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 (36)

• 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
• Dynamical density-density correlations in the one-dimensional Bose gas
• Universal Properties of the Ultra-Cold Fermi Gas
• The 1D interacting anyon gas: low-energy properties and Haldane exclusion statistics
• Two-dimensional dynamics of expansion of a degenerate Bose gas
• Anyon-fermion mapping and applications to ultracold gases in tight waveguides
• Fermionization and bosonization of expanding 1D anyonic fluids
• Green's function for magnetically incoherent interacting electrons in one dimension
• Universal correlations of trapped one-dimensional impenetrable bosons
• Correlation functions of one-dimensional anyonic fluids
• Universal properties of Fermi gases in arbitrary dimensions
• Correlation Functions of One-Dimensional Lieb-Liniger Anyons
• Ground-state properties of one-dimensional anyon gases
• Junctions of anyonic Luttinger wires
• 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
• One-particle density matrix and momentum distribution function of one-dimensional anyon gases
• Impurity Green's function of a one-dimensional Fermi-gas
• Entanglement properties and moment distributions of a system of hard-core anyons on a ring
• Long-distance behavior of temperature correlation functions in the one-dimensional Bose gas
• Statistical Phases and Momentum Spacings for One-Dimensional Anyons
• 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
• Universal Tan relations for quantum gases in one dimension
• One-dimensional anyons with competing $\delta$-function and derivative $\delta$-function potentials
• Finite-temperature correlations in a quantum spin chain near saturation
• Quantum Inverse Scattering Method with anyonic grading
• Condensation of Anyons in Frustrated Quantum Magnets
• Quantum phase transition in a multicomponent anyonic Lieb-Liniger model
• Anyonic Liquids in Nearly Saturated Spin Chains
• Quasimomentum distribution and expansion of an anyonic gas
• Dualities for anyons
• One-particle irreducible density matrix for the spin disordered infinite $U$ Hubbard chain

Cited by in corpus (1)

• Non-equilibrium dynamics of the anyonic Tonks-Girardeau gas at finite temperature