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Bosonic self-energy functional theory
Department of Physics, Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universität München, Munich, Germany.
Department of Physics, University of Fribourg, Fribourg, Switzerland.
Department of Physics, Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universität München, Munich, Germany.
Department of Physics, University of Fribourg, Fribourg, Switzerland.ORCID iD: 0000-0002-7263-4403
2016 (English)In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 94, no 19, article id 195119Article in journal (Refereed) Published
Abstract [en]

We derive the self-energy functional theory for bosonic lattice systems with broken U(1) symmetry by parametrizing the bosonic Baym-Kadanoff effective action in terms of one- and two-point self-energies. 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 dynamical-mean field theory when constraining to local fields, whereas when neglecting kinetic contributions of non-condensed bosons it reduces to the static mean-field approximation. To benchmark the theory we study the Bose-Hubbard model on the two- and three-dimensional cubic lattice, comparing with exact results from path integral quantum Monte Carlo. We also study the frustrated square lattice with next-nearest neighbor 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 self-energy 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 non-trivial gauge fields or frustration). Self-energy 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. 

Place, publisher, year, edition, pages
American Physical Society, 2016. Vol. 94, no 19, article id 195119
National Category
Condensed Matter Physics
Identifiers
URN: urn:nbn:se:oru:diva-89964DOI: 10.1103/PhysRevB.94.195119ISI: 000387537100004Scopus ID: 2-s2.0-84994592930OAI: oai:DiVA.org:oru-89964DiVA, id: diva2:1531240
Note

Funding Agencies:

FP7/ERC starting Grant 278023 306897

FP7/Marie-Curie Career Integration Grant 321918

Available from: 2021-02-25 Created: 2021-02-25 Last updated: 2021-02-26Bibliographically approved

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Strand, Hugo

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