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arXiv:2112.05349 · Physical Review C

Cooper quartet correlations in infinite symmetric nuclear matter

Yixin Guo, Hiroyuki Tajima, Haozhao Liang

Published Feb 17, 2022• 18 citations
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Abstract

We investigate the quartet correlations in four-component fermionic systems at the thermodynamic limit within a variational many-body theory. The Bardeen-Cooper-Schrieffer (BCS)--type variational wave function is extended to the systems with the coexistence of pair and quartet correlations at zero temperature. Special attention is paid to the application of the present framework to an $\ensuremath{\alpha}$-particle condensation in symmetric nuclear matter, where the coexistence of deuteron and $\ensuremath{\alpha}$ condensations is anticipated. We also discuss how physical properties, such as quasiparticle dispersion, can be modified by the pair and quartet correlations and show a hierarchical structure of in-medium cluster formations in infinite nuclear matter. The present results may also contribute to the interdisciplinary understanding of fermionic condensations beyond the BCS paradigm in many-body systems.

DOI
10.1103/physrevc.105.024317

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We investigate the quartet correlations in four-component fermionic systems at the thermodynamic limit within a variational many-body theory. The Bardeen-Cooper-Schrieffer (BCS)--type variational wave function is extended to the systems with the coexistence of pair and quartet correlations at zero temperature. Special attention is paid to the application of the present framework to an \ensuremathα\ensuremath{\alpha}\ensuremathα-particle condensation in symmetric nuclear matter, where the coexistence of deuteron and \ensuremathα\ensuremath{\alpha}\ensuremathα condensations is anticipated. We also discuss how physical properties, such as quasiparticle dispersion, can be modified by the pair and quartet correlations and show a hierarchical structure of in-medium cluster formations in infinite nuclear matter. The present results may also contribute to the interdisciplinary understanding of fermionic condensations beyond the BCS paradigm in many-body systems.
We theoretically investigate a quartet superfluid state in fermionic matter by using the quartet Bardeen-Cooper-Schrieffer (BCS) variational theory and the Green's function method. We demonstrate that the quartet BCS theory with the multiple-infinite-product ansatz successfully reproduces an exact four-body result in a one-dimensional four-component Fermi gas at the dilute limit, in contrast to the single-infinite-product ansatz. To see the validity of the quartet BCS state, we derive the self-consistent equation for the quartet superfluid order parameter within the generalized imaginary-time Nambu-Gor'kov formalism, which is found to be consistent with the quartet BCS variational equation. Moreover, by numerically computing the momentum-resolved single-particle spectral function in a one-dimensional system, we discuss how the single-particle spectra evolve with increasing the strength of the four-body cluster formation. We show that a coherent BCS-like quasiparticle branch on the weak-coupling side evolves into a strongly damped, continuum-dominated spectrum in the strong-coupling side, while nonzero quartet superfluid order parameter persists throughout the crossover regime. Our results would be useful for understanding beyond-BCS pairing effects and four-body cluster formations in fermionic systems in an interdisciplinary way.
Four-particle correlations in fermion systems at finite temperatures are investigated with special attention to the formation of a condensate. Instead of the instability of the normal state with respect to the onset of pairing described by the Gorkov equation, a new equation is obtained which describes the onset of ``quartetting.'' Applying to symmetric nuclear matter, below a critical density, the four-particle condensation ( $\ensuremath{\alpha}$-like quartetting) is found to be favored over deuteron condensation (triplet pairing). This pairing-quartetting competition is expected to be a general feature of interacting fermion systems, such as the exciton-biexciton system in excited semiconductors. Possible experimental consequences are pointed out.
Nonrelativistic nuclear matter is considered as a special example of a many-particle system. Quantum statistical methods are applied to treat the formation and dissolution of bound states in dense matter. The formation of quantum condensates is investigated. Special aspects are the transition from Bose-Einstein condensation (BEC) to Bardeen-Cooper-Schrieffer (BCS) pairing as well as the occurrence of quartetting. Consequences for the structure of nuclei are compared with experimental data. Exercises to illustrate the main features of in-medium effects in nuclear matter are given.
The condensation of Cooper pairs, originating from the Fermi-surface instability due to a weakly attractive interaction between two fermions, opened a new frontier for exploring many-body physics in interdisciplinary contexts. In this work, we discuss the possible condensation of Cooper triples, which are three-body counterparts of Cooper pairs for three-component fermions with a three-body attraction. Although each composite trimer-like state obeys the Fermi-Dirac statistics, its aggregate can form a condensate at zero center-of-mass momentum in the presence of the internal degrees of freedom associated with the relative momenta of constituent particles of momenta close to the Fermi surface. Such condensation can be regarded as bosonization in infinite-component fermions. We propose a variational wave function for the condensate of Cooper triples in analogy with the Bardeen-Cooper-Schrieffer ground state, and we obtain the ground-state energy.
We develop a theory of superconductivity (or superfluidity) based on condensed fermion quartets focusing on the dilute spin-12\frac{1}{2}21​ systems at zero temperature. In the spirit of the Bardeen--Cooper--Schrieffer ansatz, a variational wavefunction is constructed such that, within the so-called ``dilute quartet approximation", it is the ground state of an effective quartic Hamiltonian. For a given two-body interaction in favor of quartetting, the gap parameter is suitably defined and the gap equation is also derived. As to the excited states, an intuitive physical picture based on a sixteen-dimensional ``occupation space" is depicted and the associated eigen-energies are obtained. This theory is applied to compute the superfluid fraction, which is found to be the same as in conventional superconductors, despite the interacting nature of the quartet problem.
The two-particle spectrum in a dense Fermion system is treated using a thermodynamic Green function approach. A self-consistent description of possible bound states and a superfluid condensate in a correlated medium is given. A detailed understanding of superfluidity and superconductivity in correlated Fermion systems, especially the transition from the Cooper-paired state (weak-coupling limit) to the Bose condensed state of tightly bound pairs of Fermions (strong coupling limit) [1], is of great interest for very different physical systems. The problem of a unified treatment of Bose–Einstein condensation (BEC) and the Bardeen–Cooper–Schrieffer (BCS) phase arises not only in describing the electron structure of strongly correlated electron superfluids such as superconductors [2], the electronhole system in semiconductors [3], spin-polarized hydrogen and liquid He [4], but also in the theory of nuclear matter [5] and quark–gluon systems [6]. Recently, there have been several new approaches to this stimulating problem. A Monte-Carlo simulation of a finite He system at zero temperature has been performed in Ref. [7]. The microscopic theory of strongly coupled quantum fluids has been treated within the Jastrow approximation (cf. Ref. [8]) to obtain the ground state and low-lying excited states of strongly correlated boson quantum fluids. The crossover from weak to strong coupling superconductivity has been considered using a functional integral representation [2] (see also Ref. [7]).