Correlation functions of one-dimensional strongly interacting two-component gases

Abstract

We address the problem of calculating the correlation functions of one-dimensional two-component gases with strong repulsive contact interactions. The model considered in this paper describes particles with fractional statistics and in appropriate limits reduces to the Gaudin-Yang model or the spinor Bose gas. In the case of impenetrable particles we derive a Fredholm determinant representation for the temperature-, time-, and space-dependent correlation functions which is very easy to implement numerically and constitute the starting point for the analytical investigation of the asymptotics. Making use of this determinant representation and the solution of an associated Riemann-Hilbert problem we derive the low-energy asymptotics of the correlators in the spin-incoherent regime characterized by near ground-state charge degrees of freedom but a highly thermally disordered spin sector. The asymptotics present features reminiscent of spin-charge separation with the spin part exponentially decaying in space separation and oscillating with a period proportional to the statistics parameter while the charge part presents scaling with anomalous exponents which cannot be described by any unitary conformal field theory. The momentum distribution and the Fourier transform of the dynamical Green's function are asymmetrical for arbitrary statistics, a direct consequence of the broken space-reversal symmetry. Due to the exponential decay the momentum distribution $n(k)$ at zero temperature does not present algebraic singularities but the tails obey the universal decay ${\lim }_{k\to \pm \infty }n(k)\sim C/k^4$ with the amplitude $C$ given by Tan's contact. As a function of the statistics parameter the contact is a monotonic function reaching its minimum for the fermionic system and the maximum for the bosonic system.

35 pages, 10 figures, RevTeX 4.1

References in corpus (106)

