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.

23 pages, no figures; v2: minor revision

References in corpus (32)

• Many-Body Physics with Ultracold Gases
• Realization of a Laughlin quasiparticle interferometer: Observation of fractional statistics
• Dynamical density-density correlations in the one-dimensional Bose gas
• The 1D interacting anyon gas: low-energy properties and Haldane exclusion statistics
• Anyon-fermion mapping and applications to ultracold gases in tight waveguides
• Correlation functions of the one-dimensional attractive Bose gas
• Correlation functions of one-dimensional anyonic fluids
• Mean values of local operators in highly excited Bethe states
• Universal contact for a Tonks-Girardeau gas at finite temperature
• 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
• Analytical expression for a post-quench time evolution of the one-body density matrix of one-dimensional hard-core bosons
• Generalized exclusion statistics and degenerate signature of strongly interacting anyons
• Local Correlations in the Super Tonks-Girardeau Gas
• Bethe Ansatz for 1D interacting anyons
• One-particle density matrix and momentum distribution function of one-dimensional anyon gases
• 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
• Three-body local correlation function in the Lieb-Liniger model: bosonization 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
• Correlation functions of one-dimensional bosons at low temperature
• Correlation functions of one-dimensional strongly interacting two-component gases
• Atom Fock state preparation by trap reduction
• Bethe Ansatz Matrix Elements as Non-Relativistic Limits of Form Factors of Quantum Field Theory
• Correlation functions and momentum distribution of one-dimensional hard-core anyons in optical lattices
• Temperature-driven crossover in the Lieb-Liniger model
• 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