Stability of the Semimetallic Phase in strongly interacting Weyl semimetals*

Using a combination of analytical arguments and diagrammatic Monte Carlo simulations, we show that the corrections to the dispersion in interacting Weyl semimetals are determined by the ultraviolet cutoff and the inverse screening length. If both of these are finite, then the diagrammatic series is convergent even in the low-temperature limit, which implies that the semimetallic phase is protected by a symmetry of the self energy. We also find that the frequency dependent part of the self energy gives an extremely small correction to the Greens function of the interacting system, implying that the impact of interactions almost entirely takes the form of a renormalisation of the single particle dispersion.