112 research outputs found
A complex path around the sign problem
We review recent attempts at dealing with the sign problem in Monte Carlo
calculations by deforming the region of integration in the path integral from
real to complex fields. We discuss the theoretical foundations, the algorithmic
issues and present some results for low dimensional field theories in both
imaginary and real time.Comment: Write up of the talk delivered al Lattice 201
Aharonov-Bohm effect and nucleon-nucleon phase shifts on the lattice
We propose a method for the lattice QCD computation of nucleon-nucleon
low-energy interactions. It consists in simulating QCD in the background of a
''electromagnetic" field whose potential is non-vanishing, but whose field
strength is zero. By tuning the background field, phase-shifts at any (but
small) momenta can be determined by measuring the shift of the ground state
energy. Lattice sizes as small as 5 Fermi can be sufficient for the calculation
of phase shifts up to momenta of order of
Goldstone modes in the neutron star core
We formulate a theory of Goldstone bosons and their interactions in the
superfluid and superconducting phase of dense nucleonic matter at densities of
relevance to the neutron star core. For typical neutron star temperatures in
the range T = 10^6 to 10^9 K, the Goldstone mode associated with rotational
symmetry, called angulons, couple weakly to each other and to electrons.
Consequently, these modes have anomalously large mean free paths and can
contribute to both diffusive and ballistic transport of heat and momentum. In
contrast, the two Goldstone bosons associated with density oscillations of the
neutron and electron + proton fluids, called superfluid phonons, mix and couple
strongly to electrons. They have shorter mean free paths, and their
contribution to transport is negligible. Long-wavelength superfluid phonons and
angulons can play a role in neutron star seismology, and lead to interesting
phenomenology as angulons couple to magnetic fields and have anisotropic
dispersion relations.Comment: 4 pages, 1 figur
A Monte Carlo algorithm for simulating fermions on Lefschetz thimbles
A possible solution of the notorious sign problem preventing direct Monte
Carlo calculations for systems with non-zero chemical potential is to deform
the integration region in the complex plane to a Lefschetz thimble. We
investigate this approach for a simple fermionic model. We introduce an easy to
implement Monte Carlo algorithm to sample the dominant thimble. Our algorithm
relies only on the integration of the gradient flow in the numerically stable
direction, which gives it a distinct advantage over the other proposed
algorithms. We demonstrate the stability and efficiency of the algorithm by
applying it to an exactly solvable fermionic model and compare our results with
the analytical ones. We report a very good agreement for a certain region in
the parameter space where the dominant contribution comes from a single
thimble, including a region where standard methods suffer from a severe sign
problem. However, we find that there are also regions in the parameter space
where the contribution from multiple thimbles is important, even in the
continuum limit.Comment: 16 pages, 7 figure
How to Renormalize the Gap Equation in High Density QCD
We discuss two technical issues related to the gap equation in high-density
QCD: i) how to obtain the asymptotic solution with well controlled
approximations, and ii) the renormalization of four-quark operators in the
high-density effective field theory.Comment: 8 pages, LaTeX, 1 eps figur
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