Bethe Ansatz for 1D interacting anyons

Abstract

This article gives a pedagogic derivation of the Bethe Ansatz solution for 1D interacting anyons. This includes a demonstration of the subtle role of the anyonic phases in the Bethe Ansatz arising from the anyonic commutation relations. The thermodynamic Bethe Ansatz equations defining the temperature dependent properties of the model are also derived, from which some groundstate properties are obtained.

22 pages, two references added, small improvements to text

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Cited by in corpus (40)

• Correlation Functions of One-Dimensional Lieb-Liniger Anyons
• Junctions of anyonic Luttinger wires
• Ground-state properties of hard-core anyons in one-dimensional optical lattices
• Exact dynamics following an interaction quench in a one-dimensional anyonic gas
• Exact solution of the p+ip pairing Hamiltonian and a hierarchy of integrable models
• Dynamical properties of hard-core anyons in one-dimensional optical lattices
• Ground-state properties of anyons in a one-dimensional lattice
• Quantum Walks of Two Interacting Anyons in 1D Optical Lattices
• 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
• Entanglement between particle partitions in itinerant many-particle states
• One-particle density matrix of a trapped Lieb-Liniger anyonic 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
• Off-diagonal correlations in one-dimensional anyonic models: A replica approach
• Quantum entanglement of particles on a ring with fractional statistics
• Correlation functions of one-dimensional strongly interacting two-component gases
• Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the Lieb-Liniger model
• 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
• One-Dimensional Impenetrable Anyons in Thermal Equilibrium. IV. Large Time and Distance Asymptotic Behavior of the Correlation Functions
• Deviations from Off-Diagonal Long-Range Order in One-Dimensional Quantum Systems
• Quantum Inverse Scattering Method with anyonic grading
• Correlation functions and momentum distribution of one-dimensional hard-core anyons in optical lattices
• One-Body Density Matrix and Momentum Distribution of Strongly Interacting One-Dimensional Spinor Quantum Gases
• Condensation of Anyons in Frustrated Quantum Magnets
• Quantum phase transition in a multicomponent anyonic Lieb-Liniger model
• Non-equilibrium dynamics of the anyonic Tonks-Girardeau gas at finite temperature
• Large-Distance Asymptotic Behavior of the Correlation Functions of 1D Impenetrable Anyons at Finite Temperatures
• Something interacting and solvable in 1d
• One-dimensional hard-core anyon gas in a harmonic trap at finite temperature
• Quantum Integrable 1D anyonic Models: Construction through Braided Yang-Baxter Equation
• Determinant formula for the field form factor in the anyonic Lieb-Liniger model
• Generalized Bose-Fermi mapping and strong coupling ansatz wavefunction for one dimensional strongly interacting spinor quantum gases
• Approaching off-diagonal long-range order for 1+1-dimensional relativistic anyons
• Dualities for anyons
• Thermodynamics of Statistical Anyons
• Chirally-protected state manipulation by tuning one-dimensional statistics
• Quench Dynamics of Anyon Tonks-Girardeau Gases
• Necessity of orthogonal basis vectors for the two-anyon problem in one-dimensional lattice