Seminario
"The sign problem and the Lefschetz thimble"
Relatore: Dott. Luigi Scorzato ECT* Trento
Sala Feynman
05 Febbraio 2013 ore 16.30
Abstract

Abstract: It is sometimes speculated that the sign problem
that afflicts many quantum field theories might be reduced
or even eliminated by choosing an alternative domain of
integration within a complexified extension of the path
integral (in the spirit of the stationary phase integration
method). I show that it is possible to regularize the
lattice theory on a Lefschetz thimble, where the imaginary
part of the action is constant and disappears from all
observables. This regularization can be justified in terms
of symmetries and perturbation theory. Moreover, it is
possible to design a Monte Carlo algorithm that samples the
configurations in the thimble. This is done by simulating,
effectively, a five dimensional system. I describe the
algorithm in detail and analyze its expected cost and
stability. Finally, I show why a residual sign remain, but I
argue that it should not lead to a sign problem. Preliminary
results on a Bose gas on a small lattice are encouraging.


