The 1D interacting anyon gas: low-energy properties and Haldane exclusion statistics

Abstract

The low energy properties of the one-dimensional anyon gas with $\delta$-function interaction are discussed in the context of its Bethe ansatz solution. It is found that the anyonic statistical parameter and the dynamical coupling constant induce Haldane exclusion statistics interpolating between bosons and fermions. Moreover, the anyonic parameter may trigger statistics beyond Fermi statistics for which the exclusion parameter $\alpha$ is greater than one. The Tonks-Girardeau and the weak coupling limits are discussed in detail. The results support the universal role of $\alpha$ in the dispersion relations.

4 pages, 2 figures, minor corrections, to appear in Phys. Rev. Lett

References in corpus (13)

• Topologically-Protected Qubits from a Possible Non-Abelian Fractional Quantum Hall State
• 1/2-Anyons in small atomic Bose-Einstein condensates
• Realization of a Laughlin quasiparticle interferometer: Observation of fractional statistics
• Beyond Tonks-Girardeau: strongly correlated regime in quasi-one-dimensional Bose gases
• Braid Topologies for Quantum Computation
• Exact Dynamical Correlation Functions of Calogero-Sutherland Model and One-Dimensional Fractional Statistics
• Thermodynamics of an one-dimensional ideal gas with fractional exclusion statistics
• Exact solution of double-delta function Bose gas through interacting anyon gas
• Fractional Statistics in One-Dimension: View From An Exactly Solvable Model
• Signatures of fractional statistics in noise experiments in quantum Hall fluids
• Evidence for the super Tonks-Girardeau gas
• Quasi-one-dimensional Bose gases with large scattering length
• Thomas-Fermi Method For Particles Obeying Generalized Exclusion Statistics

Cited by in corpus (94)

