Ground-state energy and excitation spectrum of the Lieb-Liniger model : accurate analytical results and conjectures about the exact solution

Abstract

We study the ground-state properties and excitation spectrum of the Lieb-Liniger model, i.e. the one-dimensional Bose gas with repulsive contact interactions. We solve the Bethe-Ansatz equations in the thermodynamic limit by using an analytic method based on a series expansion on orthogonal polynomials developed in \cite{Ristivojevic} and push the expansion to an unprecedented order. By a careful analysis of the mathematical structure of the series expansion, we make a conjecture for the analytic exact result at zero temperature and show that the partially resummed expressions thereby obtained compete with accurate numerical calculations. This allows us to evaluate the density of quasi-momenta, the ground-state energy, the local two-body correlation function and Tan's contact. Then, we study the two branches of the excitation spectrum. Using a general analysis of their properties and symmetries, we obtain novel analytical expressions at arbitrary interaction strength which are found to be extremely accurate in a wide range of intermediate to strong interactions.

References in corpus (36)

• Many-Body Physics with Ultracold Gases
• Bosonizing one-dimensional cold atomic gases
• Continuous Matrix Product States for Quantum Fields
• Universal theory of nonlinear Luttinger liquids
• An introduction to integrable techniques for one-dimensional quantum systems
• Dynamical density-density correlations in the one-dimensional Bose gas
• An exactly solvable model of the BCS-BEC crossover
• Dynamical structure factor of one-dimensional Bose gases: experimental signatures of beyond-Luttinger liquid physics
• Universal correlations of trapped one-dimensional impenetrable bosons
• Mean values of local operators in highly excited Bethe states
• Universal contact for a Tonks-Girardeau gas at finite temperature
• Polarizability and dynamic structure factor of the one-dimensional Bose gas near the Tonks-Girardeau limit at finite temperatures
• High-momentum tails as magnetic structure probes for strongly-correlated $SU(\kappa )$ fermionic mixtures in one-dimensional traps
• Spatial nonlocal pair correlations in a repulsive 1D Bose gas
• Local Correlations in the Super Tonks-Girardeau Gas
• Continuous Matrix Product States for Quantum Fields: an Energy Minimization Algorithm
• Exact correlations in the Lieb-Liniger model and detailed balance out-of-equilibrium
• Three-body local correlation function in the Lieb-Liniger model: bosonization approach
• A note on the spin-1/2 XXZ chain concerning its relation to the Bose gas
• Excitation spectrum of bosons in a finite one-dimensional circular waveguide via the Bethe ansatz
• Dynamic structure factor and drag force in a one-dimensional strongly-interacting Bose gas at finite temperature
• Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems
• Local correlations in the attractive 1D Bose gas: from Bethe ansatz to the Gross-Pitaevskii equation
• Dynamical structure factor of one-dimensional hard rods
• Low-energy excitations of a one-dimensional Bose gas with weak contact repulsion
• Tan's contact of a harmonically trapped one-dimensional Bose gas: strong-coupling expansion and conjectural approach at arbitrary interactions
• Unitary dynamics of strongly-interacting Bose gases with time-dependent variational Monte Carlo in continuous space
• One-dimensional multicomponent Fermi gas in a trap: quantum Monte Carlo study
• Motion of an impurity particle in an ultracold quasi-one-dimensional gas of hard-core bosons
• A connection between non-local one-body and local three-body correlations of the Lieb-Liniger model
• Decay of Bogoliubov excitations in one-dimensional Bose gases
• Analytic solutions of the 1D finite coupling delta function Bose gas
• Ground state energy of the $\delta$-Bose and Fermi gas at weak coupling from double extrapolation
• Effective mass of elementary excitations in Galilean-invariant integrable models
• Thermal solitons as revealed by static structure factor
• Thermodynamics of a one-dimensional system of point bosons: comparison of the traditional approach with a new one

Cited by in corpus (36)

• Thermalization near integrability in a dipolar quantum Newton's cradle
• Diffusion in generalized hydrodynamics and quasiparticle scattering
• Generalized Hydrodynamics in the 1D Bose gas: theory and experiments
• Polaron Interactions and Bipolarons in One-Dimensional Bose Gases in the Strong Coupling Regime
• Strongly interacting trapped one-dimensional quantum gases: an exact solution
• Strongly correlated quantum droplets in quasi-1D dipolar Bose gas
• A Pure Confinement Induced Trimer in One-Dimensional Atomic Waveguides
• Thermodynamic behavior of a one-dimensional Bose gas at low temperature
• Tan's contact of a harmonically trapped one-dimensional Bose gas: strong-coupling expansion and conjectural approach at arbitrary interactions
• A connection between non-local one-body and local three-body correlations of the Lieb-Liniger model
• Variational Bethe Ansatz approach for dipolar one-dimensional bosons
• Ultrawide dark solitons and droplet-soliton coexistence in a dipolar Bose gas with strong contact interactions
• Deviations from Off-Diagonal Long-Range Order in One-Dimensional Quantum Systems
• Persistent currents in ultracold gases
• Formation and fragmentation of quantum droplets in a quasi-one dimensional dipolar Bose gas
• Spectrum of elementary excitations in Galilean-invariant integrable models
• Dark solitons revealed in Lieb-Liniger eigenstates
• Gaussian Continuous Tensor Network States for Simple Bosonic Field Theories
• Polarization angle dependence of the breathing modes in confined one-dimensional dipolar bosons
• Order indices and entanglement production in quantum systems
• Classical and quantum metrology of the Lieb-Liniger model
• Finite Temperature Off-Diagonal Long-Range Order for Interacting Bosons
• Quasimomentum of an elementary excitation for a system of point bosons under zero boundary conditions
• Scaling limits of bosonic ground states, from many-body to nonlinear Schr{ö}dinger
• Beyond Gross-Pitaevskii equation for 1D gas: quasiparticles and solitons
• Momentum reconstruction and contact of the one-dimensional Bose-Fermi mixture
• Gradient corrections to the local density approximation in the one-dimensional Bose gas
• Effect of transverse confinement on a quasi-one dimensional dipolar Bose gas
• Evolution of static and dynamical density correlations in a one-dimensional soft-core gas from the Tonks-Girardeau limit to a clustering fluid
• Effective theory for strongly attractive one-dimensional fermions
• Phase diagram and elementary excitations of strongly interacting droplets with non-local interactions
• Thermodynamics at zero temperature: inequalities for the ground state of a quantum many-body system
• Time-dependent variational Monte Carlo study of the dynamic response of bosons in an optical lattice
• Hole-induced anomaly in the thermodynamic behavior of a one-dimensional Bose gas
• Mesoscopic electron transport and atomic gases, a review of Frank W. J. Hekking's scientific work
• Love--Lieb integral equations: applications, theory, approximations, and computation