Determinant formula for the field form factor in the anyonic Lieb-Liniger model

Abstract

We derive an exact formula for the field form factor in the anyonic Lieb-Liniger model, valid for arbitrary values of the interaction $c$, anyonic parameter $\kappa$, and number of particles $N$. Analogously to the bosonic case, the form factor is expressed in terms of the determinant of a $N\times N$ matrix, whose elements are rational functions of the Bethe quasimomenta but explicitly depend on $\kappa$. The formula is efficient to evaluate, and provide an essential ingredient for several numerical and analytical calculations. Its derivation consists of three steps. First, we show that the anyonic form factor is equal to the bosonic one between two special off-shell Bethe states, in the standard Lieb-Liniger model. Second, we characterize its analytic properties and provide a set of conditions that uniquely specify it. Finally, we show that our determinant formula satisfies these conditions.

arXiv comment23 pages, no figures; v2: minor revision

References in corpus (90)

• Many-Body Physics with Ultracold Gases
• Nonequilibrium dynamics of closed interacting quantum systems
• One dimensional Bosons: From Condensed Matter Systems to Ultracold Gases
• Time evolution of local observables after quenching to an integrable model
• Solution for an interaction quench in the Lieb-Liniger Bose gas
• Stability and phase coherence of trapped 1D Bose gases
• Pair correlations in a finite-temperature 1D Bose gas
• Short-Distance Correlation Properties of the Lieb-Liniger System and Momentum Distributions of Trapped One-Dimensional Atomic Gases
• Realization of a Laughlin quasiparticle interferometer: Observation of fractional statistics
• Computation of dynamical correlation functions of Heisenberg chains in a field
• The Quench Action
• Statistically induced Phase Transitions and Anyons in 1D Optical Lattices
• Dynamical density-density correlations in the one-dimensional Bose gas
• Exact solution of double-delta function Bose gas through interacting anyon gas
• Computation of dynamical correlation functions of Heisenberg chains: the gapless anisotropic regime
• The 1D interacting anyon gas: low-energy properties and Haldane exclusion statistics
• One-particle dynamical correlations in the one-dimensional Bose gas
• Anyons and Chiral Solitons on a Line
• Exact local correlations and full counting statistics for arbitrary states of the one-dimensional interacting Bose gas
• The Anyon Hubbard Model in One-Dimensional Optical Lattices
• Multi-particle bound state formation following a quantum quench to the one-dimensional Bose gas with attractive interactions
• Finite temperature correlations in the Lieb-Liniger 1D Bose gas
• Anyon-fermion mapping and applications to ultracold gases in tight waveguides
• High-momentum tail in the Tonks gas under harmonic confinement
• Determinant representation for dynamical correlation functions of the Quantum nonlinear Schrödinger equation
• Correlation functions of the one-dimensional attractive Bose gas
• Exact steady states for quantum quenches in integrable Heisenberg spin chains
• Signatures of fractional statistics in noise experiments in quantum Hall fluids
• Expectation Values in the Lieb-Liniger Bose Gas
• 1D Lieb-Liniger Bose Gas as Non-Relativistic Limit of the Sinh-Gordon Model
• Correlation functions of integrable models: a description of the ABACUS algorithm
• Floquet realization and signatures of one-dimensional anyons in an optical lattice
• Local correlations in a strongly interacting 1D Bose gas
• Exact three-body local correlations for excited states of the 1D Bose gas
• Correlation functions of one-dimensional anyonic fluids
• Nonequilibrium dynamics of one-dimensional hard-core anyons following a quench: Complete relaxation of one-body observables
• Exact prefactors in static and dynamic correlation functions of 1D quantum integrable models: applications to the Calogero-Sutherland, Lieb-Liniger and XXZ models
• From GPE to KPZ: finite temperature dynamical structure factor of the 1D Bose gas
• Mean values of local operators in highly excited Bethe states
• Universal contact for a Tonks-Girardeau gas at finite temperature
• Nonuniversal prefactors in correlation functions of 1D quantum liquids
