Quantum-Mechanical Position Operator and Localization in Extended Systems
arXiv:cond-mat/9810348 · doi:10.1103/PhysRevLett.82.2560
Abstract
We introduce a fundamental complex quantity, $z_{L}$, which allows us to discriminate between a conducting and non-conducting thermodynamic phase in extended quantum systems. Its phase can be related to the expectation value of the position operator, while its modulus provides an appropriate definition of a localization length. The expressions are valid for {\it any} fractional particle filling. As an illustration we use $z_{L}$ to characterize insulator to ``superconducting'' and Mott transitions in one-dimensional lattice models with infinite on-site Coulomb repulsion at quarter filling.
4 pages, REVTEX, 1 ps figures