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 Sz=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.
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BibTeX
@misc{dag2026quantum,
title = {{Quantum Hall Ferromagnetism in a Cavity Vacuum}},
author = {Ceren B. Dag and Luis Brey and Ganpathy Murthy and H. A. Fertig},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14838},
eprint = {2609.14838},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14838},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum Hall Ferromagnetism in a Cavity Vacuum
AU - Ceren B. Dag
AU - Luis Brey
AU - Ganpathy Murthy
AU - H. A. Fertig
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2609.14838
UR - https://arxiv.org/abs/2609.14838
AB - 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.
ER -