• Statistically induced Phase Transitions and Anyons in 1D Optical Lattices
• The Anyon Hubbard Model in One-Dimensional Optical Lattices
• Phase Transitions and Pairing Signature in Strongly Attractive Fermi Atomic Gases
• Fermionization and bosonization of expanding 1D anyonic fluids
• Floquet realization and signatures of one-dimensional anyons in an optical lattice
• Emergence of curved light-cones in a class of inhomogeneous Luttinger liquids
• Correlation functions of one-dimensional anyonic fluids
• An Interaction-Driven Many-Particle Quantum Heat Engine: Universal Behavior
• Ferromagnetic behaviour in the strongly interacting two-component Bose gas
• Correlation Functions of One-Dimensional Lieb-Liniger Anyons
• Junctions of anyonic Luttinger wires
• Ground-state properties of one-dimensional anyon gases
• Ground-state properties of hard-core anyons in one-dimensional optical lattices
• Generalized exclusion statistics and degenerate signature of strongly interacting anyons
• Transition from Tonks-Girardeau gas to super-Tonks-Girardeau gas as an exact many-body dynamics problem
• 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
• 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
• Ground-state properties of anyons in a one-dimensional lattice
• Quantum Walks of Two Interacting Anyons in 1D Optical Lattices
• Bosonic continuum theory of one-dimensional lattice anyons
• 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
• Asymmetric Particle Transport and Light-Cone Dynamics Induced by Anyonic Statistics
• Entanglement between particle partitions in itinerant many-particle states
• Strongly interacting mesoscopic systems of anyons in one dimension
• Anyonic tight-binding models of parafermions and of fractionalized fermions
• Critical points of the anyon-Hubbard model
• One-particle density matrix of a trapped Lieb-Liniger anyonic gas
• Anyons from Three-Body Hard-Core Interactions in One Dimension
• One-dimensional anyons with competing $\delta$-function and derivative $\delta$-function potentials
• 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
• Off-diagonal correlations in one-dimensional anyonic models: A replica approach
• Quantum entanglement of particles on a ring with fractional statistics
• Topological Exchange Statistics in One Dimension
• Exactly-solvable system of one-dimensional trapped bosons with short and long-range interactions
• Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the Lieb-Liniger model
• Correlation functions of one-dimensional strongly interacting two-component gases
• Probing the exchange statistics of one-dimensional anyon models
• Ground state properties of hard-core anyons in a harmonic potential
• 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
• One-Dimensional Impenetrable Anyons in Thermal Equilibrium. IV. Large Time and Distance Asymptotic Behavior of the Correlation Functions
• Quantum Inverse Scattering Method with anyonic grading
• Fermionization and fractional statistics in the strongly interacting one-dimensional Bose gas
• Creating anyons from photons using a nonlinear resonator lattice subject to dynamic modulation
• Correlation functions and momentum distribution of one-dimensional hard-core anyons in optical lattices
• Exact ground states of quantum many-body systems under confinement
• Multiple Exclusion Statistics
• Condensation of Anyons in Frustrated Quantum Magnets
• Weakly nonadditive Polychronakos statistics
• Three-body interaction effects on the ground state of one-dimensional anyons
• One-Body Density Matrix and Momentum Distribution of Strongly Interacting One-Dimensional Spinor Quantum Gases
• Quantum phase transition in a multicomponent anyonic Lieb-Liniger model
• Non-equilibrium dynamics of the anyonic Tonks-Girardeau gas at finite temperature
• Electric circuit emulation of topological transitions driven by quantum statistics
• Exact results for polaron and molecule in one-dimensional spin-1/2 Fermi gas
• Large-Distance Asymptotic Behavior of the Correlation Functions of 1D Impenetrable Anyons at Finite Temperatures
• Statistics tuned entanglement of the boundary modes in coupled Su-Schrieffer-Heeger chains
• Exact Dynamical Correlations of Hard-Core Anyons in One-Dimensional Lattices
• Anyonic Liquids in Nearly Saturated Spin Chains
• One-Dimensional Quantum Systems with Ground-State of Jastrow Form Are Integrable
• Non-conformal asymptotic behavior of the time-dependent field-field correlators of 1D anyons
• Evidences for interaction-induced Haldane fractional exclusion statistics in one and higher dimensions
• Statistics-tuned phases of pseudofermions in one dimension
• Quasimomentum distribution and expansion of an anyonic gas
• Fractional exclusion statistics and thermodynamics of the Hubbard chain in the spin-incoherent Luttinger liquid regime
• Exact spectral function of the Tonks-Girardeau gas at finite temperature
• Determinant formula for the field form factor in the anyonic Lieb-Liniger model
• Quantum Alchemy and Universal Orthogonality Catastrophe in One-Dimensional Anyons
• Quantum Integrable 1D anyonic Models: Construction through Braided Yang-Baxter Equation
• q-Boson in Quantum Integrable Systems
• Beyond braid statistics: Constructing a lattice model for anyons with exchange statistics intrinsic to one dimension
• Revisiting the Fermion Sign Problem from the Structure of Lee-Yang Zeros. I. The Form of Partition Function for Indistinguishable Particles and Its Zeros at 0~K
• Approaching off-diagonal long-range order for 1+1-dimensional relativistic anyons
• Generalized Bose-Fermi mapping and strong coupling ansatz wavefunction for one dimensional strongly interacting spinor quantum gases
• Bosonization study of a generalized statistics model with four Fermi points
• Dualities for anyons
• Thermodynamics of Statistical Anyons
• Nonequilibrium dynamics in one-dimensional strongly interacting two-component gases
• Momentum distribution and non-local high order correlation functions of 1D strongly interacting Bose gas
• Fermionic anyons: entanglement and quantum computation from a resource-theoretic perspective
• Taxonomy of integrable and ground-state solvable models: Jastrow wave functions on graphs and parent Hamiltonians
• Universal properties and dynamical bosonization of strongly interacting one-dimensional anyons
• Quench Dynamics of Anyon Tonks-Girardeau Gases
• Love--Lieb integral equations: applications, theory, approximations, and computation
• Necessity of orthogonal basis vectors for the two-anyon problem in one-dimensional lattice
• Boson-Anyon-Fermion Mapping and Anyon Construction in One Dimension
• One-dimensional anyons in relativistic field theory
• Triple Antidot Molecules