Universal scaling of density and momentum distributions in Lieb-Liniger gases

Abstract

We present an exact numerical study of the scaling of density and momentum distribution functions of harmonically trapped one-dimensional bosons with repulsive contact interactions at zero and finite temperatures. We use path integral quantum Monte Carlo with worm updates in our calculations at finite interaction strengths, and the Bose-Fermi mapping in the Tonks-Girardeau regime. We discuss the homogeneous case and, within the local density approximation, use it to motivate the scaling in the presence of a harmonic trap. For the momentum distribution function, we pay special attention to the high momentum tails and their $k^{-4}$ asymptotic behavior.

13 pages,12 figures

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• The Inhomogeneous Gaussian Free Field, with application to ground state correlations of trapped 1d Bose gases
• Tan's Contact for Trapped Lieb-Liniger Bosons at Finite Temperature
• One-particle density matrix of trapped one-dimensional impenetrable bosons from conformal invariance
• Relaxation of Bosons in One Dimension and the Onset of Dimensional Crossover
• Quantum Quench in a Harmonically Trapped One-Dimensional Bose Gas
• Expansion of one-dimensional lattice hard-core bosons at finite temperature
• Universal Tan relations for quantum gases in one dimension
• Rapidity and momentum distributions of 1D dipolar quantum gases
• A coordinate Bethe ansatz approach to the calculation of equilibrium and nonequilibrium correlations of the one-dimensional Bose gas
• Tan's contact of a harmonically trapped one-dimensional Bose gas: strong-coupling expansion and conjectural approach at arbitrary interactions
• One-dimensional multicomponent Fermi gas in a trap: quantum Monte Carlo study
• Higher-order local and non-local correlations for 1D strongly interacting Bose gas
• Beyond-Luttinger-Liquid thermodynamics of a one-dimensional contact repulsive Bose gas
• Information measures for a local quantum phase transition: Lattice fermions in a one-dimensional harmonic trap
• Analytic thermodynamic properties of the Lieb-Liniger gas
• Self-Pinning Transition of a Tonks-Girardeau Gas in a Bose-Einstein Condensate
• Impenetrable SU(N) fermions in one-dimensional lattices
• Spatial entanglement entropy in the ground state of the Lieb-Liniger model
• Correlation properties of a one-dimensional repulsive Bose gas at finite temperature
• Scaling properties of the Tan's contact: embedding pairs and correlation effect in the Tonks limit
• Tan's contact scaling behaviour for trapped Lieb-Liniger bosons: from two to many
• Density-Matrix Renormalization Group for Continuous Quantum Systems
• Full Counting Statistics of the momentum occupation numbers of the Tonks-Girardeau gas
• Exact results of dynamical structure factor of Lieb-Liniger model
• Spin-incoherent Luttinger liquid of one-dimensional spin-1 Tonks-Girardeau Bose gas: Spin-dependent properties
• Spin-incoherent Luttinger liquid of one-dimensional SU($\kappa$) fermions
• One-particle density matrix and momentum distribution of the out-of-equilibrium 1D Tonks-Girardeau gas: Analytical results at large $N$
• Finite temperature contact for SU(2) fermions trapped in a 1D harmonic confinement
• Spin-incoherent one-dimensional spin-1 Bose Luttinger liquid
• Thermal fading of the $1/k^4$-tail of the momentum distribution induced by the hole anomaly
• Multiband Effects and the Bose-Hubbard Model in One-Dimensional Lattices
• One-body dynamical correlation function of Lieb-Liniger model at finite temperature
• Statistical properties of the momentum occupation numbers of the Tonks-Girardeau gas in a harmonic trap
• Momentum distribution and non-local high order correlation functions of 1D strongly interacting Bose gas
• $n$-body Correlation of Tonks-Girardeau Gas
• One-body correlations and momentum distributions of trapped one-dimensional Bose gases at finite temperature
• Exotic critical states as fractional Fermi seas in the one-dimensional Bose gas