New stochastic treatment of fermions with application to a double-chain polymer

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Abstract
An extension of the stochastic algorithm as applied to Hamiltonian lattice field theories is developed. This new scheme will converge in problems that have intrinsic negative signs in the matrix elements. As an example, this scheme is applied to a two-chain polymer problem with (spinless) fermions that have a pairwise interaction. Because of the multiple connected structure of the double chain, this problem has intrinsic minus signs. It cannot be transformed into a bosonic problem with only positive matrix elements. Numerical results from this application of the new algorithm are presented for the energy and certain correlation functions for moderately long chains. A discussion of a modification of the method which will allow the treatment of much larger systems is discussed.