• Local correlations in the 1D Bose gas from a scaling limit of the XXZ chain
• Quantum quenches to the attractive one-dimensional Bose gas: exact results
• Correlation Functions of One-Dimensional Lieb-Liniger Anyons
• Ground-state properties of one-dimensional anyon gases
• Spatial nonlocal pair correlations in a repulsive 1D Bose gas
• Junctions of anyonic Luttinger wires
• Exact Results for Three-Body Correlations in a Degenerate One-Dimensional Bose Gas
• Analytical expression for a post-quench time evolution of the one-body density matrix of one-dimensional hard-core bosons
• Relaxation dynamics of local observables in integrable systems
• Generalized exclusion statistics and degenerate signature of strongly interacting anyons
• Local Correlations in the Super Tonks-Girardeau Gas
• Bethe Ansatz for 1D interacting anyons
• Exact dynamics following an interaction quench in a one-dimensional anyonic gas
• Dynamical properties of hard-core anyons in one-dimensional optical lattices
• The Inhomogeneous Gaussian Free Field, with application to ground state correlations of trapped 1d Bose gases
• 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
• One-particle density matrix of trapped one-dimensional impenetrable bosons from conformal invariance
• Entanglement properties and moment distributions of a system of hard-core anyons on a ring
• Exact numerical simulations of a one-dimensional, trapped Bose gas
• Long-distance behavior of temperature correlation functions in the one-dimensional Bose gas
• Bosonization at Finite Temperature and Anyon Condensation
• Three-body local correlation function in the Lieb-Liniger model: bosonization approach
• 1D generalized statistics gas: A gauge theory approach
• One-Dimensional Impenetrable Anyons in Thermal Equilibrium. I. Anyonic Generalization of Lenard's Formula
• One-Dimensional Impenetrable Anyons in Thermal Equilibrium. II. Determinant Representation for the Dynamic Correlation Functions
• Coulomb blockade of anyons
• Strongly interacting mesoscopic systems of anyons in one dimension
• The form factors in the finite volume
• Exact formulas for the form factors of local operators in the Lieb-Liniger model
• Tan's contact of a harmonically trapped one-dimensional Bose gas: strong-coupling expansion and conjectural approach at arbitrary interactions
• Correlation lengths of the repulsive one-dimensional Bose gas
• Correlation functions of one-dimensional bosons at low temperature
• Higher-order local and non-local correlations for 1D strongly interacting Bose gas
• One-body reduced density matrix of trapped impenetrable anyons in one dimension
• Anyons and the Bose-Fermi duality in the finite-temperature Thirring model
• Off-diagonal correlations in one-dimensional anyonic models: A replica approach
• Correlation functions of one-dimensional strongly interacting two-component gases
• Ground state properties of hard-core anyons in a harmonic potential
• Bethe Ansatz Matrix Elements as Non-Relativistic Limits of Form Factors of Quantum Field Theory
• Atom Fock state preparation by trap reduction
• Finite-Temperature Behavior of an Inter-species Fermionic Superfluid with Population Imbalance
• One-Dimensional Impenetrable Anyons in Thermal Equilibrium. III. Large distance asymptotics of the space correlations
• One-Dimensional Impenetrable Anyons in Thermal Equilibrium. IV. Large Time and Distance Asymptotic Behavior of the Correlation Functions
• Correlation functions and momentum distribution of one-dimensional hard-core anyons in optical lattices
• Large-Distance Asymptotic Behavior of the Correlation Functions of 1D Impenetrable Anyons at Finite Temperatures
• Temperature-driven crossover in the Lieb-Liniger model
• Adjacent Spin Operator Dynamical Structure Factor of the S=1/2 Heisenberg Chain
• Current algebra, statistical mechanics and quantum models

Cited by in corpus (4)

• One-particle density matrix of a trapped Lieb-Liniger anyonic gas
• Non-equilibrium dynamics of the anyonic Tonks-Girardeau gas at finite temperature
• Beyond braid statistics: Constructing a lattice model for anyons with exchange statistics intrinsic to one dimension
• Nonequilibrium dynamics in one-dimensional strongly interacting two-component gases