A quantum system exhibits off-diagonal long-range order (ODLRO) when the largest eigenvalue λ0 of the one-body-density matrix scales as λ0 ∼ N, where N is the total number of particles. Putting λ0 ∼ NC to define the scaling exponent C, then C = 1 corresponds to ODLRO and C = 0 to the single-particle occupation of the density matrix orbitals. When 0 < C <1, C can be used to quantify deviations from ODLRO. In this paper we study the exponent C 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 C is close to 1, implying a mesoscopic condensation, i.e., a value of the zero temperature "condensate" fraction λ0/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 C = 1 and 0. The behaviour of C for these systems is found to be non-monotonic both with respect to the coupling constant and the statistical parameter.

Deviations from off-diagonal long-range order in one-dimensional quantum systems / Colcelli, A.; Mussardo, G.; Trombettoni, A.. - In: EUROPHYSICS LETTERS. - ISSN 0295-5075. - 122:5(2018), pp. 1-7. [10.1209/0295-5075/122/50006]

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

Colcelli, A.;Mussardo, G.;Trombettoni, A.
2018-01-01

Abstract

A quantum system exhibits off-diagonal long-range order (ODLRO) when the largest eigenvalue λ0 of the one-body-density matrix scales as λ0 ∼ N, where N is the total number of particles. Putting λ0 ∼ NC to define the scaling exponent C, then C = 1 corresponds to ODLRO and C = 0 to the single-particle occupation of the density matrix orbitals. When 0 < C <1, C can be used to quantify deviations from ODLRO. In this paper we study the exponent C 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 C is close to 1, implying a mesoscopic condensation, i.e., a value of the zero temperature "condensate" fraction λ0/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 C = 1 and 0. The behaviour of C for these systems is found to be non-monotonic both with respect to the coupling constant and the statistical parameter.
2018
122
5
1
7
50006
https://iopscience.iop.org/article/10.1209/0295-5075/122/50006/meta
https://arxiv.org/abs/1804.04084
Colcelli, A.; Mussardo, G.; Trombettoni, A.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/88164
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