Universality of Internal Correlations of Strongly Interacting $p$-Wave Fermions in One-Dimensional Geometry

Universality of Internal Correlations of Strongly Interacting $p$ -Wave Fermions in One-Dimensional Geometry

Przemysław Kościk and Tomasz Sowiński

Phys. Rev. Lett. 130, 253401 – Published 23 June 2023

Abstract

We consider the many-body ground state of polarized fermions interacting via zero-range $p$ -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.

Received 10 March 2023
Revised 27 April 2023
Accepted 5 June 2023

DOI:https://doi.org/10.1103/PhysRevLett.130.253401

Physics Subject Headings (PhySH)

Cold atoms & matter waves Entanglement in quantum gases Spinless fermions

1-dimensional systems

Exact solutions for many-body systems

Condensed Matter, Materials & Applied PhysicsAtomic, Molecular & Optical

Authors & Affiliations

Przemysław Kościk ¹ and Tomasz Sowiński ²

¹Department of Computer Sciences, University of Applied Sciences, ulica Mickiewicza 8, PL-33100 Tarnów, Poland
²Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, PL-02668 Warsaw, Poland