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arXiv:2602.14437

Fermionic Stoner-Dicke phase transition in Circuit Quantum Magnetostatics

Adel Ali, Alexey Belyanin

quant-phSubmitted Feb 16, 2026• Announced Feb 17, 2026• 0 citations
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Abstract

We present a minimal tunable many-body system of fermions coupled to quantum magnetic flux, which is analytically diagonalizable and exhibits a variety of many-body phenomena such as Stoner orbital instability and Dicke-like quantum phase transition. In contrast to standard cavity quantum electrodynamics with its electric-dipole coupling of the electric field operators with matter, here it is the quantized magnetic field of an LC-resonator which is coupled to the angular momentum of particles. Adding the 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 the tight-binding systems that exhibit a tunable nonlinearity representing artificial JJ, but without actual JJs included in the circuit.

Comments
11 pages, 3 figures

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We study effective light-matter interactions in a circuit QED system consisting of a single LCLCLC resonator, which is coupled symmetrically to multiple superconducting qubits. Starting from a minimal circuit model, we demonstrate that, in addition to the usual collective qubit-photon coupling, the resulting Hamiltonian contains direct qubit-qubit interactions, which have a drastic effect on the ground- and excited-state properties of such circuits in the ultrastrong-coupling regime. In contrast to the superradiant phase transition expected from the standard Dicke model, we find an opposite mechanism, which at very strong interactions completely decouples the photon mode and projects the qubits into a highly entangled ground state. These findings resolve previous controversies over the existence of superradiant phases in circuit QED, but they more generally show that the physics of two- or multiatom cavity QED settings can differ significantly from what is commonly assumed.
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We found analytically a first-order quantum phase transition in a Cooper pair box array of NNN low-capacitance Josephson junctions capacitively coupled to resonant photons in a microwave cavity. The Hamiltonian of the system maps on the extended Dicke Hamiltonian of NNN spins 1/21/21/2 with infinitely coordinated antiferromagnetic (frustrating) interaction. This interaction arises from the gauge-invariant coupling of the Josephson-junction phases to the vector potential of the resonant photons field. In the $N\ensuremath{\gg}1$ semiclassical limit, we found a critical coupling at which the ground state of the system switches to one with a net collective electric dipole moment of the Cooper pair boxes coupled to a super-radiant equilibrium photonic condensate. This phase transition changes from the first to second order if the frustrating interaction is switched off. A self-consistently ``rotating'' Holstein-Primakoff representation for the Cartesian components of the total superspin is proposed, that enables one to trace both the first- and the second-order quantum phase transitions in the extended and standard Dicke models, respectively.