Superradiant phase transitions in one-dimensional correlated Fermi gases with cavity-induced umklapp scattering

Superradiant phase transitions of one dimensional correlated Fermi gases in a transversely driven optical cavity, under the umklapp condition that the cavity wavenumber equals two times of Fermi wavenumber, are studied with the bosonization and renormalization group (RG) techniques. The bosonization of Fermi fields gives rise to an all-to-all sine-Gordon (SG) model due to the cavity-assisted non-local interactions, where the Bose fields at any two spatial points are coupled. The superradiant phase transition is then mapped to the Kosterlitz-Thouless phase transition of the all-to-all SG model. The nesting effect, in which the superradiant phase transition can be triggered by infinitely small atom-cavity coupling strength, is shown to be preserved for any non-attractive local interactions. For attractive local interactions, the phase transition occurs at finite critical coupling strength. Nevertheless, the analysis of scaling dimension indicates that the perturbation of non-local cosine term is indeed relevant (irrelevant) when the scaling dimension is lower (higher) than the critical dimension, similar to the case of ordinary local SG model. Our work provides an analytical framework for understanding the superradiant phase transitions in low-dimensional correlated intra-cavity Fermi gases.s