An Exact Solution for Spin and Charge Correlations in Quantum Dots: The Effect of Level Fluctuations and Zeeman Splitting

TL;DR

This paper provides an exact analytical solution for spin and charge correlations in quantum dots, revealing how level fluctuations and Zeeman splitting influence properties near the Stoner instability, with implications for experimental tests.

Contribution

It introduces a novel exact solution for the non-Abelian problem of interactions in quantum dots near the Stoner instability, including effects of level fluctuations and Zeeman splitting.

Findings

Spin susceptibility follows a Curie law with an effective spin near the Stoner instability.

Tunneling density of states shows non-monotonous behavior due to enhanced spin correlations.

Level fluctuations cause a logarithmic temperature dependence of the effective spin.

Abstract

The inclusion of charging and spin-exchange interactions within the Universal Hamiltonian description of quantum dots is challenging as it leads to a non-Abelian action. Here we present an exact analytical solution of the probem, in particular, in the vicinity of the Stoner instabilty. We calculate the tunneling density of states and the spin susceptibility. We demonstrate that near the Stoner instability the spin susceptibility follows a Curie law with an effective spin. The latter depends logarithmically on temperature due to the statistical fluctuations of the single-particle levels. Near the Stoner instability the tunneling density of states exhibits a non-monotonous behavior as function of the tunneling energy, even at temperatures higher than the exchange energy. This is due to ehnanced spin correlations. Our results could be tested in quantum dots made of nearly ferromagnetic materials.