54 research outputs found
Directed-loop Monte Carlo simulations of vertex models
We show how the directed-loop Monte Carlo algorithm can be applied to study
vertex models. The algorithm is employed to calculate the arrow polarization in
the six-vertex model with the domain wall boundary conditions (DWBC). The model
exhibits spatially separated ordered and ``disordered'' regions. We show how
the boundary between these regions depends on parameters of the model. We give
some predictions on the behavior of the polarization in the thermodynamic limit
and discuss the relation to the Arctic Circle theorem.Comment: Extended version with autocorrelations and more figures. Added 2
reference
Exact Results for Three-Body Correlations in a Degenerate One-Dimensional Bose Gas
Motivated by recent experiments we derive an exact expression for the
correlation function entering the three-body recombination rate for a
one-dimensional gas of interacting bosons. The answer, given in terms of two
thermodynamic parameters of the Lieb-Liniger model, is valid for all values of
the dimensionless coupling and contains the previously known results
for the Bogoliubov and Tonks-Girardeau regimes as limiting cases. We also
investigate finite-size effects by calculating the correlation function for
small systems of 3, 4, 5 and 6 particles.Comment: 4 pages, 2 figure
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
Finite temperature Drude weight of an integrable Bose chain
We study the Drude weight at finite temperatures of an integrable
bosonic model where the particles interact via nearest-neighbour coupling on a
chain. At low temperatures, is shown to be universal in the sense that
this region is equivalently described by a Gaussian model. This low-temperature
limit is also relevant for the integrable one-dimensional Bose gas. We then use
the thermodynamic Bethe ansatz to confirm the low-temperature result, to obtain
the high temperature limit of and to calculate numerically.Comment: 11 pages, 2 figure
Three-body local correlation function in the Lieb-Liniger model: bosonization approach
We develop a method for the calculation of vacuum expectation values of local
operators in the Lieb-Liniger model. This method is based on a set of new
identities obtained using integrability and effective theory (``bosonization'')
description. We use this method to get an explicit expression for the
three-body local correlation function, measured in a recent experiment [1].Comment: 40 pages, 2 figure
Edge exponent in the dynamic spin structure factor of the Yang-Gaudin model
The dynamic spin structure factor of a system of
spin-1/2 bosons is investigated at arbitrary strength of interparticle
repulsion. As a function of it is shown to exhibit a power-law
singularity at the threshold frequency defined by the energy of a magnon at
given The power-law exponent is found exactly using a combination of the
Bethe Ansatz solution and an effective field theory approach.Comment: 4 pages, 2 figure
Dynamical properties of the one-dimensional spin-1/2 Bose-Hubbard model near Mott-insulator to ferromagnetic liquid transition
We investigate the dynamics of the one-dimensional strongly repulsive
spin-1/2 Bose-Hubbard model for filling While at the system
is a Hubbard-Mott insulator exhibiting dynamical properties of the Heisenberg
ferromagnet, at it is a ferromagnetic liquid with complex spin
dynamics. We find that close to the insulator-liquid transition the system
admits for a complete separation of spin and density degrees of freedom valid
at {\it all} energy and momentum scales within the approximation. This
allows us to derive the propagator of transverse spin waves and the shape of
the magnon peak in the dynamic spin structure factor.Comment: 4 pages, 2 figures, version accepted for publication in Phys. Rev.
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