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"The sign problem and the Lefschetz thimble"

Relatore: Dott. Luigi Scorzato- ECT* Trento

Sala Feynman
05 Febbraio 2013 ore 16.30

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.