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.

arXiv commentAuthors' version accepted for publication

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• Cooper pairing and tripling in one-dimensional spinless fermions with attractive two- and three-body forces
• Precision Measurement of Spin-Dependent Dipolar Splitting in ${}^6$Li p-Wave Feshbach Resonances
• Universal composite boson formation in strongly interacting one-dimensional fermionic systems
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• Molecular excited state in the interaction quench dynamics of two different atoms in a two-dimensional anisotropic trap
• 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