Exact solution for infinitely strongly interacting Fermi gases in tight waveguides

Abstract

We present an exact analytical solution of the fundamental systems of quasi-one-dimensional spin-1/2 fermions with infinite repulsion for arbitrary confining potential. The eigenfunctions are constructed by the combination of Gireardeau's hard-core contacting boundary condition and group theoretical method which guarantees the obtained states to be simultaneously the eigenstates of $S$ and $S_z$ and fulfill the antisymmetry under odd permutation. We show that the total ground-state density profile behaves like the polarized noninteracting fermions, whereas the spin-dependent densities display different properties for different spin configurations. We also discuss the splitting of the ground states for large but finite repulsion.

4 pages, 3 figures, version accepted for publication in Phys. Rev. Lett

References in corpus (19)

• Atomic Scattering in Presence of an External Confinement and a Gas of Impenetrable Bosons
• Transition from a strongly interacting 1D superfluid to a Mott insulator
• Realization of Bose-Einstein condensates in lower dimensions
• Pairing and Phase Separation in a Polarized Fermi Gas
• Fermionic Superfluidity with Imbalanced Spin Populations and the Quantum Phase Transition to the Normal State
• Exciting Collective Oscillations in a Trapped 1D Gas
• Confinement induced molecules in a 1D Fermi gas
• Spin-charge separation in ultra-cold quantum gases
• Exact Solution of Strongly Interacting Quasi-One-Dimensional Spinor Bose Gases
• Soluble Models of Strongly Interacting Ultracold Gas Mixtures in Tight Waveguides
• Polarization of interacting bosons with spin
• Interacting fermions in quasi-one-dimensional harmonic traps
• Ground-state properties of one-dimensional ultracold Bose gases in a hard-wall trap
• Evolution from a Bose-Einstein condensate to a Tonks-Girardeau gas: An exact diagonalization study
• Correlations in Ultracold Trapped Few-Boson Systems: Transition from Condensation to Fermionization
• Charge and spin dynamics of interacting Fermions in a one dimensional harmonic trap
• Density-functional theory of strongly correlated Fermi gases in elongated harmonic traps
• Rigorous Proof of Pseudospin Ferromagnetism in Two-Component Bosonic Systems with Component-Independent Interactions
• Stability of spinor Fermi gases in tight waveguides

Cited by in corpus (87)

