Dr Ferenc Pittler (Eötvös University)
The spectrum of the two-dimensional continuum Dirac operator in the presence of a uniform background magnetic field consists of Landau levels, which are degenerate and separated by gaps. On the lattice the Landau levels are spread out by discretization artefacts, but a remnant of their structure is clearly visible (Hofstadter butterfly). If one switches on a non-Abelian interaction, the butterfly structure will be smeared out, but the lowest Landau level will still be separated by a gap from the rest of the spectrum. In this talk we discuss how the eigenmodes of the four-dimensional QCD Dirac operator are built out of the two-dimensional eigenmodes of the Dirac operator diagonalized on each slice at fixed (z,t). In particular, starting from this decomposition, we consider how well certain physical quantities are approximated by using only the two-dimensional eigenmodes belonging to the lowest Landau level.
Dr Falk Bruckmann (University of Regensburg) Dr Ferenc Pittler (Eötvös University) Dr Gergely Endrodi (University of Frankfurt) Mr Jacob Wellnhofer (Universität Regensburg) Dr Matteo Giordano (Eotvos University, Budapest) Prof. Sándor Katz (Eötvös University, Budapest) Prof. Tamás Kovács (MTA Atomki, Debrecen)