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TT: Fachverband Tiefe Temperaturen
TT 55: Low-Dimensional Systems: 2D – Theory
TT 55.7: Talk
Wednesday, March 18, 2015, 11:00–11:15, H 3010
Composite boson mean-field theory for strongly correlated systems — •Daniel Huerga1,2 and Jorge Dukelsky1 — 1Instituto de Estructura de la Materia, C.S.I.C., Madrid, Spain — 2Institut fur Theoretische Physik III, University of Stuttgart, Stuttgart, Germany
We present a method applicable to spin and bosonic model Hamiltonians of strongly correlated systems. The method is based on the identification of clusters of the original spin and bosonic degrees of freedom as the building blocks which capture the essential quantum correlations to describe the phases emerging in the model. We present a canonical mapping which relates the original spin and bosonic operators to a new set of composite boson (CB) operators that describe the quantum states of the cluster. As the mapping is canonical, we can rewrite the original Hamiltonian in terms of CBs and approach it by standard many-body techniques, with the advantage that short-range correlations are computed exactly from the onset.
A simple Gutzwiller wave function of CBs allows us to uncover the phase diagram of two-dimensional frustrated models such as a model of spins with ring-exchange interaction, or a system of bosons in the presence of artificial magnetic fields. A Bogoliubov approach to the CB quantum fluctuations allows us to accurately describe the recently measured Higgs and Goldstone excitation modes of a system of cold atoms loaded in a two-dimensional optical lattice. The algebraic framework set by the mapping allows for further extensions of the method.