Berlin 2015 – scientific programme

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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 Huerga^1,2 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.