• Fermi gases in one dimension: From Bethe Ansatz to experiments
• Antiferromagnetic Heisenberg Spin Chain of a Few Cold Atoms in a One-Dimensional Trap
• Strongly interacting confined quantum systems in one dimension
• Quantum magnetism without lattices in strongly interacting one-dimensional spinor gases
• One-dimensional mixtures of several ultracold atoms: a review
• Strong-coupling ansatz for the one-dimensional Fermi gas in a harmonic potential
• Fermionization of two-component few-fermion systems in a one-dimensional harmonic trap
• Few interacting fermions in one-dimensional harmonic trap
• Strongly Interacting Quantum Gases in One-Dimensional Traps
• An Interaction-Driven Many-Particle Quantum Heat Engine: Universal Behavior
• Ground-State Ferromagnetic Transition in Strongly Repulsive One-Dimensional Fermi Gases
• Effective spin-chain model for strongly interacting one-dimensional atomic gases with an arbitrary spin
• Exact solution for the degenerate ground-state manifold of a strongly interacting one-dimensional Bose-Fermi mixture
• Super-Tonks-Girardeau gas of spin-1/2 interacting fermions
• Pairing in a system of a few attractive fermions in a harmonic trap
• 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
• Energy and contact of the one-dimensional Fermi polaron at zero and finite temperature
• Pairing of few Fermi atoms in one dimension
• One-Dimensional Traps, Two-Body Interactions, Few-Body Symmetries: I. One, Two, and Three Particles
• A variational approach to repulsively interacting three-fermion systems in a one-dimensional harmonic trap
• Density-functional theory of two-component Bose gases in one-dimensional harmonic traps
• Spin-chain model for strongly interacting one-dimensional Bose-Fermi mixtures
• One-Dimensional Traps, Two-Body Interactions, Few-Body Symmetries: II. $N$ Particles
• Few-fermion thermometry
• One-dimensional multicomponent fermions with delta function interaction in strong and weak coupling limits: Two-component Fermi gas
• Fractional energy states of strongly-interacting bosons in one dimension
• Three interacting atoms in a one-dimensional trap: A benchmark system for computational approaches
• Topological Mott insulators of ultracold atomic mixtures induced by interactions in one-dimensional optical superlattices
• Engineering quantum magnetism in one-dimensional trapped Fermi gases with p-wave interactions
• Exploring the few- to many-body crossover using cold atoms in one dimension
• Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems
• Exact Solution for 1D Spin-Polarized Fermions with Resonant Interactions
• CONAN -- the cruncher of local exchange coefficients for strongly interacting confined systems in one dimension
• Strongly interacting Bose-Fermi mixtures in one dimension
• Ultracold few fermionic atoms in needle-shaped double wells: spin chains and resonating spin clusters from microscopic Hamiltonians emulated via antiferromagnetic Heisenberg and t-J models
• Universal quantum behaviors of interacting fermions in 1D traps: from few particles to the trap thermodynamic limit
• Strongly interacting one-dimensional quantum gas mixtures with weak p-wave interactions
• Static and dynamic properties of a few spin $1/2$ interacting fermions trapped in an harmonic potential
• Ground-state properties of the one-dimensional attractive Hubbard model with confinement: a comparative study
• 2kF-Friedel to 4kF-Wigner oscillations in one-dimensional Fermi gases under confinement
• Spin-Orbit Coupled One-Dimensional Fermi Gases with Infinite Repulsion
• Magnetism and quantum phase transitions in spin-1/2 attractive fermions with polarization
• Dynamical Fermionization in One Dimensional Spinor Gases
• Dynamics of spin and density fluctuations in strongly interacting few-body systems
• One-Body Density Matrix and Momentum Distribution of Strongly Interacting One-Dimensional Spinor Quantum Gases
• Exact ordering of energy levels for one-dimensional interacting Fermi gases with $SU(n)$ symmetry
• Particle-number scaling of the quantum work statistics and Loschmidt echo in Fermi gases with time-dependent traps
• Spinless Bosons or Spin 1/2 Fermions in a 1D Harmonic Trap with Repulsive Delta Function Interparticle Interaction I - General Theory
• Comparing models for the ground state energy of a trapped one-dimensional Fermi gas with a single impurity
• Hard-core Bose-Fermi mixture in one-dimensional split traps
• Dynamical fermionization in a one-dimensional Bose-Fermi mixture
• Ground State Energy for Fermions in a 1D Harmonic Trap with Delta Function Interaction
• Entanglement production by statistical operators
• Tuning an effective spin chain of three strongly interacting one-dimensional fermions with the transversal confinement
• Sum rules for spin-$1/2$ quantum gases in states with well-defined spins: spin-independent interactions and spin-dependent external fields
• Exact closed-form analytic wave functions in two dimensions: Contact-interacting fermionic spinful ultracold atoms in a rapidly rotating trap
• Computation of local exchange coefficients in strongly interacting one-dimensional few-body systems: local density approximation and exact results
• Mixture of Tonks-Girardeau gas and Fermi gas in one-dimensional optical lattices
• A generalized effective spin-chain formalism for strongly interacting spinor gases in optical lattice
• Identical Wells, Symmetry Breaking, and the Near-Unitary Limit
• One-particle Green's function of interacting two electrons using analytic solutions for a three-body problem: comparison with exact Kohn--Sham system
• Long-lived states with well-defined spins in spin-$1/2$ homogeneous Bose gases
• Strongly bound fermion pairs on a ring: a composite-boson approach
• The Goldilocks model of separable, zero-range, few-body interactions in one-dimensional harmonic traps
• Dynamical fermionization in one-dimensional spinor gases at finite temperature
• Out-of-equilibrium dynamics of repulsive Fermi gases in quasi-periodic potentials: a Density Functional Theory study
• Density functional theory versus quantum Monte Carlo simulations of Fermi gases in the optical-lattice arena
• Emergence of junction dynamics in a strongly interacting Bose mixture
• Wigner crystal versus Fermionization for one-dimensional Hubbard models with and without long-range interactions
• Spectroscopy and spin dynamics for strongly interacting few spinor bosons in one-dimensional traps
• The lowest scattering state of one-dimensional Bose gas with attractive interactions
• Generalized Bose-Fermi mapping and strong coupling ansatz wavefunction for one dimensional strongly interacting spinor quantum gases
• Improvement of the matching of the exact solution and variational approaches in an interacting two-fermion system
• Nonequilibrium dynamics in one-dimensional strongly interacting two-component gases
• Fermi super-Tonks-Girardeau state for attractive Fermi gases in an optical lattice
• Exact spectral function and nonequilibrium dynamics of the strongly interacting Hubbard model
• Sum rules for spin-$1/2$ quantum gases in states with well-defined spins: II. Spin-dependent two-body interactions
• Ferromagnetic to antiferromagnetic transition of one-dimensional spinor Bose gases with spin-orbit coupling
• Numerical methods and analytic results for one-dimensional strongly interacting spinor gases
• Strongly Repulsive 1D Gases at Higher Branches: Spin-Charge Correlation and Coupled Spin-Chain Model
• Effective theory for strongly attractive one-dimensional fermions
• Densities probabilities of a Bose-Fermi Mixture in 1D Double well potential
• Several fermions strongly interacting with a heavy mobile impurity in a one-dimensional harmonic trap
• Few strongly interacting fermions of different mass driven in the vicinity of a critical point
• Exact solutions of a one-dimensional mixture of spinor bosons and spinor fermions