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SUMMARY:Powerful and deceptive Feynman diagrammatic series - Evgeny Kozik\
 , King's College London
DTSTART:20151112T141500Z
DTEND:20151112T151500Z
UID:TALK61617@talks.cam.ac.uk
CONTACT:Dr G Moller
DESCRIPTION:Development of the diagrammatic Monte Carlo (DiagMC) technique
  has allowed summation of Feynman diagrammatic series to high order\, pote
 ntially leading to unbiased results. I will discuss how DiagMC can be used
  to address the Hubbard model on the square lattice in the region of moder
 ate on-site repulsion U<4 (in the units of hopping t) and filling n<0.7 wi
 thout uncontrolled approximations. In particular\, I will present an accur
 ate ground-state phase diagram in the (n\,U) plane\, describing competitio
 n between the p- and d-wave superfluid states. On the other hand\, access 
 to high orders has revealed serious fundamental problems with Feynman diag
 rammatics. In particular\, I will demonstrate that diagrammatic expansions
  in the correlated regime can be dangerously misleading even when they con
 verge. This can be traced back to the fact that the Luttinger-Ward functio
 nal for the Hubbard interaction---which expresses the thermodynamic grand 
 potential in terms of the interacting single-particle Green’s function G
 ---is at least double valued with a distinct unphysical branch. Although t
 he skeleton (bold-line) series in terms of G is found to converge despite 
 this pathology (at least at moderate temperatures)\, at stronger interacti
 ons its convergence is to the *unphysical* branch\, which reveals a new sc
 enario of breaking down of diagrammatic expansions.  
LOCATION:TCM Seminar Room\, Cavendish Laboratory
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