How localized is an extended quantum system ?

Details How localized is an extended quantum system ? How localized is an extended quantum system ?

1999-10-29

arxiv.org/abs/cond-mat/9910490v4

Physics

Condensed Matter

5 pages; 1 figure (revtex)

Scientific paper

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.

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