Hopping Coefficients Research Articles

EVOLUTION OF FERMIONIC SYSTEMS AS AN EXPECTATION OVER POISSON PROCESSES

We derive an exact probabilistic representation for the evolution of a Hubbard model with site- and spin-dependent hopping coefficients and site-dependent interactions in terms of an associated stochastic dynamics of a collection of Poisson processes.

Planar and lamellar antiferromagnetism in Hubbard models

The Hubbard model with extended hoppings on a cubic lattice is shown to have antiferromagnetic phases displaying long-range order, when the temperature is small and the repulsive Coulomb potential is sufficiently strong. Our results are rigorous in the case of the asymmetric Hubbard model. Besides chessboard states, stabilizing effects of hopping yield other phases, such as planar and lamellar ones, depending on the relative strength of the hopping coefficients.

$$\left\langle {\bar \Psi \Psi } \right\rangle$$ in the Schwinger model with Wilson and naive fermions

The coefficients of an expansion series in the hopping coefficients are determined. This allows to calculate\(\left\langle {\bar \Psi \Psi } \right\rangle\) analytically for any coupling constant and fermion mass in 1+1 dimensions.