Current, conduction, and localization in quantum many-body systems

TL;DR

This paper introduces a new framework for representing current in quantum many-body systems, capable of distinguishing different types of conduction, and demonstrates ideal conduction in strongly correlated models through full diagonalization.

Contribution

It presents a novel scheme for current representation that accounts for ideal conduction, extends to lattice systems, and analyzes transport in strongly correlated models.

Findings

The scheme can distinguish superconductors, superfluids, and conductors.

Full diagonalization shows ideal conduction with all charge carriers moving simultaneously.

The flux quantization rule is generalized for different charge carrier units.

Abstract

A representation of current is presented which can account for ideal conduction and distinguish superconductors, superfluids, ideal, and non-ideal conductors. The idea of the scheme is that different current operators and transport weights can be constructed based on the number of charge carriers in basic units of conduction. Ideal conductors with basic units of $p$ charge carriers exhibit a flux quantization rule of $\Phi_B=nhc/(pe)$ (for example $p=2$ for BCS). Extension of the current operators to lattice systems is also presented. A full diagonalization calculation for an interacting model of spinless fermions of all the transport coefficients is carried out. It is shown that in a number of strongly correlated models ideal conduction involving the simultaneous motion of all charge carriers is possible.