Melting of devil's staircases in the long-range Dicke-Ising model
Phys. Rev. B 111, 224427 – Published 23 June, 2025
DOI: https://doi.org/10.1103/syps-9r7r
Abstract
We present ground-state phase diagrams for the antiferromagnetic long-range Ising model under a linear coupling to a single bosonic mode on the square and triangular lattice. In the limit of zero coupling, the ground-state magnetization forms a devil's staircase structure of magnetization plateaux as a function of an applied longitudinal field in Ising direction. Apart from a paramagnetic superradiant phase with a finite photon density at strong linear coupling to a single bosonic mode, the long-range interactions lead to a plethora of intermediate phases that break the translational symmetry of the lattice and have a finite photon density at the same time. To qualitatively study the ground-state phase diagrams, we apply an adaption of the unit-cell-based mean-field calculations, which capture all possible magnetic unit cells up to a chosen extent. Further, we exploit an exact mapping of the nonsuperradiant phases to an effective pure Dicke model in order to calculate upper bounds for phase transitions towards superradiant phases. Finally, to treat quantum fluctuations in a quantitative fashion, we extend a wormhole quantum Monte Carlo algorithm for Dicke-spin systems to long-range spin-spin interactions. 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 nontrivial 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. Further, we classify the nature of the quantum phase transitions between different phases. Concretely, between normal and superradiant phases with the same (different) magnetic order, the transition is 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 of continuous second-order behavior.
