We consider a one-dimensional gas of spin-1/2 fermions interacting through $delta$-function repulsive potential of an arbitrary strength. For the case of all fermions but one having spin up, we calculate time-dependent two-point correlation function
of the spin-down fermion. This impurity Greens function is represented in the thermodynamic limit as an integral of Fredholm determinants of integrable linear integral operators.
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.
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].
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 L
ieb-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.
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 te
mperature. 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.
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 spati
ally 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.
