Bosonic selfenergy functional theory

Hügel, Dario
Department of Physics, Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, LudwigMaximiliansUniversität München,Germany

Werner, Philipp
Department of Physics, University of Fribourg, Switzerland

Pollet, Lode
Department of Physics, Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, LudwigMaximiliansUniversität München,Germany

Strand, Hugo U. R.
Department of Physics, University of Fribourg, Switzerland
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Published in:
 Physical Review B.  2016, vol. 94, no. 19, p. 195119
English
We derive the selfenergy functional theory for bosonic lattice systems with broken U(1) symmetry by parametrizing the bosonic BaymKadanoff effective action in terms of one and twopoint selfenergies. The formalism goes beyond other approximate methods such as the pseudoparticle variational cluster approximation, the cluster composite boson mapping, and the Bogoliubov+U theory. It simplifies to bosonic dynamicalmeanfield theory when constraining to local fields, whereas when neglecting kinetic contributions of noncondensed bosons, it reduces to the static meanfield approximation. To benchmark the theory, we study the BoseHubbard model on the two and threedimensional cubic lattice, comparing with exact results from path integral quantum Monte Carlo. We also study the frustrated square lattice with nextnearestneighbor hopping, which is beyond the reach of Monte Carlo simulations. A reference system comprising a single bosonic state, corresponding to three variational parameters, is sufficient to quantitatively describe phase boundaries and thermodynamical observables, while qualitatively capturing the spectral functions, as well as the enhancement of kinetic fluctuations in the frustrated case. On the basis of these findings, we propose selfenergy functional theory as the omnibus framework for treating bosonic lattice models, in particular, in cases where path integral quantum Monte Carlo methods suffer from severe sign problems (e.g., in the presence of nontrivial gauge fields or frustration). Selfenergy functional theory enables the construction of diagrammatically sound approximations that are quantitatively precise and controlled in the number of optimization parameters but nevertheless remain computable by modest means.

Faculty
 Faculté des sciences et de médecine

Department
 Département de Physique

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Physics

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https://folia.unifr.ch/unifr/documents/305296
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