Grassmannization of classical models
2016 (English)In: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 18, no 11, 113025Article in journal (Refereed) Published
Applying Feynman diagrammatics to non-fermionic strongly correlated models with local constraints might seem generically impossible for two separate reasons: (i) the necessity to have a Gaussian (non-interacting) limit on top of which the perturbative diagrammatic expansion is generated by Wick's theorem, and (ii) Dyson's collapse argument implying that the expansion in powers of coupling constant is divergent. We show that for arbitrary classical lattice models both problems can be solved/circumvented by reformulating the high-temperature expansion (more generally, any discrete representation of the model) in terms of Grassmann integrals. Discrete variables residing on either links, plaquettes, or sites of the lattice are associated with the Grassmann variables in such a way that the partition function (as well as all correlation functions) of the original system and its Grassmann-field counterpart are identical. The expansion of the latter around its Gaussian point generates Feynman diagrams. Our work paves the way for studying lattice gauge theories by treating bosonic and fermionic degrees of freedom on equal footing. © 2016 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.
Place, publisher, year, edition, pages
Institute of Physics (IOP), 2016. Vol. 18, no 11, 113025
diagrammatic Monte Carlo, Grassmann variables, Ising model, Degrees of freedom (mechanics), Expansion, Quantum theory, Correlation function, Coupling constants, Discrete variables, High-temperature expansion, Lattice gauge theory, Local constraints, Partition functions, Lattice theory
IdentifiersURN: urn:nbn:se:kth:diva-202276DOI: 10.1088/1367-2630/18/11/113025ScopusID: 2-s2.0-84996549522OAI: oai:DiVA.org:kth-202276DiVA: diva2:1078649
Correspondence Address: Pollet, L.; Department of Physics, Arnold Sommerfeld Center for Theoretical Physics, Theresienstrasse 37, Germany; email: Lode.Pollet@lmu.de. QC 201703062017-03-062017-03-062017-03-06Bibliographically approved