Spin and Charge Correlations in Quantum Dots: An Exact Solution

TL;DR

This paper provides an exact analytical solution for spin and charge correlations in quantum dots with interactions, revealing non-monotonous behaviors near the Stoner instability and enabling predictions for various observables.

Contribution

It introduces a novel exact solution to the non-Abelian problem of charging and spin-exchange interactions in quantum dots, especially near the Stoner instability.

Findings

TDOS shows non-monotonous behavior near the instability

Solution applicable to various observables like susceptibility and absorption spectrum

Results relevant for nearly ferromagnetic materials

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 {\it exact} analytical solution of the probem, in particular, in the vicinity of the Stoner instabilty point. We calculate several observables, including the tunneling density of states (TDOS) and the spin susceptibility. Near the instability point the TDOS exhibits a non-monotonous behavior as function of the tunneling energy, even at temperatures higher than the exchange energy. Our approach is generalizable to a broad set of observables, including the a.c. susceptibility and the absorption spectrum for anisotropic spin interaction. Our results could be tested in nearly ferromagnetic materials.