Efficient construction of many-body Fock states having the lowest energies

Abstract

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 build 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.

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• Quantum chaos in interacting Bose-Bose mixtures
• Unconventional pairing in few-fermion systems at finite temperature
• Geometry-induced entanglement in a mass-imbalanced few-fermion system
• Quantum correlations and spatial localization in trapped one-dimensional ultra-cold Bose-Bose-Bose mixtures
• Fundamental limitations of the eigenvalue continuation approach
• Pair-correlation ansatz for the ground state of interacting bosons in an arbitrary one-dimensional potential
• Sudden quench of harmonically trapped mass-imbalanced fermions
• Unconventional pairing in few-fermion systems tuned by external confinement
• On the direct diagonalization method for a few particles trapped in harmonic potentials
• Impurity immersed in a two-component few-fermion mixture in a one-dimensional harmonic trap