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CATEGORIES:Theory of Condensed Matter
SUMMARY:Powerful and deceptive Feynman diagrammatic series
- Evgeny Kozik\, King's College London
DTSTART;TZID=Europe/London:20151112T141500
DTEND;TZID=Europe/London:20151112T151500
UID:TALK61617AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/61617
DESCRIPTION:Development of the diagrammatic Monte Carlo (DiagM
C) technique has allowed summation of Feynman diag
rammatic series to high order\, potentially leadin
g to unbiased results. I will discuss how DiagMC c
an be used to address the Hubbard model on the squ
are lattice in the region of moderate on-site repu
lsion U<4 (in the units of hopping t) and filling
n<0.7 without uncontrolled approximations. In part
icular\, I will present an accurate ground-state p
hase diagram in the (n\,U) plane\, describing comp
etition between the p- and d-wave superfluid state
s. On the other hand\, access to high orders has r
evealed serious fundamental problems with Feynman
diagrammatics. In particular\, I will demonstrate
that diagrammatic expansions in the correlated reg
ime can be dangerously misleading even when they c
onverge. This can be traced back to the fact that
the Luttinger-Ward functional for the Hubbard inte
raction---which expresses the thermodynamic grand
potential in terms of the interacting single-parti
cle Greenâ€™s function G---is at least double valued
with a distinct unphysical branch. Although the s
keleton (bold-line) series in terms of G is found
to converge despite this pathology (at least at mo
derate temperatures)\, at stronger interactions it
s convergence is to the *unphysical* branch\, whic
h reveals a new scenario of breaking down of diagr
ammatic expansions.
LOCATION:TCM Seminar Room\, Cavendish Laboratory
CONTACT:Dr G Moller
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