35 research outputs found
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
Chiral perturbation theory in a magnetic background - finite-temperature effects
We consider chiral perturbation theory for SU(2) at finite temperature in
a constant magnetic background . We compute the thermal mass of the pions
and the pion decay constant to leading order in chiral perturbation theory in
the presence of the magnetic field. The magnetic field gives rise to a
splitting between and as well as between
and . We also calculate the free energy and the
quark condensate to next-to-leading order in chiral perturbation theory. Both
the pion decay constants and the quark condensate are decreasing slower as a
function of temperature as compared to the case with vanishing magnetic field.
The latter result suggests that the critical temperature for the chiral
transition is larger in the presence of a constant magnetic field. The increase
of as a function of is in agreement with most model calculations but
in disagreement with recent lattice calculations.Comment: 24 pages and 9 fig
QCD with Chemical Potential in a Small Hyperspherical Box
To leading order in perturbation theory, we solve QCD, defined on a small
three sphere in the large N and Nf limit, at finite chemical potential and map
out the phase diagram in the (mu,T) plane. The action of QCD is complex in the
presence of a non-zero quark chemical potential which results in the sign
problem for lattice simulations. In the large N theory, which at low
temperatures becomes a conventional unitary matrix model with a complex action,
we find that the dominant contribution to the functional integral comes from
complexified gauge field configurations. For this reason the eigenvalues of the
Polyakov line lie off the unit circle on a contour in the complex plane. We
find at low temperatures that as mu passes one of the quark energy levels there
is a third-order Gross-Witten transition from a confined to a deconfined phase
and back again giving rise to a rich phase structure. We compare a range of
physical observables in the large N theory to those calculated numerically in
the theory with N=3. In the latter case there are no genuine phase transitions
in a finite volume but nevertheless the observables are remarkably similar to
the large N theory.Comment: 44 pages, 18 figures, jhep3 format. Small corrections and
clarifications added in v3. Conclusions cleaned up. Published versio
Developments in lattice quantum chromodynamics for matter at high temperature and density
A brief overview of the QCD phase diagram at nonzero temperature and density is provided. It is explained why standard lattice QCD techniques are not immediately applicable for its determination, due to the sign problem. We then discuss a selection of recent lattice approaches that attempt to evade the sign problem and classify them according to the underlying principle: constrained simulations (density of states, histograms), holomorphicity (complex Langevin, Lefschetz thimbles), partial summations (clusters, subsets, bags) and change in integration order (strong coupling, dual formulations)