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arXiv · 2606.03733

Mott transition of photons: quantum Monte Carlo study of Gross-Neveu criticality in a cavity

João C. Inácio·Natanael C. Costa·Fakher F. Assaad
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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 Gross-Neveu O(3) universality class. We couple this system to a single linearly polarised cavity photon mode. The light-matter coupling is such that the photon number remains an intensive quantity as is the case for an empty cavity. For this interacting light-matter model, we formulate a negative-sign-free fermion quantum Monte Carlo algorithm that allows for bias-free 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 spectral function couples to the optical conductivity of the electronic system. The cavity photons thereby undergo a Mott transition, and the photon spectral function acts as a contact-free non-invasive probe for Mott criticality.

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João C. Inácio, Natanael C. Costa, Fakher F. Assaad. 2026-06-02. Mott transition of photons: quantum Monte Carlo study of Gross-Neveu criticality in a cavity. https://arxiv.org/abs/2606.03733

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