Finite temperature off-diagonal long-range order for interacting bosons
Characterizing the scaling with the total particle number (N) of the largest eigenvalue of the one-body density matrix (λ0) provides information on the occurrence of the off-diagonal long-range order (ODLRO) according to the Penrose-Onsager criterion. Setting λ0∼NC0, then C0=1 corresponds in ODLRO....
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| Hauptverfasser: | , , , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
17 November 2020
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| In: |
Physical review
Year: 2020, Jahrgang: 102, Heft: 18 |
| ISSN: | 2469-9969 |
| DOI: | 10.1103/PhysRevB.102.184510 |
| Online-Zugang: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1103/PhysRevB.102.184510 Verlag, lizenzpflichtig, Volltext: https://link.aps.org/doi/10.1103/PhysRevB.102.184510 
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| Verfasserangaben: | A. Colcelli, N. Defenu, G. Mussardo, and A. Trombettoni |
| Zusammenfassung: | Characterizing the scaling with the total particle number (N) of the largest eigenvalue of the one-body density matrix (λ0) provides information on the occurrence of the off-diagonal long-range order (ODLRO) according to the Penrose-Onsager criterion. Setting λ0∼NC0, then C0=1 corresponds in ODLRO. The intermediate case, 0<C0<1, corresponds in translational invariant systems to the power-law decaying of (nonconnected) correlation functions and it can be seen as identifying quasi-long-range order. The goal of the present paper is to characterize the ODLRO properties encoded in C0 (and in the corresponding quantities Ck≠0 for excited natural orbitals) exhibited by homogeneous interacting bosonic systems at finite temperature for different dimensions in presence of short-range repulsive potentials. We show that Ck≠0=0 in the thermodynamic limit. In one dimension it is C0=0 for nonvanishing temperature, while in three dimensions it is C0=1 (C0=0) for temperatures smaller (larger) than the Bose-Einstein critical temperature. We then focus our attention to D=2, studying the XY and the Villain models, and the weakly interacting Bose gas. The universal value of C0 near the Berezinskii-Kosterlitz-Thouless temperature TBKT is 7/8. The dependence of C0 on temperatures between T=0 (at which C0=1) and TBKT is studied in the different models. An estimate for the (nonperturbative) parameter ξ entering the equation of state of the two-dimensional Bose gases is obtained using low-temperature expansions and compared with the Monte Carlo result. We finally discuss a “double jump” behavior for C0, and correspondingly of the anomalous dimension η, right below TBKT in the limit of vanishing interactions. |
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| Beschreibung: | Gesehen am 14.01.2020 |
| Beschreibung: | Online Resource |
| ISSN: | 2469-9969 |
| DOI: | 10.1103/PhysRevB.102.184510 |