No abstract

The scrambling rate λL associated with the exponential growth of out-of-time-ordered correlators can be used to characterize quantum chaos. Here we use the Majorana Fermion representation of spin 1/2 systems to study quantum chaos in the Dicke model. We take the system to be in thermal equilibrium and compute λL throughout the phase diagram to leading order in 1/N . We find that the chaotic behavior is strongest close to the critical point. At high temperatures λL is nonzero over an extended region that includes both the normal and super-radiant phases. At low temperatures λL is nonzero in (a) close vicinity of the critical point and (b) a region within the super-radiant phase. In the process we also derive a new effective theory for the super-radiant phase at finite temperatures. Our formalism does not rely on the assumption of total spin conservation. arXiv:1808.02038v2 [cond-mat.stat-mech]

Quantum field theory predicts Weyl semimetals to possess a peculiar response of the longitudinal current density to the application of a DC magnetic field. This peculiar response, known as the Chiral Magnetic effect (CME), has been proposed as one of the signatures of the unique chiral anomaly of Weyl nodes. Here we show that such a response can in principle exist in a model without Weyl nodes. On the other hand, such a CME to be at odds with a general result showing the vanishing of the bulk current in an equilibrium system on any real material with a lattice in an external magnetic field. Here we resolve this apparent contradiction by introducing a model where a current flows in response to a magnetic field even without Weyl nodes. We point out that the previous derivation of a vanishing CME in the limit of vanishing real frequency is a consequence of the assumption of periodic boundary conditions of the system. Consistent with recent work, we found the finite frequency CME to be non-vanishing in general when there was a non-vanishing Berry curvature on the Fermi surface. This does not necessitate having a topological Berry flux as in the case of a Weyl node. Finally, we study how the perturbation theory in magnetic field might be more stable in the presence of disorder. We find that in a realistic disordered system, the chiral magnetic response is really a dynamical phenomena and vanishes in the DC limit.