Non-analytic localization length at the metal-insulator phase transition in the Hubbard-Holstein model

Recently, theoretical and methodical advances generated re-increased interest in the interplay between strongly correlated electrons and quantized lattice vibrations (phonons). While non-local couplings give rise to various new phenomena, such as high-T_C phonon-mediated superconductivity (arXiv:2203.07380), the phase diagram of the protoypic Hubbard-Holstein model featuring a local electron-phonon coupling only is still far from being completely understood. In particular, this is the case in the regime where electron-electron and electron-phonon interactions are comparable to the phonon frequency, a regime in which a metallic phase is known to exist. Using recent developments in the field of tensor network methods, we reinvestigated the transition from the metallic into the insulating, charge ordered phase. Here, large-scale numerics allows us to carefully identify and resolve finite-size effects, allowing for a high precision calculation of generically challenging quantities, such as the localization length, or the central charge. Our findings reveal a novel perspective to the microscopic origin of the phase transition from a metallic into the insulating phase.