Higher-rank deconfined quantum criticality at the Lifshitz transition and the exciton Bose condensate

Deconfined quantum critical points are characterized by the presence of an emergent gauge field and exotic fractionalized particles, which exist as well-defined excitations only at the critical point. We here demonstrate the existence of quantum critical points described by an emergent tensor gauge theory featuring subdimensional excitations, in close relation to fracton theories. We begin by reexamining a previously studied Lifshitz transition between two valence bond solid (VBS) phases on a bilayer honeycomb lattice. We show that the critical theory maps onto a rank-2 tensor gauge theory featuring one-dimensional particles. In a slightly different context, the same tensor gauge theory also describes a Lifshitz quantum critical point between a two-dimensional superfluid and a finite-momentum Bose condensate, both of which are dual to rank-1 gauge theories. This represents an entirely new class of deconfined quantum criticality, in which a critical tensor gauge theory arises on top of a stable conventional gauge theory. Furthermore, we propose that this quantum critical point gives rise to a new finite-temperature phase of bosons, behaving as an exciton Bose condensate, in which excitons (boson-hole pairs) are condensed but individual bosons are not. We discuss how small modifications of this theory give rise to the stable quantum ``exciton Bose liquid'' phase studied in Paramekanti, Balents, and Fisher, Phys. Rev. B 66, 054526 (2002).