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

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.

Automated summary

We investigate the ground state of polarized fermions interacting through zero-range p-wave forces in one dimension. We prove that in the limit of infinite attraction, the spectral properties of any-order reduced density matrix describing arbitrary subsystems are independent of the shape of an external potential. Furthermore, we show that the purity of these matrices, which quantifies the amount of quantum correlations, can be analytically obtained for any number of particles without diagonalization. This observation serves as a rigorous benchmark for models and methods studying strongly interacting p-wave fermions.