10 research outputs found
One-dimensional anyons with competing -function and derivative -function potentials
We propose an exactly solvable model of one-dimensional anyons with competing
-function and derivative -function interaction potentials. The
Bethe ansatz equations are derived in terms of the -particle sector for the
quantum anyonic field model of the generalized derivative nonlinear
Schr\"{o}dinger equation. This more general anyon model exhibits richer physics
than that of the recently studied one-dimensional model of -function
interacting anyons. We show that the anyonic signature is inextricably related
to the velocities of the colliding particles and the pairwise dynamical
interaction between particles.Comment: 9 pages, 2 figures, minor changes, references update
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
Time-dependent correlation function of the Jordan-Wigner operator as a Fredholm determinant
We calculate a correlation function of the Jordan-Wigner operator in a class
of free-fermion models formulated on an infinite one-dimensional lattice. We
represent this function in terms of the determinant of an integrable Fredholm
operator, convenient for analytic and numerical investigations. By using Wick's
theorem, we avoid the form-factor summation customarily used in literature for
treating similar problems.Comment: references added, introduction and conclusion modified, version
accepted for publication in J. Stat. Mec
Quantum Inverse Scattering Method with anyonic grading
We formulate the Quantum Inverse Scattering Method for the case of anyonic
grading. This provides a general framework for constructing integrable models
describing interacting hard-core anyons. Through this method we reconstruct the
known integrable model of hard core anyons associated with the XXX model, and
as a new application we construct the anyonic model. The energy spectrum
for each model is derived by means of a generalisation of the algebraic Bethe
ansatz. The grading parameters implementing the anyonic signature give rise to
sector-dependent phase factors in the Bethe ansatz equations.Comment: 14 pages, revised version, some clarifications in text, references
added and upate
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
One-body density matrix and momentum distribution of strongly interacting one-dimensional spinor quantum gases
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