A quantum dot close to Stoner instability: the role of Berry's Phase

TL;DR

This paper develops a geometric bosonization approach incorporating Berry's phase to analyze a quantum dot near the Stoner instability, accurately predicting magnetic susceptibility in this strongly interacting regime.

Contribution

It introduces a novel geometric method for functional bosonization that accounts for Berry's phase effects in the Stoner regime of quantum dots.

Findings

Magnetic susceptibility near Stoner instability matches exact solutions

Berry phase plays a crucial role in the effective bosonic action

Method effectively captures strong exchange interactions in mesoscopic systems

Abstract

The physics of a quantum dot with electron-electron interactions is well captured by the so called "Universal Hamiltonian" if the dimensionless conductance of the dot is much higher than unity. Within this scheme interactions are represented by three spatially independent terms which describe the charging energy, the spin-exchange and the interaction in the Cooper channel. In this paper we concentrate on the exchange interaction and generalize the functional bosonization formalism developed earlier for the charging energy. This turned out to be challenging as the effective bosonic action is formulated in terms of a vector field and is non-abelian due to the non-commutativity of the spin operators. Here we develop a geometric approach which is particularly useful in the mesoscopic Stoner regime, i.e., when the strong exchange interaction renders the system close the the Stoner instability. We show that it is sufficient to sum over the adiabatic paths of the bosonic vector field and, for these paths, the crucial role is played by the Berry phase. Using these results we were able to calculate the magnetic susceptibility of the dot. The latter, in close vicinity of the Stoner instability point, matches very well with the exact solution [I.S. Burmistrov, Y. Gefen, M.N. Kiselev, JETP Lett. 92 (2010) 179].