Finite temperature off-diagonal long-range order for interacting bosons
Year: 2020
Authors: Colcelli A., Defenu N., Mussardo G., Trombettoni A.
Autors Affiliation: SISSA, Via Bonomea 265, I-34136 Trieste, Italy; Ist Nazl Fis Nucl, Sez Trieste, Via Bonomea 265, I-34136 Trieste, Italy; Swiss Fed Inst Technol, Inst Theoret Phys, Wolfgang Pauli Str 27, CH-8093 Zurich, Switzerland; Heidelberg Univ, Inst Theoret Phys, D-69120 Heidelberg, Germany; Univ Trieste, Dept Phys, Str Costiera 11, I-34151 Trieste, Italy; CNR IOM DEMOCRITOS Simulat Ctr, Via Bonomea 265, I-34136 Trieste, Italy.
Abstract: Characterizing the scaling with the total particle number (N) of the largest eigenvalue of the one-body density matrix (lambda(0)) provides information on the occurrence of the off-diagonal long-range order (ODLRO) according to the Penrose-Onsager criterion. Setting lambda(0) similar to N-C0, then C-0 = 1 corresponds in ODLRO. The intermediate case, 0 < C-0 < 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 C-0 (and in the corresponding quantities C-k not equal 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 C-k not equal 0 = 0 in the thermodynamic limit. In one dimension it is C-0 = 0 for nonvanishing temperature, while in three dimensions it is C-0 = 1 (C-0 = 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 C-0 near the Berezinskii-Kosterlitz-Thouless temperature TBKT is 7/8. The dependence of C-0 on temperatures between T = 0 (at which C-0 = 1) and TBKT is studied in the different models. An estimate for the (nonperturbative) parameter 4 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 C-0, and correspondingly of the anomalous dimension eta, right below T-BKT in the limit of vanishing interactions. Journal/Review: PHYSICAL REVIEW B
Volume: 102 (18) Pages from: 184510-1 to: 184510-13
More Information: We thank T. Enss, L. Lepori, D. Lundholm, and I. Nandori for discussions and J. Yngvason and M. Hasenbusch for useful correspondence. A.T. acknowledges the kind hospitality at Mathematical physics of anyons and topological states of matter, taking place in Nordita, Stockholm (Sweden), March 2019, where parts of present work have been fruitfully discussed with participants to the conference. This work is supported by the Deut sche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC-2181/1-390900948 (the Heidelberg STRUCTURES Excellence Cluster). N.D. and A.T. acknowledge support from the CNR/MTA Italy-Hungary 2019-2021 Joint Project Strongly interacting systems in confined geometries.KeyWords: Bose-Einstein condensation; Bosons; Eigenvalues and eigenfunctions; Equations of state of gases; Invariance; Statistical mechanicsDOI: 10.1103/PhysRevB.102.184510ImpactFactor: 4.036Citations: 6data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2024-11-10References taken from IsiWeb of Knowledge: (subscribers only)
