Deviations from Off-Diagonal Long-Range Order in One-Dimensional Quantum Systems

Abstract

A quantum system exhibits off-diagonal long-range order (ODLRO) when the largest eigenvalue ${\lambda }_0$ of the one-body-density matrix scales as ${\lambda }_0\sim N$, where $N$ is the total number of particles. Putting ${\lambda }_0\sim N^{\mathcal{C}}$ to define the scaling exponent $\mathcal{C}$, then $\mathcal{C}=1$ corresponds to ODLRO and $\mathcal{C}=0$ to the single-particle occupation of the density matrix orbitals. When $0<\mathcal{C}<1$, $\mathcal{C}$ can be used to quantify deviations from ODLRO. In this paper we study the exponent $\mathcal{C}$ in a variety of one-dimensional bosonic and anyonic quantum systems. For the $1D$ Lieb-Liniger Bose gas we find that for small interactions $\mathcal{C}$ is close to $1$, implying a mesoscopic condensation, i.e. a value of the "condensate" fraction ${\lambda }_0/N$ appreciable at finite values of $N$ (as the ones in experiments with $1D$ ultracold atoms). $1D$ anyons provide the possibility to fully interpolate between $\mathcal{C}=1$ and $0$. The behaviour of $\mathcal{C}$ for these systems is found to be non-monotonic both with respect to the coupling constant and the statistical parameter.

arXiv comment8 pages, 4 figures

References in corpus (25)

• The density-matrix renormalization group
• Atomic Scattering in Presence of an External Confinement and a Gas of Impenetrable Bosons
• One dimensional Bosons: From Condensed Matter Systems to Ultracold Gases
• Regimes of quantum degeneracy in trapped 1D gases
• Extension of Bogoliubov theory to quasi-condensates
• Short-Distance Correlation Properties of the Lieb-Liniger System and Momentum Distributions of Trapped One-Dimensional Atomic Gases
• An introduction to integrable techniques for one-dimensional quantum systems
• Dynamical density-density correlations in the one-dimensional Bose gas
• Exact solution of double-delta function Bose gas through interacting anyon gas
• The 1D interacting anyon gas: low-energy properties and Haldane exclusion statistics
• Finite one dimensional impenetrable Bose systems: Occupation numbers
• Finite temperature correlations in the Lieb-Liniger 1D Bose gas
• Local correlations in a strongly interacting 1D Bose gas
• Correlation functions of one-dimensional anyonic fluids
• Exact prefactors in static and dynamic correlation functions of 1D quantum integrable models: applications to the Calogero-Sutherland, Lieb-Liniger and XXZ models
• Nonuniversal prefactors in correlation functions of 1D quantum liquids
• Ground-state properties of one-dimensional anyon gases
• Bethe Ansatz for 1D interacting anyons
• Ground-state energy and excitation spectrum of the Lieb-Liniger model : accurate analytical results and conjectures about the exact solution
• One-particle density matrix and momentum distribution function of one-dimensional anyon gases
• Correlation lengths of the repulsive one-dimensional Bose gas
• Ground state properties of hard-core anyons in a harmonic potential
• Analytic solutions of the 1D finite coupling delta function Bose gas
• Energy-pressure relation for low-dimensional gases
• Density ripples in expanding low-dimensional gases as a probe of correlations

Cited by in corpus (13)

• One-dimensional mixtures of several ultracold atoms: a review
• Strongly interacting trapped one-dimensional quantum gases: an exact solution
• Anyonic tight-binding models of parafermions and of fractionalized fermions
• One-particle density matrix of a trapped Lieb-Liniger anyonic gas
• Correlation functions of one-dimensional strongly interacting two-component gases
• Universal off-diagonal long-range order behaviour for a trapped Tonks-Girardeau gas
• Non-equilibrium dynamics of the anyonic Tonks-Girardeau gas at finite temperature
• Strange correlators for topological quantum systems from bulk-boundary correspondence
• Order indices and entanglement production in quantum systems
• Exact results of dynamical structure factor of Lieb-Liniger model
• Finite Temperature Off-Diagonal Long-Range Order for Interacting Bosons
• Approaching off-diagonal long-range order for 1+1-dimensional relativistic anyons
• One-body dynamical correlation function of Lieb-Liniger model at finite temperature