101 research outputs found
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
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
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
Something interacting and solvable in 1D
We present a two-parameter family of exactly solvable quantum many-body
systems in one spatial dimension containing the Lieb-Liniger model of
interacting bosons as a particular case. The principal building block of this
construction is the previously-introduced (arXiv:1712.09375) family of
two-particle scattering matrices. We discuss an transformation
connecting the models within this family and make a correspondence with
generalized point interactions. The Bethe equations for the ground state are
discussed with a special emphasis on "non-interacting modes" connected by the
modular subgroup of . The bound state solutions are discussed and are
conjectured to follow some correlated version of the string hypothesis. The
excitation spectrum of the new models in this family is derived in analogy to
the Lieb-Liniger model and we show that for certain choices of parameters a
spectrum inversion occurs such that the Umklapp solutions become the new ground
state.Comment: 11 pages, 6 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
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