“…This assumption breaks down in the so-called ultrastrong coupling (USC) regime [1,2,3], where the interaction energy can be comparable to the bare energy of the photons. Such conditions can be reached in solid-state [4,5,6,7,8,9,10] and molecular cavity QED experiments [11,12,13,14,15], where modifications of chemical reactions [16,17] or phase transitions [18] have been observed and interpreted as vacuum-induced changes of thermodynamic potentials [19]. Together with the ability to realize even stronger couplings between artificial superconducting atoms and microwave photons [20,21,22,23,24], these observations have led to a growing interest [2,3] in the ground and thermal states of light-matter systems under conditions where the coupling between the individual parts can no longer be neglected.…”