QCD Anderson transition at zero and non-zero external magnetic fields
The QCD Anderson transition is believed to be connected to both deconfinement and chiral crossovers. These crossovers are substantially affected when external magnetic fields ($B$) are present, most prominently, e.g., via magnetic catalysis and inverse magnetic catalysis. In this work, we use lattice QCD to investigate the Anderson transition in two different setups: (1) at $B=0$ by studying the low-lying eigenmodes of the overlap operator using gauge configurations with $2+1+1$ quark flavors of twisted-mass Wilson fermions. We estimate the mobility edge below which eigenmodes are localized via the inflection point of the so-called relative volume. Previous work has shown that, contrary to expectations, this estimate does not vanish at the temperature of the chiral phase transition. A possible scenario for this apparent contradiction was discussed, and in this work, we present an alternative observable for measuring localization that supports this scenario. And (2) by studying the localization properties of the staggered Dirac operator at $B\neq0$ on configurations with $2+1$ dynamical staggered fermions and 2 stout-smearing steps. Our preliminary results on two lattice spacings ($24^3\times 6$ and $24^3\times 8$) indicate a non-monotonic behavior of the mobility edge with the magnetic field across different temperatures, which hints at a reduction in the Anderson transition temperature in the presence of an external magnetic field.