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arXiv · cond-mat/9810348

Quantum-Mechanical Position Operator and Localization in Extended Systems

A. A. Aligia·G. Ortiz
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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.

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A. A. Aligia, G. Ortiz. 1998-10-26. Quantum-Mechanical Position Operator and Localization in Extended Systems. https://doi.org/10.1103/physrevlett.82.2560

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