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arXiv:2606.03733

Probing metal-insulator criticality with cavity photons

João C. Inácio, Natanael C. Costa, Fakher F. Assaad

cond-mat.str-elquant-phSubmitted Jun 2, 2026• Announced Jun 3, 2026• 0 citations• Revised Sep 28, 2026 (v2)
v1 · Jun 2, 2026v2 · Sep 28, 2026
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Abstract

The Hubbard model on the honeycomb lattice is a pristine realisation of a semimetal-to-insulator Mott transition belonging to the O(3) Gross-Neveu universality class. We couple this system to a single linearly polarised, uniform cavity photon mode. For this interacting light-matter model, we formulate a negative-sign-free fermion quantum Monte Carlo algorithm that allows for unbiased results on finite system sizes. Our numerical results show that the coupling to the cavity is irrelevant at criticality, even at strong electron-photon coupling. On the other hand, we observe, and show analytically, that the photon spectrum acquires finite corrections in the form of the optical conductivity. In the semimetal phase, gapless particle-hole excitations produce a low-energy polaritonic mode, which is suppressed in the Mott insulator phase. Furthermore, we show that the photon spectra can be used to detect universal information about the quantum critical point. Thereby, our results establish that a single, uniform cavity photon mode acts as a contact-free non-invasive probe for Mott criticality. Our results can be generalised to any cavity where an intensive number of uniform linearly polarised photon modes couple to the electronic system.

Comments
30 pages, 8 figures

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The entanglement entropy is a unique probe to reveal universal features of strongly interacting many-body systems. In two or more dimensions these features are subtle, and detecting them numerically requires extreme precision, a notoriously difficult task. This is especially challenging in models of interacting fermions, where many such universal features have yet to be observed. In this Letter we tackle this challenge by introducing a new method to compute the Rényi entanglement entropy in auxiliary-field quantum Monte Carlo simulations, where we treat the entangling region itself as a stochastic variable. We demonstrate the efficiency of this method by extracting, for the first time, universal subleading logarithmic terms in a two-dimensional model of interacting fermions, focusing on the half-filled honeycomb Hubbard model at T=0. We detect the universal corner contribution due to gapless fermions throughout the Dirac semi-metal phase and at the Gross-Neveu-Yukawa critical point, where the latter shows a pronounced enhancement depending on the type of entangling cut. Finally, we observe the universal Goldstone mode contribution in the antiferromagnetic Mott insulating phase.