Fermionic Stoner-Dicke phase transition in circuit quantum magnetostatics
Phys. Rev. B 114, 115405 – Published 7 August, 2026
DOI: https://doi.org/10.1103/s3bf-hwxz
Abstract
We present a minimal, tunable many-body system of fermions coupled to quantum magnetic flux. The model is analytically diagonalizable and exhibits collective many-body phenomena, including an orbital Stoner instability and a Dicke-like quantum phase transition. The many-body interactions are mediated by zero-point fluctuations of a quantized magnetic flux whose oscillator mode remains in its ground state. In contrast to standard cavity quantum electrodynamics, where the dominant coupling is the electric-dipole coupling between matter and electric-field operators, here the quantized magnetic field of an LC resonator couples to the orbital angular momentum of the particles. Because the transition is driven by an orbital-current sector and the diamagnetic term is retained explicitly, the instability is not a conventional electric-dipole Dicke soft-mode transition. Adding a Josephson junction (JJ) to the linear LC circuit allows us to explore nonlinear flux-matter phases and sector-selective photon dressing in regimes relevant to circuit QED and mesoscopic rings. Furthermore, we consider tight-binding systems that exhibit a tunable nonlinearity representing a synthetic JJ without including an actual JJ in the circuit.
