Deviations from off-diagonal long-range order in one-dimensional quantum systems

¹ SISSA and INFN, Sezione di Trieste - via Bonomea 265, I-34136 Trieste, Italy
² International Centre for Theoretical Physics (ICTP) - strada Costiera 11, I-34151, Trieste, Italy
³ Institute for Theoretical Physics, Utrecht University - Utrecht, The Netherlands
⁴ CNR-IOM DEMOCRITOS Simulation Center - via Bonomea 265, I-34136 Trieste, Italy

Received: 11 April 2018
Accepted: 18 June 2018

Abstract

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