Hierarchical mean-field theory: recent results on frustrated magnetism and cold atom systems
11.04.2017 at 14:00
We present a method to apporach spin and bosonic Hamiltonians of strongly correlated systems. The method is based on the use of clusters of the original spin or bosonic degrees of freedom as the building blocks capturing the short-range quantum correlations that allow to describe the main features of the phases appearing in the model of interest. Quantum states of the clusters can be represented by the action of a new set of ''composite boson'' (CB) operators. As the algebraic relation between the original spin or bosonic operators and the new set of CBs can be cast in a canonical mapping , the Hamiltonian can be rewritten in terms of CBs and approached by standard many-body techniques, with the advantage that short-range correlations are computed exactly from the onset. A simple Gutzwiller ansatz of uncorrelated clusters permits to uncover the ground state phase diagram of various frustrated systems: bosons with ring-exchange interactions  or in the pressence synthetic magnetic fields , or the XXZ Kagome Heisenberg antiferromagnet . Low-lying excitations over the ground state can be computed by a Bogoliubov approximation over the CBs, which has allowed to describe the Goldstone and amplitude (''Higgs'') mode over the superfluid phase in the Bose-Hubbard model . To conclude, I will comment on the various lines in which the method can be extended.
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