Drude and Superfluid Weights in Extended Systems: The Role of Discontinuities and δ-Peaks in the One-and Two-Body Momentum Densities
Author(s)
Date
2012-01-05Source Title
Journal of the Physical Society of Japan
Print ISSN
0031-9015
Electronic ISSN
1347-4073
Publisher
Institute of Pure and Applied Physics
Volume
81
Issue
2
Pages
023701-1 - 023701-4
Language
English
Type
ArticleItem Usage Stats
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Abstract
The question of conductivity is revisited. Using the total momentum shift operator to construct the perturbed many-body Hamiltonian and ground state wave function the second derivative of the ground state energy with respect to the perturbing field is expressed in terms of the one and two-body momentum densities. The distinction between the adiabatic and envelope function derivatives, hence that between the Drude and superfluid weights, can be introduced in a straightforward manner. It is shown that a discontinuity in the momentum density leads to a contribution to the Drude weight, but not the superfluid weight, however a delta-function contribution in the two-body momentum density (such as in the BCS wave-funtion) contributes to both quantities. The connection between the discontinuity in the momentum density and localization is also demonstrated.