Emergent Phases of Fractonic Matter

TL;DR

This paper explores various emergent phases of fractonic matter at finite densities, revealing phenomena like microemulsions, Fermi liquids, and quantum Hall states, thus initiating the condensed matter study of fractons.

Contribution

It introduces the study of finite-density fracton systems, analyzing their phases and transitions, which extends the understanding beyond the small-particle interactions of prior models.

Findings

Fractons can form microemulsion phases with small clusters.

Finite-density dipoles can create Fermi liquids with a Fermi surface.

Chiral quantum Hall phases of dipoles exhibit edge states and ground state degeneracies.

Abstract

Fractons are emergent particles which are immobile in isolation, but which can move together in dipolar pairs or other small clusters. These exotic excitations naturally occur in certain quantum phases of matter described by tensor gauge theories. Previous research has focused on the properties of small numbers of fractons and their interactions, effectively mapping out the "Standard Model" of fractons. In the present work, however, we consider systems with a finite density of either fractons or their dipolar bound states, with a focus on the $U(1)$ fracton models. We study some of the phases in which emergent fractonic matter can exist, thereby initiating the study of the "condensed matter" of fractons. We begin by considering a system with a finite density of fractons, which we show can exhibit microemulsion physics, in which fractons form small-scale clusters emulsed in a phase dominated by long-range repulsion. We then move on to study systems with a finite density of mobile dipoles, which have phases analogous to many conventional condensed matter phases. We focus on two major examples: Fermi liquids and quantum Hall phases. A finite density of fermionic dipoles will form a Fermi surface and enter a Fermi liquid phase. Interestingly, this dipolar Fermi liquid exhibits a finite-temperature phase transition, corresponding to an unbinding transition of fractons. Finally, we study chiral two-dimensional phases corresponding to dipoles in "quantum Hall" states of their emergent magnetic field. We study numerous aspects of these generalized quantum Hall systems, such as their edge theories and ground state degeneracies.