Critical properties of the Bose-Hubbard model

Author: Dennis Hinrichs
Supervisor: Prof. Dr. Martin Holthaus
Co-Supervisor: Priv.-Doz. Dr. Axel Pelster
Title:
Abstract:: In this thesis methods are presented, which allow one to gain access to certain critical properties of the Bose-Hubbard model. For this a diagrammatic approach for the implementation of Kato's formulation of the perturbation series is introduced. By using the method of the effective potential, one is then able to determine the phase boundary of the superfluid-to-Mott insulator phase transition with great accuracy. Furthermore, the condensate and the superfluid density of the superfluid regime can be calculated. Above that two methods are presented which lead to estimates of the critical exponents of the two densities. Both approaches deliver comparable results which are also consistent with highly accurate reference values.
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Keywords: Bose-Hubbard model, process-chain approach, phase boundary, condensate density, superfluid density, critical exponents
URL: PhDThesis_Hinrichs.pdf (pdf, 2.55 MB)