8 research outputs found
Off-diagonal correlations in one-dimensional anyonic models: A replica approach
We propose a generalization of the replica trick that allows to calculate the
large distance asymptotic of off-diagonal correlation functions in anyonic
models with a proper factorizable ground-state wave-function. We apply this new
method to the exact determination of all the harmonic terms of the correlations
of a gas of impenetrable anyons and to the Calogero Sutherland model. Our
findings are checked against available analytic and numerical results.Comment: 19 pages, 5 figures, typos correcte
One-particle density matrix and momentum distribution function of one-dimensional anyon gases
We present a systematic study of the Green functions of a one-dimensional gas
of impenetrable anyons. We show that the one-particle density matrix is the
determinant of a Toeplitz matrix whose large N asymptotic is given by the
Fisher-Hartwig conjecture. We provide a careful numerical analysis of this
determinant for general values of the anyonic parameter, showing in full
details the crossover between bosons and fermions and the reorganization of the
singularities of the momentum distribution function.
We show that the one-particle density matrix satisfies a Painleve VI
differential equation, that is then used to derive the small distance and large
momentum expansions. We find that the first non-vanishing term in this
expansion is always k^{-4}, that is proved to be true for all couplings in the
Lieb-Liniger anyonic gas and that can be traced back to the presence of a delta
function interaction in the Hamiltonian.Comment: 21 pages, 4 figure
Deviations from off-diagonal long-range order in one-dimensional quantum systems
A quantum system exhibits off-diagonal long-range order (ODLRO) when the largest eigenvalue \u3bb0 of the one-body-density matrix scales as \u3bb0 3c N, where N is the total number of particles. Putting \u3bb0 3c 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 \u3bb0/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