Strongly correlated one-dimensional Bose-Fermi quantum mixtures: symmetry and correlations

TL;DR

This paper investigates the symmetries and correlations in strongly interacting one-dimensional Bose-Fermi mixtures, revealing how their ground state symmetry influences observable momentum distribution features, with implications for experimental detection.

Contribution

It introduces a method to analyze symmetries in multi-component quantum mixtures at strong coupling and links these symmetries to measurable momentum distribution tails.

Findings

Ground state has the most symmetric wave function allowed by the mixture type.

Large-momentum tails encode the symmetry properties of the mixture.

Experimental measurement of Tan's contact can determine the mixture's symmetry.

Abstract

We consider multi-component quantum mixtures (bosonic, fermionic, or mixed) with strongly repulsive contact interactions in a one-dimensional harmonic trap. In the limit of infinitely strong repulsion and zero temperature, using the class-sum method, we study the symmetries of the spatial wave function of the mixture. We find that the ground state of the system has the most symmetric spatial wave function allowed by the type of mixture. This provides an example of the generalized Lieb-Mattis theorem. Furthermore, we show that the symmetry properties of the mixture are embedded in the large-momentum tails of the momentum distribution, which we evaluate both at infinite repulsion by an exact solution and at finite interactions using a numerical DMRG approach. This implies that an experimental measurement of the Tan's contact would allow to unambiguously determine the symmetry of any kind of multi-component mixture.