Title: Emergent Phases of Fractonic Matter,
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.