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SUMMARY:New polynomially exact integration rules on U(N) and SU(N)
DTSTART;VALUE=DATE-TIME:20160725T170500Z
DTEND;VALUE=DATE-TIME:20160725T172500Z
DTSTAMP;VALUE=DATE-TIME:20200812T155545Z
UID:indico-contribution-2644@conference.ippp.dur.ac.uk
DESCRIPTION:Speakers: Tobias Hartung (King's College London)\nIn lattice Q
FT\, we are often presented with integrals over polynomials of coefficient
s of matrices in $U(N)$ or $SU(N)$ with respect to the Haar measure. In so
me physical situations\, e.g.\, in presence of a chemical potential\, thes
e integrals are\, however\, numerically very difficult since they are high
ly oscillatory which manifests itself in form of the sign problem. In thes
e cases\, Monte Carlo methods often fail to be adequate\, rendering such c
omputations practically impossible.\n\nIn this talk\, we will propose a ne
w class of polynomially exact integration rules on $U(N)$ and $SU(N)$ whic
h are derived from polynomially exact rules on spheres. We will examine th
ese quadrature rules and their efficiency at the example of a $0+1$ dimens
ional QCD for a non-zero quark mass and chemical potential. In particular\
, we will demonstrate the failure of Monte Carlo methods in such applicati
ons but that we can obtain arbitrary precision results using the new polyn
omially exact integration rules.\n\nhttps://conference.ippp.dur.ac.uk/even
t/470/contributions/2644/
LOCATION:Highfield Campus\, University of Southampton Building 67 Room 100
3
URL:https://conference.ippp.dur.ac.uk/event/470/contributions/2644/
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