A Comment On Berry Connections
High Energy Physics - Theory
2017-06-08 v2 Mesoscale and Nanoscale Physics
Strongly Correlated Electrons
Mathematical Physics
math.MP
Abstract
When families of quantum systems are equipped with a continuous family of Hamiltonians such that there is a gap in the common spectrum one can define a notion of a Berry connection. In this note we stress that, in general, since the Hilbert bundle defining the family of quantum systems does not come with a canonical trivialization there is in fact not a single Berry connection but rather a family of Berry connections. Two examples illustrate that this remark can have physical consequences.
Cite
@article{arxiv.1706.01149,
title = {A Comment On Berry Connections},
author = {Gregory W. Moore},
journal= {arXiv preprint arXiv:1706.01149},
year = {2017}
}
Comments
17 pages. V2: Some silly misprints fixed