How localized is an extended quantum system ?
arXiv:cond-mat/9910490 · doi:10.1002/1521-3951(200007)220:1<737::AID-PSSB737>3.3.CO;2-0
Abstract
We elaborate on a geometric characterization of the electromagnetic properties of matter. A fundamental complex quantity, z_{L}, is introduced to study the localization properties of extended quantum systems. z_L, which allows us to discriminate between conducting and non-conducting thermodynamic phases, has an illuminating physical (and geometric) interpretation. Its phase can be related to the expectation value of the position operator (and a Berry phase), while its modulus is associated with quantum electric polarization fluctuations (and a quantum metric). We also study the scaling behavior of z_L in the one-dimensional repulsive Hubbard model.
5 pages; 1 figure (revtex)