Multifractality in the interacting disordered Tavis-Cummings model*

When quantum emitters and a cavity mode coherently exchange energy at a rate faster than their decay, hybrid light-matter states emerge. Such hybrid states are superpositions composed of “bright” emitter modes and cavity photons, while numerous remaining emitter states have no photon contribution, i.e., remain “dark” [Phys. Rev. B 102, 144202 (2020)]. The hybridization of N emitters with a single cavity mode is well captured by the Tavis-Cummings (TC) model. Recently, an extensive study of the single-excitation TC model has shown multifractality of all the eigenfunctions for any strength of the light-matter coupling [Phys. Rev. A 105, 023714 (2022)]. Multifractality is well known to be a meaningful feature of critical wave functions at Anderson transitions, with a multifractal spectrum that characterizes the universality class of the transition. Here we show that multifractality in the TC model is not limited to single-excitation, analyzing the system at half filling [arXiv:2302.14718 (2023)]. We demonstrate that a poissonian level statistics coexists with eigenfunctions that are multifractal (extended, but non-ergodic) in the Hilbert space, for all strengths of light-matter interactions. This is associated with a lack of thermalization for a local perturbation, which remains partially localized in the infinite-time limit. We argue that these effects are due to the combination of finite interactions and integrability of the model. When a small integrability-breaking perturbation (nearest-neighbour hopping) is introduced, typical eigenfunctions become ergodic, seemingly turning the system into a near-perfect conductor, contrary to the single-excitation non-interacting case. We propose a realization of this model with cold atoms [Nat. Phys. 19, 1128–1134 (2023)].