A quantum dot close to Stoner instability: The role of the Berry phase
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100 (Israel)
- Landau Institute for Theoretical Physics, 119334 Moscow (Russian Federation)
- Institut fuer Theorie der Kondensierten Materie, Karlsruhe Institute of Technology, 76128 Karlsruhe (Germany)
- Institut fuer Theoretische Physik, Universitaet zu Koeln, D-50973 Koeln (Germany)
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 to 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]. - Highlights: Black-Right-Pointing-Pointer We consider a conducting QD whose dynamics is governed by exchange interaction. Black-Right-Pointing-Pointer We study the model within the 'Universal Hamiltonian' framework. Black-Right-Pointing-Pointer The ensuing bosonic action is non-abelian (hence non-trivial). Black-Right-Pointing-Pointer We find that the low energy dynamics is governed by a fluctuating Berry phase term. Black-Right-Pointing-Pointer We calculate the partition function and the zero frequency magnetic susceptibility.
- OSTI ID:
- 22157105
- Journal Information:
- Annals of Physics (New York), Vol. 327, Issue 10; Other Information: Copyright (c) 2012 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
- Country of Publication:
- United States
- Language:
- English
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