|Freie Schlagwörter||lattice gauge theory, quantum chromodynamics, phase structure, HMC algorithm12.38.-t, 12.38.Gc, 11.15.Ha, 12.40.Yx, 14.65.Bt, 14.40.-n
In the year 2003 it was realized that with the Wilson twisted mass
formulation of lattice QCD at maximal twist O(a) improvement can be
obtained without the need of additional improvement coefficients. Of
course, such a theoretical proposition needs a check in practice and
hence we performed a scaling test of maximally twisted mass QCD
(mtmQCD), in the quenched approximation as a start.
The most important findings of this scaling test are the following:
thanks to the twisted mass term playing the role of an infrared
cut-off for the Dirac operator eigenvalue spectrum, it is possible to
simulate pseudo scalar masses as low as 270 MeV without having
problems with exceptional configurations. Moreover we could show that
physical observables determined with mtmQCD show no O(a) lattice artifacts.
We studied the effects of the explicit flavor symmetry breaking in
mtmQCD. They turn out to be sizable when the charged/neutral pseudo
scalar mass splitting is considered. Nevertheless, the splitting is a
lattice artifact and we could show that it vanishes proportional to
the squared lattice spacing. While simulations with pseudo scalar mass
values below 300 MeV are also possible with overlap fermions, a
comparison of computational costs revealed that simulations with
twisted mass fermions are a factor of 20 to 70 faster than simulations
with overlap fermions.
Aiming at large scale simulations in full lattice QCD we developed - in
addition to the investigation of mtmQCD as the potential formulation -
a new variant of the Hybrid Monte Carlo algorithm in order to make
full QCD simulations with light quark masses affordable. The new
variant, as presented in this work, is applicable to a wide variety of
lattice Dirac operators and moreover straightforward to implement.
Our simulations clearly show that with this new HMC variant
(full dynamical) simulations with Wilson type fermions and realistic
quark masses are possible with reasonable computational effort.
Taking the aforementioned results together, we have now a sound
basis for performing large scale simulations with light quark
masses. However, our first investigations in full lattice QCD revealed
a surprising result: we could show that close enough to the continuum
the phase structure of lattice QCD with Wilson type fermions and the
Wilson plaquette gauge action exhibits the expected continuum phase
structure distorted by lattice artifacts. Our investigation yielded
that in a range of lattice spacings between 0.2 and 0.13 fm there
exists a first order phase transition at the chiral point. The phase
structure in this range of lattice spacings was unknown so far.
This phenomenon finds its natural interpretation in terms of an
effective potential model depicted in lattice chiral perturbation
theory, where a first order phase transition is predicted as one of
two possible scenarios emerging due to lattice artifacts proportional
to the squared lattice spacing.