Chiral Symmetry Breaking in QED induced by an External Magnetic Field

Abstract

We simulate Lattice QED in a constant external magnetic field using the RHMC algorithm. We seek evidence for chiral symmetry breaking predicted by truncated Schwinger-Dyson methods. Since the predicted values of the dynamical electron mass and chiral condensate at the physical fine structure constant are too small to be measured, we simulate at a larger value $\alpha=1/5$. This requires using electron masses as low as $m=0.001$ to extrapolate to $m=0$. At a large magnetic field, the electrons occupy the lowest Landau level which has a small profile in the plane orthogonal to the magnetic field, so that we are able to use a lattice with small extent in these 2 directions. If chiral symmetry is unbroken at $m=0$ the chiral condensate is dominated by large momenta and should be insensitive to the lattice extent in the direction of the magnetic field and the time direction. When chiral symmetry is broken at $m=0$, the chiral condensate should be sensitive to the lattice size in these directions as $m \rightarrow 0$. We search for this behaviour by increasing the lattice extent in these 2 directions. Preliminary simulations show strong dependence of the chiral condensate on the lattice extent in these 2 directions for the smallest masses, and these increased condensates appear to be approaching a non-zero limit as $m \rightarrow 0$.