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

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.

arXiv comment19 pages, 6 figures

References in corpus (44)

• Many-Body Physics with Ultracold Gases
• The density-matrix renormalization group in the age of matrix product states
• Atomic Scattering in Presence of an External Confinement and a Gas of Impenetrable Bosons
• Large momentum part of fermions with large scattering length
• Energetics of a strongly correlated Fermi gas
• Exciting Collective Oscillations in a Trapped 1D Gas
• Deterministic Preparation of a Tunable Few-Fermion System
• A one-dimensional liquid of fermions with tunable spin
• Generalized Virial Theorem and Pressure Relation for a strongly correlated Fermi gas
• An SU(N) Mott insulator of an atomic Fermi gas realized by large-spin Pomeranchuk cooling
• Ultracold Fermi Gases with Emergent SU(N) Symmetry
• Fermionization of two distinguishable fermions
• Contact Measurements on Atomic BEC
• Short-Distance Correlation Properties of the Lieb-Liniger System and Momentum Distributions of Trapped One-Dimensional Atomic Gases
• Strongly interacting confined quantum systems in one dimension
• Instabilities in binary mixtures of one-dimensional quantum degenerate gases
• Tan relations in one dimension
• Quantum magnetism without lattices in strongly interacting one-dimensional spinor gases
• Finite one dimensional impenetrable Bose systems: Occupation numbers
• Exploring correlated 1D Bose gases from the superfluid to the Mott-insulator state by inelastic light scattering
• All-Optical Formation of Quantum Degenerate Mixtures
• Exact Solution of Strongly Interacting Quasi-One-Dimensional Spinor Bose Gases
• Soluble Models of Strongly Interacting Ultracold Gas Mixtures in Tight Waveguides
• High-momentum tail in the Tonks gas under harmonic confinement
• Polarization of interacting bosons with spin
• Exactly solvable case of a one-dimensional Bose-Fermi mixture
• Bose-Fermi Mixtures in One Dimension
• Exact particle and kinetic energy densities for one-dimensional confined gases of non-interacting fermions
• Applications of exact solution for strongly interacting one dimensional bose-fermi mixture: low-temperature correlation functions, density profiles and collective modes
• Effective spin-chain model for strongly interacting one-dimensional atomic gases with an arbitrary spin
• Universal properties of Fermi gases in arbitrary dimensions
• Exact solution for the degenerate ground-state manifold of a strongly interacting one-dimensional Bose-Fermi mixture
• Symmetries of Three Harmonically-Trapped Particles in One Dimension
• High-momentum tails as magnetic structure probes for strongly-correlated $SU(\kappa )$ fermionic mixtures in one-dimensional traps
• Magnetism in strongly interacting one-dimensional quantum mixtures
• Spectroscopy for a Few Atoms Harmonically-Trapped in One Dimension
• Exact density profiles and symmetry classification for strongly interacting multi-component Fermi gases in tight waveguides
• Momentum distributions and numerical methods for strongly interacting one-dimensional spinor gases
• Spin-chain model for strongly interacting one-dimensional Bose-Fermi mixtures
• One-Dimensional Traps, Two-Body Interactions, Few-Body Symmetries: II. $N$ Particles
• SU(N) Fermions in a One-Dimensional Harmonic Trap
• Multicomponent Strongly Interacting Few-Fermion Systems in One Dimension
• Analytical and numerical studies of Bose-Fermi mixtures in a one-dimensional harmonic trap
• Exact ordering of energy levels for one-dimensional interacting Fermi gases with $SU(n)$ symmetry

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• One-dimensional mixtures of several ultracold atoms: a review
• Few-body Bose gases in low dimensions -- a laboratory for quantum dynamics
• Strongly interacting trapped one-dimensional quantum gases: an exact solution
• Universal Tan relations for quantum gases in one dimension
• Optimized Configuration Interaction Approach for Trapped Multiparticle Systems Interacting Via Contact Forces
• Tan's contact in a cigar-shaped dilute Bose gas
• Scaling properties of the Tan's contact: embedding pairs and correlation effect in the Tonks limit
• Exact solution for $SU(2)$-symmetry breaking bosonic mixtures at strong interactions
• Dynamical fermionization in a one-dimensional Bose-Fermi mixture
• Tan's contact scaling behaviour for trapped Lieb-Liniger bosons: from two to many
• Simulating artificial one-dimensional physics with ultra-cold fermionic atoms: three exemplary themes
• Spin-incoherent Luttinger liquid of one-dimensional SU($\kappa$) fermions
• Quantum phase transitions and the degree of nonidentity in the system with two different species of vector bosons
• Symmetry oscillations in strongly interacting one-dimensional mixtures
• High-momentum oscillating tails of strongly interacting 1D gases in a box
• Dynamical fermionization in one-dimensional spinor gases at finite temperature
• Momentum reconstruction and contact of the one-dimensional Bose-Fermi mixture
• Symmetry shapes thermodynamics of macroscopic quantum systems
• Thermodynamics of Statistical Anyons
• Numerical methods and analytic results for one-dimensional strongly interacting spinor gases
• Expansion of one-dimensional spinor gases from power-law traps