Directed update for the stochastic Green function algorithm

In a recent paper we presented a stochastic Green function (SGF) algorithm, which has the properties of being general and easy to apply to any lattice Hamiltonian of the form $\widehat{\mathcal{H}}=\widehat{\mathcal{V}}-\widehat{\mathcal{T}}$, where $\widehat{\mathcal{V}}$ is diagonal in the chosen occupation number basis and $\widehat{\mathcal{T}}$ has only positive matrix elements. We propose here a modified version of the update scheme that keeps the simplicity and generality of the original SGF algorithm, and significantly enhances its efficiency.

Figure 1

Simplified update scheme. See text for details.

Figure 2

Directed update scheme. See text for details.

Figure 3

(Color online) An example of density profiles obtained when the trapping potential (50) is added to the Hamiltonian (49). The error bars are smaller than the symbol sizes, and are the biggest in the neighborhood of site indices 23 and 47, where they equal the size of the symbols.

Figure 4

(Color online) An example of momentum distribution functions obtained when the trapping potential (50) is added to the Hamiltonian (49). The error bars are smaller than the symbol sizes, and are the biggest for $k=0$, where they equal the size of the symbols.