7 research outputs found
Thimble regularization at work besides toy models: from Random Matrix Theory to Gauge Theories
Thimble regularization as a solution to the sign problem has been
successfully put at work for a few toy models. Given the non trivial nature of
the method (also from the algorithmic point of view) it is compelling to
provide evidence that it works for realistic models. A Chiral Random Matrix
theory has been studied in detail. The known analytical solution shows that the
model is non-trivial as for the sign problem (in particular, phase quenched
results can be very far away from the exact solution). This study gave us the
chance to address a couple of key issues: how many thimbles contribute to the
solution of a realistic problem? Can one devise algorithms which are robust as
for staying on the correct manifold? The obvious step forward consists of
applications to gauge theories.Comment: 7 pages, 1 figure. Talk given at the Lattice2015 Conferenc
Thimble regularization at work for Gauge Theories: from toy models onwards
A final goal for thimble regularization of lattice field theories is the
application to lattice QCD and the study of its phase diagram. Gauge theories
pose a number of conceptual and algorithmic problems, some of which can be
addressed even in the framework of toy models. We report on our progresses in
this field, starting in particular from first successes in the study of one
link models.Comment: 7 pages, 2 figures. Talk given at the Lattice2015 Conferenc
One-dimensional QCD in thimble regularization
QCD in 0+1 dimensions is numerically solved via thimble regularization. In
the context of this toy model, a general formalism is presented for SU(N)
theories. The sign problem that the theory displays is a genuine one, stemming
from a (quark) chemical potential. Three stationary points are present in the
original (real) domain of integration, so that contributions from all the
thimbles associated to them are to be taken into account: we show how
semiclassical computations can provide hints on the regions of parameter space
where this is absolutely crucial. Known analytical results for the chiral
condensate and the Polyakov loop are correctly reproduced: this is in
particular trivial at high values of the number of flavors N_f. In this regime
we notice that the single thimble dominance scenario takes place (the dominant
thimble is the one associated to the identity). At low values of N_f
computations can be more difficult. It is important to stress that this is not
at all a consequence of the original sign problem (not even via the residual
phase). The latter is always under control, while accidental, delicate
cancelations of contributions coming from different thimbles can be in place in
(restricted) regions of the parameter space.Comment: 20 pages, 5 figures (many more pdf files) (one reference added
An efficient method to compute the residual phase on a Lefschetz thimble
We propose an efficient method to compute the so-called residual phase that
appears when performing Monte Carlo calculations on a Lefschetz thimble. The
method is stochastic and its cost scales linearly with the physical volume,
linearly with the number of stochastic estimators and quadratically with the
length of the extra dimension along the gradient flow. This is a drastic
improvement over previous estimates of the cost of computing the residual
phase. We also report on basic tests of correctness and scaling of the code.Comment: New simulations, new plot, new appendix added. To appear in PRD. 9
pages, 3 figure