Numerical methods and analytic results for one-dimensional strongly interacting spinor gases

Abstract

One of quantum physics' fundamental, but largely unsolved, problems is the computation of the correlation functions in many-body systems. In this paper we address this problem in the case of one-dimensional spinor gases with repulsive contact interactions in the presence of a confining potential. We take advantage of the fact that in the strong coupling limit, the wavefunction factorizes with the charge degrees of freedom expressed as a Slater determinant of spinless fermions and the spin sector described by a spin chain of Sutherland type with exchange coefficients that depend only on the trapping potential. This factorization is also present in the expressions for the correlation functions. Still, analytical and numerical investigations were hindered by the fact that the local exchange coefficients and the charge component of the correlators are expressed as $N-1$ multidimensional integrals, with $N$ the number of particles, which are notoriously hard to compute using conventional methods. We introduce a new approach to calculating these integrals that is extremely simple, scales polynomially with the number of particles, and is several orders of magnitude faster than the previous methods reported in the literature. This allows us to investigate the static and dynamic properties, temperature dependence, and nonequilibrium dynamics for systems with a larger number of particles than previously considered and discover new phenomena. We show that, contrary to natural expectations, the momentum distribution of strongly interacting trapped spinor gases becomes narrower as we increase the temperature and derive simple determinant representations for the correlators in the spin incoherent regime valid for both equilibrium and nonequilibrium situations.

24 pages, 6 figures, RevTeX 4.2

References in corpus (76)

• Many-Body Physics with Ultracold Gases
• Large momentum part of fermions with large scattering length
• Energetics of a strongly correlated Fermi gas
• Fermi gases in one dimension: From Bethe Ansatz to experiments
• A one-dimensional liquid of fermions with tunable spin
• Generalized Virial Theorem and Pressure Relation for a strongly correlated Fermi gas
• Fermionization of two distinguishable fermions
• On the Numerical Evaluation of Fredholm Determinants
• Short-Distance Correlation Properties of the Lieb-Liniger System and Momentum Distributions of Trapped One-Dimensional Atomic Gases
• Exact coherent states of a harmonically confined Tonks-Girardeau gas
• Strongly interacting confined quantum systems in one dimension
• Conductance of a quantum wire in the Wigner crystal regime
• Tan relations in one dimension
• Quantum magnetism without lattices in strongly interacting one-dimensional spinor gases
• Fermionization in an expanding 1D gas of hard-core bosons
• The spin-incoherent Luttinger liquid
• Spin dynamics in a one-dimensional ferromagnetic Bose gas
• Superdiffusion in spin chains
• Exact Solution of Strongly Interacting Quasi-One-Dimensional Spinor Bose Gases
• Exact solution for infinitely strongly interacting Fermi gases in tight waveguides
• Observation of Dynamical Fermionization
• Non-Unitary Spin-Charge Separation in One-Dimensional Fermion Gas
• Strong-coupling ansatz for the one-dimensional Fermi gas in a harmonic potential
• Engineering the Dynamics of Effective Spin-Chain Models for Strongly Interacting Atomic Gases
• Polarization of interacting bosons with spin
• Few-body Bose gases in low dimensions -- a laboratory for quantum dynamics
• Green's function for magnetically incoherent interacting electrons in one dimension
• Universal correlations of trapped one-dimensional impenetrable bosons
• Strongly Interacting Quantum Gases in One-Dimensional Traps
• Correlation functions of one-dimensional anyonic fluids
• Momentum distribution dynamics of a Tonks-Girardeau gas: Bragg reflections of a quantum many-body wavepacket
• Applications of exact solution for strongly interacting one dimensional bose-fermi mixture: low-temperature correlation functions, density profiles and collective modes
• Riemann-Hilbert approach to a generalized sine kernel and applications
• Effective spin-chain model for strongly interacting one-dimensional atomic gases with an arbitrary spin
• Universal properties of Fermi gases in arbitrary dimensions
• High-momentum tails as magnetic structure probes for strongly-correlated $SU(\kappa )$ fermionic mixtures in one-dimensional traps
• Zero temperature correlation functions for the impenetrable fermion gas
• Dynamics of a one-dimensional spinor Bose liquid: a phenomenological approach
• Quantum magnetism in strongly interacting one-dimensional spinor Bose systems
• Theory of momentum resolved tunneling into a short quantum wire
• Low-temperature crossover in the momentum distribution of cold atomic gases in one dimension
• Exact nonequilibrium dynamics of finite-temperature Tonks-Girardeau gases
• Spectral functions of strongly interacting isospin-1/2 bosons in one dimension
• Temperature correlators in the two-component one-dimensional gas
• Momentum distributions and numerical methods for strongly interacting one-dimensional spinor gases
• One-Dimensional Impenetrable Anyons in Thermal Equilibrium. II. Determinant Representation for the Dynamic Correlation Functions
• Strongly interacting trapped one-dimensional quantum gases: an exact solution
• Spin-chain model for strongly interacting one-dimensional Bose-Fermi mixtures
• Asymmetric Zero-Bias Anomaly for Strongly Interacting Electrons in One Dimension
• Bosonization of strongly interacting electrons
• Spin-charge separation in a strongly correlated spin-polarized chain
• Universal Tan relations for quantum gases in one dimension
• CONAN -- the cruncher of local exchange coefficients for strongly interacting confined systems in one dimension
• Bose-Fermi Mapping and Multi-Branch Spin Chain Model for Strongly Interacting Quantum Gases in One-Dimension: Dynamics and Collective Excitations
• Strongly correlated one-dimensional Bose-Fermi quantum mixtures: symmetry and correlations
• Correlation functions of one-dimensional strongly interacting two-component gases
• Kardar-Parisi-Zhang scaling in the Hubbard model
• Dynamical Fermionization in One Dimensional Spinor Gases
• Universal scaling of spin mixing dynamics in a strongly interacting one-dimensional Fermi gas
• 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
• Thermal disruption of a Luttinger liquid
• Non-equilibrium dynamics of the anyonic Tonks-Girardeau gas at finite temperature
• Comparing models for the ground state energy of a trapped one-dimensional Fermi gas with a single impurity
• Exact solution for $SU(2)$-symmetry breaking bosonic mixtures at strong interactions
• Universality and quantum criticality of the one-dimensional spinor Bose gas
• Spin-incoherent Luttinger liquid of one-dimensional spin-1 Tonks-Girardeau Bose gas: Spin-dependent properties
• Spin-incoherent Luttinger liquid of one-dimensional SU($\kappa$) fermions
• Spin-incoherent one-dimensional spin-1 Bose Luttinger liquid
• Finite temperature contact for SU(2) fermions trapped in a 1D harmonic confinement
• Interference dynamics of matter-waves of SU($N$) fermions
• Symmetry oscillations in strongly interacting one-dimensional mixtures
• Exact one-particle density matrix for SU($N$) fermionic matter-waves in the strong repulsive limit
• Dynamical fermionization in one-dimensional spinor gases at finite temperature
• Generalized Bose-Fermi mapping and strong coupling ansatz wavefunction for one dimensional strongly interacting spinor quantum gases
• Nonequilibrium dynamics in one-dimensional strongly interacting two-component gases

Cited by in corpus (1)

• Dynamical probing of high-order spin coherence in one-dimensional mixtures