout the BCS-BEC crossover but at zero temperature only, on the other hand.…”

Section: Appendix A: Analytic Results For the Fermionic One-particle ...mentioning

confidence: 92%

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Spatial emergence of off-diagonal long-range order throughout the BCS-BEC crossover

2022

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In a superfluid system, off-diagonal long-range order is expected to be exhibited in the appropriate reduced density matrices when the relevant particles (either bosons or fermion pairs) are considered to recede sufficiently far apart from each other. This concept is usually exploited to identify the value of the condensate density, without explicit concern, however, as to the spatial range over which this asymptotic condition can effectively be achieved. Here, based on a diagrammatic approach that includes beyond-mean-field pairing fluctuations in the broken-symmetry phase at the level of the t-matrix also with the inclusion of the Gorkov-Melik-Barkhudarov (GMB) correction, we present a systematic study of the two-particle reduced density matrix for a superfluid fermionic system undergoing the BCS-BEC crossover, when the entities to recede far apart from each other evolve with continuity from largely overlapping Cooper pairs in the BCS limit to dilute composite bosons in the BEC limit. By this approach, we not only provide the coupling and temperature dependence of the condensate density at the level of our diagrammatic approach, which includes the GMB correction, but we also obtain the evolution of the spatial dependence of the two-particle reduced density matrix, from a power law at low temperature to an exponential dependence at high temperature in the superfluid phase, when the interparticle coupling spans the BCS-BEC crossover. Our results put limitations on the minimum spatial extent of a finite-size system for which superfluid correlations can effectively be established.

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“…12, these plots reflect the same behavior reported in Ref. [34] across the BCS-BEC crossover, albeit at zero temperature only.…”

Section: Appendix A: Analytic Results For the Fermionic One-particle ...supporting

confidence: 85%

“…[33] both at T = 0 and T → T − c but only in the BCS (weakcoupling) limit, and more recently in Ref. [34] throughout the BCS-BEC crossover but only at T = 0.…”

Section: Normal Contribution To Hmentioning

confidence: 56%

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Spatial emergence of off-diagonal long-range order throughout the BCS-BEC crossover

2022

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“…[33] both at T = 0 and T → T − c but only in the BCS (weak-coupling) limit, and more recently in Ref. [34] throughout the BCS-BEC crossover but only at T = 0.…”

Section: Normal Contribution To H2mentioning

confidence: 60%

Spatial emergence of Off-Diagonal Long-Range Order throughout the BCS-BEC crossover

Pisani,

Pieri,

Strinati

2021

Preprint

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“…We refer to those that are recognized by another attribute. For instance, the manybody localization transition which manifests itself through a change in the entanglement dynamics [6,7], the BEC-BCS crossover that can be detected by the decay of the correlation functions [8,9], and the so-called topological phases of matter [10,11] that are distinguished by the evaluation of topological invariants such as the Chern number [12].…”

Section: Introductionmentioning

confidence: 99%

Artificial neural network for the single-particle localization problem in quasiperiodic one-dimensional lattices

Castro

Gutiérrez²

2023

Rev. Mex. Fís.

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The use of machine learning algorithms to address classification problems in several scientific branches has increased over the past years. In particular, the supervised learning technique with artificial neural networks has been successfully employed in classifying phases of matter. In this article, we use a fully connected feed-forward neural network to classify extended and localized single-particle states that arise from quasiperiodic one-dimensional lattices. We demonstrate that our neural network achieves to correctly uncover the nature of the single-particle states even when the wave functions come from a more complex Hamiltonian than the one used to train the network.

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Spatial structure of the pair wave function and the density correlation functions throughout the BEC-BCS crossover

Cited by 5 publications

References 70 publications

Spatial emergence of off-diagonal long-range order throughout the BCS-BEC crossover

Spatial emergence of off-diagonal long-range order throughout the BCS-BEC crossover

Spatial emergence of Off-Diagonal Long-Range Order throughout the BCS-BEC crossover

Artificial neural network for the single-particle localization problem in quasiperiodic one-dimensional lattices

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