Electromagnetic coupling in tight-binding models for strongly correlated light and matter
Jiajun Li, Denis Golež, G. Mazza, Andrew J. Millis, Antoine Georges, Martin Eckstein
Abstract
The rapidly developing collaboration of condensed matter and quantum optical physics opens up exciting new possibilities for creating novel photon-matter states that allow manipulating material properties using optical cavities. This paper addresses the important challenge of formulating consistent, accurate, and convenient forms of the light-matter coupling for the low-energy tight-binding-type models useful for theoretical analysis. It achieves this by constructing precise mappings from the fundamental $a\phantom{\rule{0}{0ex}}b$ $i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o$ description of the cavity-matter system to low-energy theories, producing a truncated Hamiltonian coupling to a quantum Peierls phase. In a simple model system, the authors demonstrate the quick convergence of the truncated Hamiltonian with the number of bands, paving the way for rigorous theoretical studies in this emerging research field.