Back and forth from Fock space to Hilbert space: a guide for commuters
Abstract
Quantum states of systems made of many identical particles, e.g. those described by Fermi-Hubbard and Bose-Hubbard models, are conveniently depicted in the Fock space. However, in order to evaluate some specific observables or to study the system dynamics, it is often more effective to employ the Hilbert space description. Moving effectively from one description to the other is thus a desirable feature, especially when a numerical approach is needed. Here we recall the construction of the Fock space for systems of indistinguishable particles, and then present a set of recipes and advices for those students and researchers in the need to commute back and forth from one description to the other. The two-particle case is discussed in some details and few guidelines for numerical implementations are given.
Cite
@article{arxiv.1805.04552,
title = {Back and forth from Fock space to Hilbert space: a guide for commuters},
author = {Andrea Beggi and Ilaria Siloi and Claudia Benedetti and Enrico Piccinini and Luca Razzoli and Paolo Bordone and Matteo G. A. Paris},
journal= {arXiv preprint arXiv:1805.04552},
year = {2018}
}
Comments
20 pages, 4 figures