Spin-incoherent Luttinger liquid of one-dimensional SU($\kappa$) fermions

Abstract

We theoretically investigate one-dimensional (1D) SU($\kappa$) fermions in the regime of spin-incoherent Luttinger liquid. We specifically focus on the Tonks-Girardeau gas limit where its density is sufficiently low that effective repulsions between atoms become infinite. In such case, spin exchange energy of 1D SU($\kappa$) fermions vanishes and all spin configurations are degenerate, which automatically puts them into spin-incoherent regime. In this limit, we are able to express the single-particle density matrices in terms of those of anyons. This allows us to numerically simulate the number of particles up to $N=32$. We numerically calculate single-particle density matrices in two cases: (1) equal populations for each spin components (balanced) and (2) all $S_z$ manifolds included. In contrast to noninteracting multi-component fermions, the momentum distributions are broadened due to strong interactions. As $\kappa$ increases, the momentum distributions are less broadened for fixed $N$, while they are more broadened for fixed number of particle per spin component. We then compare numerically calculated high momentum tails with analytical predictions which are proportional to $1/p^4$, in good agreement. Thus, our theoretical study provides a comparison with the experiments of repulsive multicomponent alkaline-earth fermions with a tunable SU($\kappa$) spin-symmetry in the spin-incoherent regime.

arXiv comment8 pages and 5 figures

References in corpus (57)

• Atomic Scattering in Presence of an External Confinement and a Gas of Impenetrable Bosons
• One dimensional Bosons: From Condensed Matter Systems to Ultracold Gases
• Two-orbital SU(N) magnetism with ultracold alkaline-earth atoms
• Energetics of a strongly correlated Fermi gas
• Realization of an Excited, Strongly-Correlated Quantum Gas Phase
• Fermi gases in one dimension: From Bethe Ansatz to experiments
• Spin-Imbalance in a One-Dimensional Fermi Gas
• A one-dimensional liquid of fermions with tunable spin
• Confinement induced molecules in a 1D 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
• Exact Relations for a Strongly-interacting Fermi Gas from the Operator Product Expansion
• Ultracold Gases of Ytterbium: Ferromagnetism and Mott States in an SU(6) Fermi System
• The unitary gas in an isotropic harmonic trap: symmetry properties and applications
• Short-Distance Correlation Properties of the Lieb-Liniger System and Momentum Distributions of Trapped One-Dimensional Atomic Gases
• Ground state properties of a one-dimensional condensate of hard core bosons in a harmonic trap
• Strongly interacting confined quantum systems in one dimension
• Number of closed-channel molecules in the BEC-BCS crossover
• Universal Properties of the Ultra-Cold Fermi Gas
• Tan relations in one dimension
• Quantum magnetism without lattices in strongly interacting one-dimensional spinor gases
• The spin-incoherent Luttinger liquid
• Finite one dimensional impenetrable Bose systems: Occupation numbers
• Exact Solution of Strongly Interacting Quasi-One-Dimensional Spinor Bose Gases
• Shadow band in the one-dimensional large $U$ Hubbard model
• Anyon-fermion mapping and applications to ultracold gases in tight waveguides
• High-momentum tail in the Tonks gas under harmonic confinement
• Exact Relations for a Strongly-interacting Fermi Gas near a Feshbach Resonance
• Non-Unitary Spin-Charge Separation in One-Dimensional Fermion Gas
• Green's function for magnetically incoherent interacting electrons in one dimension
• Strongly Interacting Quantum Gases in One-Dimensional Traps
• Virial theorems for trapped cold atoms
• Ground-state properties of hard core bosons in one-dimensional harmonic traps
• Effective spin-chain model for strongly interacting one-dimensional atomic gases with an arbitrary spin
• Universal scaling of density and momentum distributions in Lieb-Liniger gases
• High-momentum tails as magnetic structure probes for strongly-correlated $SU(\kappa )$ fermionic mixtures in one-dimensional traps
• Spectral properties of a spin-incoherent Luttinger Liquid
• Entropy dependence of correlations in one-dimensional SU(N) antiferromagnets
• Adiabatic loading of one-dimensional SU(N) alkaline earth fermions in optical lattices
• Low-temperature crossover in the momentum distribution of cold atomic gases in one dimension
• Momentum distributions and numerical methods for strongly interacting one-dimensional spinor gases
• Quantum Monte Carlo simulation of thermodynamic properties of SU(2N) ultracold fermions in optical lattices
• Spin-chain model for strongly interacting one-dimensional Bose-Fermi mixtures
• SU(N) Fermions in a One-Dimensional Harmonic Trap
• Tan's contact of a harmonically trapped one-dimensional Bose gas: strong-coupling expansion and conjectural approach at arbitrary interactions
• One-dimensional multicomponent Fermi gas in a trap: quantum Monte Carlo study
• Strongly correlated one-dimensional Bose-Fermi quantum mixtures: symmetry and correlations
• Thermodynamics, contact and density profiles of the repulsive Gaudin-Yang model
• One-body reduced density matrix of trapped impenetrable anyons in one dimension
• Finite temperature spectral-functions of strongly correlated one-dimensional electron systems
• Ground state properties of hard-core anyons in a harmonic potential
• One-Body Density Matrix and Momentum Distribution of Strongly Interacting One-Dimensional Spinor Quantum Gases
• Tan's contact in a cigar-shaped dilute Bose gas
• Spin-incoherent Luttinger liquid of one-dimensional spin-1 Tonks-Girardeau Bose gas: Spin-dependent properties
• Spin-incoherent one-dimensional spin-1 Bose Luttinger liquid
• Universality class of quantum criticality in the two-dimensional Hubbard model at intermediate temperatures ($t^2/U\ll T\ll t$)

Cited by in corpus (7)

• Evidence for Bosonization in a three-dimensional gas of SU($N$) fermions
• One-particle density matrix of a trapped Lieb-Liniger anyonic gas
• Quantum dynamics of impenetrable SU(N) fermions in one-dimensional lattices
• Impenetrable SU(N) fermions in one-dimensional lattices
• Dynamical fermionization in a one-dimensional Bose-Fermi mixture
• State selective cooling of $\mathrm{SU}(N)$ Fermi-gases
• Numerical methods and analytic results for one-dimensional strongly interacting spinor gases