Efficient Construction of Many-Body Fock States Having the Lowest Energies

A. Chrostowski, T. Sowiński Institute of Physics, Polish Academy of Sciences, Aleja Lotnikow 32/46, PL-02668 Warsaw, Poland

Received: August 7, 2019; revised version 22 September, 2019; in final form September 23, 2019

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To perform efficient many-body calculations in the framework of the exact diagonalization of the Hamiltonian one needs an appropriately tailored Fock basis built from the single-particle orbitals. The simplest way to compose the basis is to choose a finite set of single-particle wave functions and find all possible distributions of a given number of particles in these states. It is known, however, that this construction leads to very inaccurate results since it does not take into account different many-body states having the same energy on equal footing. Here we present a fast and surprisingly simple algorithm for generating the many-body Fock basis built from many-body Fock states having the lowest non-interacting energies. The algorithm is insensitive to details of the distribution of single-particle energies and it can be used for an arbitrary number of particles obeying bosonic or fermionic statistics. Moreover, it can be easily generalized to a larger number of components. Taking as a simple example the system of two ultra-cold bosons in an anharmonic trap, we show that exact calculations in the basis generated with the algorithm are substantially more accurate than calculations performed within the standard approach.

DOI:10.12693/APhysPolA.136.566 topics: Fock base generator, exact diagonalization