Quantum Hall Ferromagnetism in a Cavity Vacuum

Abstract

We uncover a continuous phase transition in a quantum Hall ferromagnet (QHF) at filling factor $ν=1$, driven by vacuum fluctuations of a cavity. Our analysis starts with a Landau level projection in dipole gauge, where we find the states to be well-represented by a tensor product of the electronic and photonic degrees of freedom. Through analytic spin wave calculations, mean-field theory and density matrix renormalization group (DMRG) simulations, we show that for a spatially antisymmetric cavity field, the uniform QHF state is stable only for weak light-matter coupling and gives way to states of inhomogeneous electron density above a critical coupling. These states involve "flanks" of uniform QHF fluids, separated by a "compact core" of doubly occupied orbitals with the core size being the order parameter, which we dub as "compact-core phases". While the fully spin polarized electronic states are product states, entanglement builds up between the uniform QHF flanks across the compact core in the $S_z=0$ magnetic sector, motivating an ansatz for the compact-core electronic states. The transition boundary is exactly derived for product electronic states in terms of matter and cavity parameters, and numerically confirmed by DMRG. We also study the thin-cylinder limit near the critical point where quantum fluctuations are enhanced, and the many-body excited states in both phases by focusing on the entanglement spectrum degeneracies. Remarkably, the photon number is found to probe the order parameter of the transition, providing a possible experimental signature of the electronic transition and the compact-core states. Our study offers a rare example of a phase of electrons stabilized solely by coupling to the enhanced vacuum fluctuations of a cavity mode.