Emergent Phases of Fractonic Matter

TL;DR

This work initiates a condensed‑matter program for fractons by studying finite densities of immobile fractons and mobile dipoles within $U(1)$ tensor gauge theories. It reveals microemulsion regimes where short‑range attraction and long‑range repulsion bind fractons into finite clusters, alongside dipolar phases that form Fermi surfaces and, at two dimensions, generalized quantum Hall states via tensor Chern‑Simons theories. The paper shows that dipolar Fermi liquids can host a finite‑temperature fracton unbinding transition driven by a logarithmic interfracton potential, while dipolar quantum Hall states exhibit integer and fractional Hall responses with two chiral edge modes and novel boundary physics. These findings establish a framework for exploring fracton “condensed matter,” including potential topological dipolar phases and richer multi‑species and higher‑rank generalizations with significant implications for quantum matter with constrained mobility. The work also opens avenues for experimental diagnostics via Friedel oscillations, edge modes, and thermal Hall signatures in spin liquids and related systems.

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.

Figures (7)

• Figure 1: $V(r)$ vs $r$. The decaying potential has both long-range and "hard-core" repulsions, with a region of attraction just outside the core.
• Figure 2: We consider a cluster of fractons that is approximately close-packed, assuming a hard-core radius $a$ for the fractons. The radius of the cluster scales as $R\sim N^{1/3}$.
• Figure 3: $V(r)$ vs $r$. The growing potential has a similar profile to the decaying case, except that the long-range repulsive potential now grows unbounded in magnitude, destabilizing the microemulsion.
• Figure 4: The anisotropic nature of the interaction between dipoles will cause the Fermi surface to elongate in the direction of the dipole moment, forming roughly a prolate spheroid.
• Figure 5: Fermi surfaces of different species of dipoles will be elongated along different directions, which drastically reduces their overlap, shown here by the solid black curves.