Conductance of correlated many-fermion systems from charge fluctuations

TL;DR

This paper establishes a direct relation between static charge fluctuations and conductance in correlated many-fermion systems at zero temperature, enabling easier computation of conductance via tensor network methods.

Contribution

It introduces a novel relation that links static charge fluctuations to conductance, bypassing traditional time-dependent fluctuation methods, especially useful for low-dimensional and interacting systems.

Findings

Validates the relation with quantum dot and quantum point contact systems.

Shows the relation works for systems with interacting reservoirs.

Provides a computationally efficient way to determine conductance.

Abstract

We put forward a relation between the static charge fluctuations and the conductance of correlated many-fermion systems at zero temperature, avoiding the use of time-dependent fluctuations as in the fluctuation-dissipation theorem. Static charge fluctuations can efficiently be computed for low-dimensional systems using tensor network approaches, while the conductance is often significantly more difficult to obtain, requiring a challenging low-frequency linear response computation or an explicit time evolution. We put this relation to the test for quantum dot and quantum point contact setups, where in limiting cases exact results are known. Our study includes systems in which the one-dimensional reservoirs are interacting.