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We investigate the dynamics of the one-dimensional strongly repulsive spin-1/2 Bose-Hubbard model for filling $ ule1.$ While at $ u=1$ the system is a Hubbard-Mott insulator exhibiting dynamical properties of the Heisenberg ferromagnet, at $ u<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.
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 frequenc y 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.
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, convenie nt for analytic and numerical investigations. By using Wicks theorem, we avoid the form-factor summation customarily used in literature for treating similar problems.
We investigate the propagation of spin excitations in a one-dimensional (1D) ferromagnetic Bose gas. While the spectrum of longitudinal spin waves in this system is sound-like, the dispersion of transverse spin excitations is quadratic making a direc t application of the Luttinger Liquid (LL) 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.
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