2005/12/31 by G. E. Astrakharchik, D. M. Gangardt, Yu. E. Lozovik +2
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Cold Atom Physics and Bose-Einstein Condensates #Correlation function (quantum field theory) #Crossover #Density matrix #Diagonal #Distribution (mathematics) #Distribution function #Feynman diagram #Geometry #Mathematical analysis #Mathematical physics #Mathematics #Monte Carlo method #Nonlinear Waves and Solitons #Phase (matter) #Phase diagram #Physics #Quantum #Quantum mechanics #Range (aeronautics) #Statistical physics #Statistics #cond-mat.mes-hall #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.74.021105
published as Phys. Rev. E 74, 021105 (2006) · 17 pages, 7 figures
arxiv created 2006/07/21 · openalex publication_date 2006/08/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study correlation functions of the Calogero-Sutherland model in the whole range of the interaction parameter. Using the replica method we obtain analytical expressions for the long-distance asymptotics of the one-body density matrix in addition to the previously derived asymptotics of the pair-distribution function [D.M. Gangardt and A. Kamenev, Nucl. Phys. B 610, 578 (2001)]. The leading analytic and nonanalytic terms in the short-distance expansion of the one-body density matrix are discussed. Numerical results for these correlation functions are obtained using Monte Carlo techniques for all distances. The momentum distribution and static structure factor are calculated. The potential and kinetic energies are obtained using the Hellmann-Feynman theorem. Perfect agreement is found between the analytical expressions and numerical data. These results allow for the description of physical regimes of the Calogero-Sutherland model. The zero temperature phase diagram is found to be of a crossover type and includes quasicondensation, quasicrystallization and quasisupersolid regimes.