A perfect Hashing function for exact diagonalization of many-body systems of identical particles

Abstract

In exact diagonalization studies of ground state properties of an interacting system using Lánczos, it is crucial to find an efficient mapping from the configuration space to the index of the Lánczos vector. Here, we formulate a mapping (hashing function) that is simple to calculate for identical many-body systems of both fermions and bosons. A unique feature of our hashing functions is that they map many particle configurations to a sequence of consecutive integers. They are therefore optimal in using computer memory.