Higher Rank Deconfined Quantum Criticality at the Lifshitz Transition and the Exciton Bose Condensate

TL;DR

The paper identifies a new class of deconfined quantum critical points described by emergent rank-2 tensor gauge theories with subdimensional (one-dimensional) vector charges, exemplified by a Lifshitz-type transition between valence-bond solids on a bilayer honeycomb lattice. Through a detailed duality, the critical point maps to a rank-2 tensor gauge theory, while a dual scalar description reveals a single relevant perturbation and a logarithmic interaction for the one-dimensional charges; the same framework also describes a deconfined transition between a conventional superfluid and a finite-momentum Bose condensate, interpreted as an exciton condensate with vortices corresponding to the one-dimensional charges. At zero temperature, the exciton condensate exhibits true long-range order for excitons but not for single bosons, and the critical theory naturally extends to a finite-temperature phase—the exciton Bose condensate (EBC)—with a characteristic $C\propto T$ specific heat and a BKT-like unbinding of 1D vortices at $T_{c2}$. The work further connects to the exciton Bose liquid (EBL) via lattice-model realizations and shows how small perturbations can stabilize EBL physics under subsystem symmetries, offering a broader platform for exploring deconfined tensor gauge theories and fracton-related phenomena.

Abstract

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 deconfined quantum critical point between two valence bond solid (VBS) phases on a bilayer honeycomb lattice. We show that the critical theory maps onto a rank-two tensor gauge theory featuring one-dimensional particles. In a slightly different context, the same tensor gauge theory also describes a deconfined quantum critical point between a two-dimensional superfluid and a finite-momentum Bose condensate, both of which are dual to rank-one 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 by Paramekanti, Balents, and Fisher.

Figures (9)

• Figure 1: All excitations and operators in the effective theory of the VBS-VBS$'$ transition can be mapped directly onto those of a tensor gauge theory with one-dimensional vector charges.
• Figure 2: In the VBS-VBS$'$ transition, the critical tensor gauge theory separates two gapped confined phases. In contrast, the superfluid to finite-momentum condensate transition features a critical tensor gauge theory separating two stable noncompact vector gauge theories.
• Figure 3: The $\partial_i\phi$ operators correspond to single-boson hopping processes. Similarly, the $\partial_i\partial_j\phi$ operators correspond to two-boson hopping processes conserving center of mass, which can equivalently be regarded as exciton hopping processes.
• Figure 4: The EBC quantum critical point between two conventional Bose condensates gives rise to a finite temperature EBC phase. For small nonzero $|\kappa|$, the EBC exists as an intermediate phase between the superfluid and disordered phases.
• Figure 5: Terms in the critical Hamiltonian of boson $e^{i\phi}$ on the honeycomb lattice. $\hat{+} = \frac{1}{2}\hat{x} +\frac{\sqrt{3}}{2}\hat{y}$ and $\hat{-}=-\frac{1}{2}\hat{x} +\frac{\sqrt{3}}{2}\hat{y}$