Quantum-Mechanical Position Operator and Localization in Extended Systems
Abstract
We introduce a fundamental complex quantity, zL, 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 any fractional particle filling. As an illustration we use zL 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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