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

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

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

Low-temperature crossover in the momentum distribution of cold atomic gases in one dimension

The momentum distribution function for the two-component 1D gases of bosons and fermions is studied in the limit of strong interatomic repulsion. A pronounced reconstruction of the distribution is found at a temperature much smaller than the Fermi temperature. This new temperature scale, which equals the Fermi temperature divided by the dimensionless coupling strength, is a feature of the two-component model and does not exist in the one-component case. We estimate the parameters relevant for the experimental observation of the crossover effect.Comment: 6 pages, 2 figure

Spin dynamics in a one-dimensional ferromagnetic Bose Gas.

We investigate the propagation of spin excitations in a one-dimensional ferromagnetic Bose gas. While the spectrum of longitudinal spin waves in this system is soundlike, the dispersion of transverse spin excitations is quadratic, making a direct application of the Luttinger liquid theory impossible. By using a combination of different analytic methods we derive the large time asymptotic behavior of the spin-spin dynamical correlation function for strong interparticle repulsion. The result has an unusual structure associated with a crossover from the regime of trapped spin wave to an open regime and does not have analogues in known low-energy universality classes of quantum 1D systems