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 $\gamma$ 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 $D(T)$ at finite temperatures $T$ of an integrable bosonic model where the particles interact via nearest-neighbour coupling on a chain. At low temperatures, $D(T)$ 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 $D(T)$ and to calculate $D(T)$ 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 $\mathcal{S}(k,\omega)$ of a system of spin-1/2 bosons is investigated at arbitrary strength of interparticle repulsion. As a function of $\omega$ it is shown to exhibit a power-law singularity at the threshold frequency defined by the energy of a magnon at given $k.$ 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 $\nu\le1.$ While at $\nu=1$ the system is a Hubbard-Mott insulator exhibiting dynamical properties of the Heisenberg ferromagnet, at $\nu<1$ 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 $t-J$ 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. Let