Interacting Majorana fermion model with spontaneous symmetry breaking and topological order: exact ground state with intertwined spin and pairing orders

The exact ground state of the interacting Majorana fermion model on square lattice is obtained. The ground state exhibits the coexistence of spontaneous symmetry breaking and topological order. The $Z_2$ symmetry breaking leads to the intertwined spin and pairing orders. The topological order is reflected in the $Z_2$ quantum spin liquid ground state. The interacting Majorana fermion model is possibly realized on a Majorana-zero-mode lattice

General expressions for the Moore-Penrose inverse of a 2 × 2 block matrix

AbstractThe Moore-Penrose inverse of a 2 × 2 block matrix M = m=acbd is discussed. General expressions for the Moore-Penrose inverse for the block matrix M in terms of the individual blocks A, B, C, D are delivered without any restrictions imposed. Under some conditions, the Moore-Penrose inverse can be simplified. The results extend earlier work by various authors

The Fate of Massive Closed Strings

We calculate the semi-inclusive decay rate of an average string state with toroidal compactification in the the superstring theory. We also apply this calculation to a brane-inflation model in a warped geometry and find that the decay rate is greatly suppressed if the final strings are both massive and enhanced for massless radiation.Comment: 4 pages, to appear in the proceeding of PASCOS 2005, Gyeongju, Korea, May 30-June 4, 200

Lacing topological orders in two dimensions: exactly solvable models for Kitaev's sixteen-fold way

A family of two-dimensional (2D) spin-1/2 models have been constructed to realize Kitaev's sixteen-fold way of anyon theories. Defining a one-dimensional (1D) path through all the lattice sites, and performing the Jordan-Wigner transformation with the help of the 1D path, we find that such a spin-1/2 model is equivalent to a model with $\nu$ species of Majorana fermions coupled to a static $\mathbb{Z}_2$ gauge field. Here each specie of Majorana fermions gives rise to an energy band that carries a Chern number $\mathcal{C}=1$, yielding a total Chern number $\mathcal{C}=\nu$. It has been shown that the ground states are three (four)-fold topologically degenerate on a torus, when $\nu$ is an odd (even) number. These exactly solvable models can be achieved by quantum simulations.Comment: 20 pages, 9 figure