Cavity-mediated localization and collective electron correlation phases

Abstract

Collective strong coupling of molecular ensembles to optical cavities opens a route to modifying matter through genuinely collective electronic correlations. Yet even in the absence of a cavity, Coulomb correlations are notoriously difficult to describe, and cavity coupling adds transverse correlation channels extending over the entire molecular ensemble. Here we show that this seemingly intractable problem admits a controlled description by spin glass theory, i.e., by the analytically solvable spherical Sherrington-Kirkpatrick model. Our results predict two collective correlation phases, a paracorrelated phase and a spin-glass correlation phase, beyond the conventional uncorrelated molecular regime. These phases reveal an entropy-driven localization-delocalization mechanism that transfers molecular electronic states into collectively degenerate cavity-dressed states. Analytic calculation suggest that this collective correlated state can either remain insulating or even turn metallic if the entropic occupations favor a fractional filling. Our work reveals cavity-mediated electron correlations as a microscopic mechanism for emergent phases in strongly coupled molecular ensembles.