Landau Level Mixing and Solenoidal Terms in Lowest Landau Level Currents

TL;DR

This paper calculates the lowest Landau level current in a 2D electron system, revealing it differs from previous models by solenoidal terms and cannot be derived solely within the LLL formalism.

Contribution

It provides a full Hilbert space calculation of the LLL current, highlighting differences from existing field theoretic approaches and clarifying the role of solenoidal terms.

Findings

The LLL current includes solenoidal terms absent in previous models.

The derived current differs from the Martinez and Stone formalism.

The correct LLL current cannot be obtained solely within the LLL formalism.

Abstract

We calculate the lowest Landau level (LLL) current by working in the full Hilbert space of a two dimensional electron system in a magnetic field and keeping all the non-vanishing terms in the high field limit. The answer a) is not represented by a simple LLL operator and b) differs from the current operator, recently derived by Martinez and Stone in a field theoretic LLL formalism, by solenoidal terms. Though that is consistent with the inevitable ambiguities of their Noether construction, we argue that the correct answer cannot arise naturally in the LLL formalism.