Exactly solvable model for isospin S=3/2 fermionic atoms on an optical lattice

We propose an exact solution of a model describing a low energy behavior of cold isospin S=3/2 fermionic atoms on a one-dimensional optical lattice. Depending on the band filling the effective field theory has a form of a deformed Gross-Neveu model with either $O(7)\times \mathbb{Z}_2$ (half filling) or $U(1)\times O(5)\times \mathbb{Z}_2$ symmetry.Comment: 4 pages, no figures, replaced with the final version to appear in PR

Friedel oscillations of Density of States in a one-dimensional Mott insulator and Incommensurate Charge Density Wave/Superconductor

Oscillations of local density of states generated by a single scalar impurity potential are calculated for one-dimensional systems with dynamically generated charge or spin gap. At zero temperature the oscillations develop at finite wave vector ($\pi$ for the Mott insulator and $2k_F$ for ICDW/SC) and at frequencies larger than the soliton spectral gap $m$. Their amplitude has a broad maximum at $\omega \approx 3m$, where $m$ is the gap magnitude.Comment: 4 pages, 2 figure

Confinement and deconfinement of spinons in a frustrated spin-1/2 Heisenberg model

In this publication I discuss the phase diagram of a frustrated spin-1/2 Heisenberg model suggested in A. A. Nersesyan and A. M. Tsvelik, Phys. Rev. B{\bf 67}, 024422 (2003). The phase diagram contains $(\pi,0)$ and $(\pi,\pi)$ antiferromagnetic phases separated by the Valence Bond Crystal (VBC) state. I argue that the point of the phase diagram with deconfined spinons, predicted in the aforementioned work, is situated in the middle of VBC state, at the point where the dimerization order parameter changes sign.Comment: 13 pages, 5 figures; an important reference and some explanations adde