Electron conductance and many-body marker of a cavity-embedded topological one-dimensional chain

We investigate many-body topological and transport properties of a one-dimensional Su-Schrieffer-Heeger (SSH) topological chain coupled to the quantum field of a cavity mode. The quantum conductance is determined via Green's function formalism in terms of the light-matter eigenstates calculated via exact diagonalization for a finite number of electrons. We show that the topology of the cavity-embedded many-electron system is described by a generalized electron-photon Zak marker. We reveal how the quantization of transport is modified by the cavity vacuum fields for a finite-size chain and how it is impacted by electronic disorder. Moreover, we show that electron-photon entanglement produces dramatic differences with respect to the predictions of mean-field theory, which strongly underestimates cavity-modified transport.