Frustrated superradiant phases in one- and two-dimensional lattices

Understanding how frustration and symmetry breaking shape collective behavior is a central problem in quantum many-body systems. In this work, we investigate this problem in large one- and two-dimensional arrays of coupled Dicke models on a periodic lattice, where strong light-matter coupling gives rise to a superradiant phase and competition between neighboring order parameters induces spontaneous translational symmetry breaking. Such Dicke lattice models constitute a fundamentally new class of quantum many-body systems, as they simultaneously realize the thermodynamic limit associated with the lattice size and an intrinsic thermodynamic limit arising from collective on-site interactions with quantum emitters. We show that frustration drives photonic density-wave ordering, and that the resulting broken periodicity can be predicted from the excitation spectrum of the symmetric phase, without requiring computationally prohibitive thermodynamic energy minimization. Furthermore, we demonstrate that an emergent Nambu-Goldstone mode arises near the critical point in a one-dimensional chain despite the presence of only discrete symmetry, and uncover the mechanism that enables this otherwise forbidden gapless excitation. We also find quasi-periodic ordering in the superradiant phase, reminiscent of quasicrystals, and demonstrate that synthetic magnetic flux provides a powerful knob to control the nature of translational symmetry breaking. Our results establish a new direction in quantum many-body physics where the coexistence of local and global thermodynamic limits gives rise to unconventional symmetry breaking and emergent collective behavior.