• Large momentum part of fermions with large scattering length
• Energetics of a strongly correlated Fermi gas
• Generalized Virial Theorem and Pressure Relation for a strongly correlated Fermi gas
• Exact Relations for a Strongly-interacting Fermi Gas from the Operator Product Expansion
• 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
• Computation of dynamical correlation functions of Heisenberg chains in a field
• Statistically induced Phase Transitions and Anyons in 1D Optical Lattices
• General relations for quantum gases in two and three dimensions. Two-component fermions
• Dynamical density-density correlations in the one-dimensional Bose gas
• Conductance of a quantum wire in the Wigner crystal regime
• Universal Properties of the Ultra-Cold Fermi Gas
• Two-spinon dynamic structure factor of the one-dimensional S=1/2 Heisenberg antiferromagnet
• Tan relations in one dimension
• Exact solution of double-delta function Bose gas through interacting anyon gas
• The 1D interacting anyon gas: low-energy properties and Haldane exclusion statistics
• Exact relations for quantum-mechanical few-body and many-body problems with short-range interactions in two and three dimensions
• Two-dimensional dynamics of expansion of a degenerate Bose gas
• General relations for quantum gases in two and three dimensions. II. Bosons and mixtures
• The spin-incoherent Luttinger liquid
• Form factor approach to dynamical correlation functions in critical models
• Temperature Correlations of Quantum Spins
• The 4-spinon dynamical structure factor of the Heisenberg chain
• The Anyon Hubbard Model in One-Dimensional Optical Lattices
• Finite temperature correlations in the Lieb-Liniger 1D Bose gas
• Anyon-fermion mapping and applications to ultracold gases in tight waveguides
• Non-Unitary Spin-Charge Separation in One-Dimensional Fermion Gas
• Fermionization and bosonization of expanding 1D anyonic fluids
• Floquet realization and signatures of one-dimensional anyons in an optical lattice
• Green's function for magnetically incoherent interacting electrons in one dimension
• Form factor approach to the asymptotic behavior of correlation functions in critical models
• Universal correlations of trapped one-dimensional impenetrable bosons
• Correlation functions of one-dimensional anyonic fluids
• Nonequilibrium dynamics of one-dimensional hard-core anyons following a quench: Complete relaxation of one-body observables
• Universal relations for the two-dimensional spin-1/2 Fermi gas with contact interactions
• Integrable Fredholm Operators and Dual Isomonodromic Deformations
• Riemann-Hilbert approach to a generalized sine kernel and applications
• Universal properties of Fermi gases in arbitrary dimensions
• Correlation Functions of One-Dimensional Lieb-Liniger Anyons
• Exact results of the ground state and excitation properties of a two-component interacting Bose system
• Two component interacting bosons: 1-d exact results
• Computation of static Heisenberg-chain correlators: Control over length and temperature dependence
• Ground-state properties of one-dimensional anyon gases
• Junctions of anyonic Luttinger wires
• Zero temperature correlation functions for the impenetrable fermion gas
• Ground-state properties of hard-core anyons in one-dimensional optical lattices
• Increasing of entanglement entropy from pure to random quantum critical chains
• Bethe Ansatz for 1D interacting anyons
• Exact dynamics following an interaction quench in a one-dimensional anyonic gas
• Short-distance thermal correlations in the massive XXZ chain
• Dynamical properties of hard-core anyons in one-dimensional optical lattices
• Engineering interactions and anyon statistics by multicolor lattice-depth modulations
• Low-temperature crossover in the momentum distribution of cold atomic gases in one dimension
• One-particle density matrix and momentum distribution function of one-dimensional anyon gases
• Long-distance asymptotic behaviour of multi-point correlation functions in massless quantum models
• Entanglement properties and moment distributions of a system of hard-core anyons on a ring
• Impurity Green's function of a one-dimensional Fermi-gas
• Statistical Phases and Momentum Spacings for One-Dimensional Anyons
• Temperature correlators in the two-component one-dimensional gas
• Quantum Walks of Two Interacting Anyons in 1D Optical Lattices
• Long-distance behavior of temperature correlation functions in the one-dimensional Bose gas
• Bosonization at Finite Temperature and Anyon Condensation
• Low-temperature large-distance asymptotics of the transversal two-point functions of the XXZ chain
• One-Dimensional Impenetrable Anyons in Thermal Equilibrium. II. Determinant Representation for the Dynamic Correlation Functions
• Luttinger Liquid in Non-equilibrium Steady State
• Coulomb blockade of anyons
• Short-distance thermal correlations in the XXZ chain
• Exact four-spinon dynamical correlation function of the Heisenberg model
• Anyonic tight-binding models of parafermions and of fractionalized fermions
• Strongly interacting mesoscopic systems of anyons in one dimension
• Temperature correlators in the one-dimensional Hubbard model in the strong coupling limit
• Universal Tan relations for quantum gases in one dimension
• Critical points of the anyon-Hubbard model
• Ground State Properties of the One-Dimensional Unconstrained Pseudo-Anyon Hubbard Model
• Time and temperature-dependent correlation function of an impurity in a one-dimensional Fermi gas as a Fredholm determinant
• Correlation lengths of the repulsive one-dimensional Bose gas
• Time and temperature dependent correlation functions of the 1D impenetrable electron gas
• One-dimensional anyons with competing $\delta$-function and derivative $\delta$-function potentials
• One-body reduced density matrix of trapped impenetrable anyons in one dimension
• Temperature Correlation of Quantum Spins
• Off-diagonal correlations in one-dimensional anyonic models: A replica approach
• Anyons and the Bose-Fermi duality in the finite-temperature Thirring model
• Quantum entanglement of particles on a ring with fractional statistics
• Probing the exchange statistics of one-dimensional anyon models
• Finite-temperature correlations in a quantum spin chain near saturation
• Thermal form factor approach to the ground-state correlation functions of the XXZ chain in the antiferromagnetic massive regime
• Ground state properties of hard-core anyons in a harmonic potential
• Do anyons solve Heisenberg's Urgleichung in one dimension
• One-Dimensional Impenetrable Anyons in Thermal Equilibrium. III. Large distance asymptotics of the space correlations
• Deviations from Off-Diagonal Long-Range Order in One-Dimensional Quantum Systems
• Correlations in the impenetrable electron gas
• One-Dimensional Impenetrable Anyons in Thermal Equilibrium. IV. Large Time and Distance Asymptotic Behavior of the Correlation Functions
• Thermodynamics of the spin-$1/2$ Heisenberg-Ising chain at high temperatures: a rigorous approach
• Quantum Inverse Scattering Method with anyonic grading
• One-Body Density Matrix and Momentum Distribution of Strongly Interacting One-Dimensional Spinor Quantum Gases
• Three-body interaction effects on the ground state of one-dimensional anyons
• Long-distance and large-time asymptotic behaviour of dynamic correlation functions in the massless regime of the XXZ spin-1/2 chain
• Condensation of Anyons in Frustrated Quantum Magnets
• Quantum phase transition in a multicomponent anyonic Lieb-Liniger model
• Anyonic Liquids in Nearly Saturated Spin Chains
• One-dimensional hard-core anyon gas in a harmonic trap at finite temperature
• Quasimomentum distribution and expansion of an anyonic gas
• Asymptotics of correlation functions of the Heisenberg-Ising chain in the easy-axis regime
• Quantum Integrable 1D anyonic Models: Construction through Braided Yang-Baxter Equation
• Dualities for anyons
• One-particle irreducible density matrix for the spin disordered infinite $U$ Hubbard chain

Cited by in corpus (12)

• One-particle density matrix of a trapped Lieb-Liniger anyonic gas
• Topological Exchange Statistics in One Dimension
• Large time and long distance asymptotics of the thermal correlators of the impenetrable anyonic lattice gas
• On the Dynamics of Free-Fermionic Tau-Functions at Finite Temperature
• Non-equilibrium dynamics of the anyonic Tonks-Girardeau gas at finite temperature
• Exact spectral function of the Tonks-Girardeau gas at finite temperature
• Determinant formula for the field form factor in the anyonic Lieb-Liniger model
• Beyond braid statistics: Constructing a lattice model for anyons with exchange statistics intrinsic to one dimension
• Anyon Quantum Transport and Noise away from Equilibrium
• Nonequilibrium dynamics in one-dimensional strongly interacting two-component gases
• Exact spectral function and nonequilibrium dynamics of the strongly interacting Hubbard model
• Numerical methods and analytic results for one-dimensional strongly interacting spinor gases