22 research outputs found
The QCD phase diagram at nonzero quark density
We determine the phase diagram of QCD on the \mu-T plane for small to
moderate chemical potentials. Two transition lines are defined with two
quantities, the chiral condensate and the strange quark number susceptibility.
The calculations are carried out on N_t =6,8 and 10 lattices generated with a
Symanzik improved gauge and stout-link improved 2+1 flavor staggered fermion
action using physical quark masses. After carrying out the continuum
extrapolation we find that both quantities result in a similar curvature of the
transition line. Furthermore, our results indicate that in leading order the
width of the transition region remains essentially the same as the chemical
potential is increased.Comment: 12 pages, 6 figure
The sign problem across the QCD phase transition
The average phase factor of the QCD fermion determinant signals the strength
of the QCD sign problem. We compute the average phase factor as a function of
temperature and baryon chemical potential using a two-flavor NJL model. This
allows us to study the strength of the sign problem at and above the chiral
transition. It is discussed how the anomaly affects the sign problem.
Finally, we study the interplay between the sign problem and the endpoint of
the chiral transition.Comment: 9 pages and 9 fig
Degenerate distributions in complex Langevin dynamics: one-dimensional QCD at finite chemical potential
We demonstrate analytically that complex Langevin dynamics can solve the sign
problem in one-dimensional QCD in the thermodynamic limit. In particular, it is
shown that the contributions from the complex and highly oscillating spectral
density of the Dirac operator to the chiral condensate are taken into account
correctly. We find an infinite number of classical fixed points of the Langevin
flow in the thermodynamic limit. The correct solution originates from a
continuum of degenerate distributions in the complexified space.Comment: 20 pages, several eps figures, minor comments added, to appear in
JHE
A practical solution to the sign problem in a matrix model for dynamical compactification
The matrix model formulation of superstring theory offers the possibility to
understand the appearance of 4d space-time from 10d as a consequence of
spontaneous breaking of the SO(10) symmetry. Monte Carlo studies of this issue
is technically difficult due to the so-called sign problem. We present a
practical solution to this problem generalizing the factorization method
proposed originally by two of the authors (K.N.A. and J.N.). Explicit Monte
Carlo calculations and large-N extrapolations are performed in a simpler matrix
model with similar properties, and reproduce quantitative results obtained
previously by the Gaussian expansion method. Our results also confirm that the
spontaneous symmetry breaking indeed occurs due to the phase of the fermion
determinant, which vanishes for collapsed configurations. We clarify various
generic features of this approach, which would be useful in applying it to
other statistical systems with the sign problem.Comment: 44 pages, 64 figures, v2: some minor typos correcte