Universality of internal correlations of strongly interacting p-wave fermions in one-dimensional geometry

Abstract

We consider the many-body ground state of polarized fermions interacting via zero-range $\mathfrak{p}$-wave forces in a one-dimensional geometry. We rigorously prove that in the limit of infinite attractions spectral properties of any-order reduced density matrix describing arbitrary subsystem are completely independent of the shape of an external potential. It means that quantum correlations between any two subsystems are in this limit insensitive to the confinement. In addition, we show that the purity of these matrices quantifying the amount of quantum correlations can be obtained analytically for any number of particles without diagonalizing them. This observation may serve as a rigorous benchmark for other models and methods describing strongly interacting p-wave fermions.

Authors' version accepted for publication

References in corpus (7)

• Reduced density matrices and coherence of trapped interacting bosons
• Ground-state properties of one-dimensional ultracold Bose gases in a hard-wall trap
• Decay by tunneling of Bosonic and Fermionic Tonks-Girardeau Gases
• One-dimensional fermionic gases with attractive p-wave interaction in a hard-wall trap
• Pairing of a harmonically trapped fermionic Tonks-Girardeau gas
• Stability against three-body clustering in one-dimensional spinless p-wave fermions
• Competition between pairing and tripling in one-dimensional fermions with coexistent s- and p-wave interactions

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• Bardeen-Cooper-Schrieffer State Representation and Pairing in the Fermionic Tonks-Girardeau Gas
• Efficient determination of eigenenergies and eigenstates of $N$ ($N=3$--$4$) identical 1D bosons and fermions under external harmonic confinement