Melting of devil's staircases in the long-range Dicke-Ising model

We present quantum phase diagrams for the antiferromagnetic long-range Ising model with a linear coupling to a single bosonic mode on the square and triangular lattice. For zero coupling, the ground-state magnetization forms a devil's staircase structure of magnetization plateaux as a function of a longitudinal field. Apart from a paramagnetic superradiant phase with a finite photon density at strong light-matter couplings, the long-range interactions lead to a plethora of intermediate phases that break the translational symmetry and have a finite photon density at the same time. We apply an adaption of the unit-cell-based mean-field calculations, which captures all possible magnetic unit cells up to a chosen extent. Further, we exploit an exact mapping of the non-superradiant phases to an effective Dicke model to calculate upper bounds for phase transitions towards superradiant phases. Finally, to treat quantum fluctuations in a quantitative fashion, we employ a generalized wormhole quantum Monte Carlo algorithm. We discuss how these three methods are used in a cooperative fashion. In the calculated phase diagrams we see several features arising from the long-range interactions: The devil's staircases of distinct magnetically ordered normal phases and non-trivial magnetically ordered superradiant phases beyond the findings for nearest-neighbor interactions. Examples are a superradiant phase with a three-sublattice magnetic order on the square lattice and the superradiant Wigner crystal with four sites per unit cell on the triangular lattice. We find the transition between normal and superradiant phases with the same (different) magnetic order to be of second order with Dicke universality (first order). Further, between superradiant phases we find first-order phase transitions, besides specially highlighted regimes for which we find indications for second-order behavior.