Long-range-ordered phase in a quantum Heisenberg chain with interactions beyond nearest neighbors

Abstract

Spin ensembles coupled to optical cavities provide a powerful platform for engineering synthetic quantum matter. Recently, we demonstrated that cavity-mediated infinite-range interactions can induce fast scrambling in a Heisenberg $\mathrm{XXZ}$ spin chain [Phys. Rev. Research 2, 043399 (2020)]. In this paper, we analyze the kaleidoscope of quantum phases that emerge in this system from the interplay of these interactions. Employing both analytical spin-wave theory as well as numerical density-matrix renormalization group calculations, we find that there is a large parameter regime where the continuous $U(1)$ symmetry of this model is spontaneously broken and the ground state of the system exhibits $\mathrm{XY}$ order. This kind of symmetry breaking and the consequent long-range order is forbidden for short-range interacting systems by the Mermin-Wagner theorem. Intriguingly, we find that the $\mathrm{XY}$ order can be induced by even an infinitesimally weak infinite-range interaction. Furthermore, we demonstrate that in the $U(1)$ symmetry-broken phase, the half-chain entanglement entropy violates the area law logarithmically. Finally, we discuss a proposal to verify our predictions in state-of-the-art quantum emulators.