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CATEGORIES:Theoretical Physics Seminars
SUMMARY:Powerful and deceptive Feynman diagrammatic series
- Dr Evgeny Kozik\, King's College London
DTSTART:20150122T134500Z
DTEND:20150122T150000Z
UID:TALK1624AT
URL:/talk/index/1624
DESCRIPTION:Diagrammatic Monte Carlo (DiagMC) is a recently in
troduced approach to correlated fermionic systems
based on unbiased stochastic summation of Feynman
diagrams to high order. I will discuss the new tec
hnique and show how DiagMC can be used to address
the Hubbard model on the square lattice in the re
gion of moderate on-site repulsion U<4 and filling
n < 0.7 without uncontrolled approximations. In p
articular\, I will present an accurate ground-stat
e phase diagram in the (n\,U) plane\, describing c
ompetition between the p- and d-wave superfluid st
ates. However\, I will also demonstrate that diagr
ammatic expansions in the correlated regime can be
seriously misleading even when they converge. Thi
s can be attributed to the fact that the Luttinger
-Ward functional for the Hubbard interaction---whi
ch expresses the thermodynamic grand potential in
terms of the interacting single-particle Greenâ€™s f
unction G---is at least double valued with a disti
nct unphysical branch. Although\, despite this pat
hology\, the skeleton (bold-line) series in terms
of G is found to converge (at least at moderate te
mperatures)\, at stronger interactions its converg
ence is to the *unphysical* branch\, which reveals
a new scenario of breaking down of diagrammatic e
xpansions.
LOCATION:Theory Library
CONTACT:Kevin Ralley
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