2003/07/31 by M A Cazalilla, M. A. Cazalilla · 5 citations
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Physics of Superconductivity and Magnetism #Quantum many-body systems #cond-mat.mes-hall #cond-mat.stat-mech
paper · pdf · doi:10.1088/0953-4075/37/7/051
published as Journal of Physics B: AMOP 37, S1-S47 (2004) · 39 pages + 14 EPS figures; typos corrected, references updated
arxiv created 2003/10/30 · openalex publication_date 2004/03/24 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
We present results for the long-distance asymptotics of correlation functions of mesoscopic one-dimensional systems with periodic and open (Dirichlet) boundary conditions, as well as at finite temperature in the thermodynamic limit. The results are obtained using Haldane's harmonic-fluid approach (also known as 'bosonization'), and are valid for both bosons and fermions, in weakly and strongly interacting regimes. The harmonic-fluid approach and the method of computing the correlation functions using conformal transformations are explained in great detail. As an application relevant to one-dimensional systems of cold atomic gases, we consider the model of bosons interacting with a zero-range potential. The Luttinger-liquid parameters are obtained from the exact solution by solving the Bethe-ansatz equations in finite-size systems. The range of applicability of the approach is discussed, and the prefactor of the one-body density matrix of bosons is fixed by finding an appropriate parametrization of the weak-coupling result. The formula thus obtained is shown to be accurate, when compared with recent diffusion Monte Carlo calculations, within less than 10%. The experimental implications of these results for Bragg scattering experiments at low and high momenta are also discussed.