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

## TL;DR

This paper introduces a novel class of deconfined quantum critical points characterized by emergent tensor gauge theories with subdimensional excitations, revealing new phases like the exciton Bose condensate and extending understanding of quantum criticality.

## Contribution

It demonstrates the existence of quantum critical points described by tensor gauge theories with subdimensional excitations, linking them to fracton theories and proposing new finite-temperature phases.

## Key findings

- Critical tensor gauge theory maps onto a deconfined quantum critical point between VBS phases.
- The same tensor gauge theory describes a transition between superfluid and Bose condensate.
- Proposes a new finite-temperature phase, the exciton Bose condensate, arising from these critical points.

## 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.