Tunnelling measurements on fractional quantum Hall systems are continuing to increase in popularity since they provide a method to probe the non-Fermi liquid behaviour of fractionally charged excitations occupying the edge states of a quantum Hall sy
stem. When considering tunnelling one must resort to an effective theory and typically a phenomenological tunnelling Hamiltonian is used analogous to that used for a conventional Luttinger liquid. It is the form of this tunnelling Hamiltonian that is investigated in this work by making a comparison to an exact microscopic calculation of the zero mode tunnelling matrix elements. The computation is performed using Monte Carlo and results were obtained for various system sizes for the $ u=1/3$ Laughlin state. Here we also present a solution to overcome the phase problem experienced in Monte Carlo calculations using Laughlin-type wavefunctions. Comparing the system size dependence of the microscopic and phenomenological calculations for the tunnelling matrix elements, it was found that only for a particular type of operator ordering in the tunnelling Hamiltonian was it possible to make a good match to the numerical calculations. From the Monte Carlo data it is also clear that for any system size the electron tunnelling is always less relevant than the quasiparticle tunnelling process, supporting the idea that when considering tunnelling at a weak barrier, the electron tunnelling process can be neglected.
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.
Electronic and transport properties of Graphene, a one-atom thick crystalline material, are sensitive to the presence of atoms adsorbed on its surface. An ensemble of randomly positioned adatoms, each serving as a scattering center, leads to the Bolz
mann-Drude diffusion of charge determining the resistivity of the material. An important question, however, is whether the distribution of adatoms is always genuinely random. In this Article we demonstrate that a dilute adatoms on graphene may have a tendency towards a spatially correlated state with a hidden Kekule mosaic order. This effect emerges from the interaction between the adatoms mediated by the Friedel oscillations of the electron density in graphene. The onset of the ordered state, as the system is cooled below the critical temperature, is accompanied by the opening of a gap in the electronic spectrum of the material, dramatically changing its transport properties.
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.
