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arXiv:2308.04737 · Physical Review A

Cooper pairing and tripling in one-dimensional spinless fermions with attractive two- and three-body forces

Yixin Guo, Hiroyuki Tajima

Published Oct 9, 2023• 3 citations
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Abstract

We theoretically investigate three-body correlations on the top of a Fermi sea in one-dimensional spinless fermions with antisymmetrized two- and three-body attractive interactions. By investigating the variational problem of three-body states above the Fermi sea, we illuminate the fate of the in-medium three-body cluster states (namely, Cooper triples in the presence of Fermi sea) in the special case with pure attractive three-body interaction as well as in the case with the coexistence of two- and three-body interactions. Our results testify that the fermion-dimer repulsion is canceled by including the three-body interactions, and stable three-body clusters can be formed. We further feature a phase diagram consisting of the $p$-wave Cooper pairing and Cooper tripling phases in a plane of $p$-wave two- and three-body coupling strengths.

DOI
10.1103/physreva.108.043303

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We theoretically investigate three-body correlations on the top of a Fermi sea in one-dimensional spinless fermions with antisymmetrized two- and three-body attractive interactions. By investigating the variational problem of three-body states above the Fermi sea, we illuminate the fate of the in-medium three-body cluster states (namely, Cooper triples in the presence of Fermi sea) in the special case with pure attractive three-body interaction as well as in the case with the coexistence of two- and three-body interactions. Our results testify that the fermion-dimer repulsion is canceled by including the three-body interactions, and stable three-body clusters can be formed. We further feature a phase diagram consisting of the ppp-wave Cooper pairing and Cooper tripling phases in a plane of ppp-wave two- and three-body coupling strengths.
We theoretically investigate in-medium two- and three-body correlations in one-dimensional spinless fermions with attractive two-body ppp-wave interaction. By investigating the variational problem of two- and three-body states above the Fermi sea, we elucidate the fate of the in-medium two- and three-body cluster states. The one-dimensional system with the strong ppp-wave interaction is found to be stable against the formation of three-body clusters even in the presence of the Fermi sea, in contrast to higher-dimensional systems that suffer the strong three-body loss associated with the trimer formation. Our results indicate that the weak two-body coupling side is more sensitive to the residual three-body interaction than the strong-coupling side. By including the dimensionless three-body coupling such that the universality associated with the scattering length is maintained, we find that an in-medium three-body state similar to a squeezed Cooper triple appears.
We theoretically investigate in-medium two- and three-body correlations in one-dimensional two-component Fermi gases with coexistent even-parity sss-wave and odd-parity ppp-wave interactions. We find the solutions of the stable in-medium three-body cluster states such as the Cooper triple by solving the corresponding in-medium variational equations. We further feature a phase diagram consisting of the sss- and ppp-wave Cooper pairing phases, and Cooper tripling phase, in a plane of sss- and ppp-wave pairing strengths. The Cooper tripling phase dominates over the pairing phases when both sss- and ppp-wave interactions are moderately strong.
We investigate many-body properties of equally populated three-component fermions with attractive threebody contact interaction in one dimension.A diagrammatic approach suggests the possible occurrence of Cooper triples at low temperature, which are three-body counterparts of Cooper pairs with a two-body attraction.We develop a minimal framework that bridges the crossover from tightly bound trimers to Cooper triples with increasing chemical potential and show how the formation of Cooper triples occurs in the grand-canonical phase diagram.Moreover, we argue that this nontrivial crossover is similar to the hadron-quark crossover proposed in dense matter.A coexistence of medium-induced triples and the underlying Fermi sea at positive chemical potential is analogous to quarkyonic matter consisting of baryonic excitations and the underlying quark Fermi sea.The comparison with the existing quantum Monte Carlo results implies that the emergence of these kinds of three-body states can be a microscopic origin of the peak of the sound velocity along the crossover.
We consider the mass-imbalance effect on the clustering in a one-dimensional two-component Fermi gas with coexistent even- and odd-wave interactions resulting in different configurations of clustering phases. We obtain the solutions of both stable two- and three-body cluster states with different mass ratios and configurations by solving the corresponding variational equations. We numerically map out phase diagrams consisting of the sss- and ppp-wave pairing phases, and {trimer} phase with different configurations, in a plane of sss- and ppp-wave pairing strengths. Within the explored ranges of sss- and ppp-wave pairing strengths, the in-vacuum three-body states are always more deeply bound than the two-body ones. While for the in-medium case, the Cooper {trimer} phase dominates over the pairing phases when both sss- and ppp-wave interactions are moderately strong. There is also a competition between different clustering configurations of three-body clustering.
We investigate many-body properties of equally populated three-component fermions with attractive three-body contact interaction. A diagrammatic approach suggests the possible occurrence of Cooper triples at low temperature, which are a three-body counterpart of Cooper pairs with a two-body attraction. In one-dimension, the presence of Cooper triples is accompanied by conformal symmetry breaking, which is in turn related to an asymptotic freedom of the low-dimensional, multi-component system. While trimer states present at sufficiently low density have the binding energy reduced by the Pauli blocking and the thermal agitation, Cooper triples are predicted to take over for the even larger Fermi surface. We develop a minimal framework that bridges such a crossover from tightly-bound trimers to Cooper triples with increasing particle number density.
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.