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arXiv:2001.01722 · International Journal of Modern Physics A

Fracton phases of matter

Michael Pretko, Xie Chen, Yizhi You

Published Feb 29, 2020• 404 citations
arXivHTMLPDF

Abstract

Fractons are a new type of quasiparticle which are immobile in isolation, but can often move by forming bound states. Fractons are found in a variety of physical settings, such as spin liquids and elasticity theory, and exhibit unusual phenomenology, such as gravitational physics and localization. The past several years have seen a surge of interest in these exotic particles, which have come to the forefront of modern condensed matter theory. In this review, we provide a broad treatment of fractons, ranging from pedagogical introductory material to discussions of recent advances in the field. We begin by demonstrating how the fracton phenomenon naturally arises as a consequence of higher moment conservation laws, often accompanied by the emergence of tensor gauge theories. We then provide a survey of fracton phases in spin models, along with the various tools used to characterize them, such as the foliation framework. We discuss in detail the manifestation of fracton physics in elasticity theory, as well as the connections of fractons with localization and gravitation. Finally, we provide an overview of some recently proposed platforms for fracton physics, such as Majorana islands and hole-doped antiferromagnets. We conclude with some open questions and an outlook on the field.

DOI
10.1142/s0217751x20300033

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Fractons are a new type of quasiparticle which are immobile in isolation, but can often move by forming bound states. Fractons are found in a variety of physical settings, such as spin liquids and elasticity theory, and exhibit unusual phenomenology, such as gravitational physics and localization. The past several years have seen a surge of interest in these exotic particles, which have come to the forefront of modern condensed matter theory. In this review, we provide a broad treatment of fractons, ranging from pedagogical introductory material to discussions of recent advances in the field. We begin by demonstrating how the fracton phenomenon naturally arises as a consequence of higher moment conservation laws, often accompanied by the emergence of tensor gauge theories. We then provide a survey of fracton phases in spin models, along with the various tools used to characterize them, such as the foliation framework. We discuss in detail the manifestation of fracton physics in elasticity theory, as well as the connections of fractons with localization and gravitation. Finally, we provide an overview of some recently proposed platforms for fracton physics, such as Majorana islands and hole-doped antiferromagnets. We conclude with some open questions and an outlook on the field.
Fracton phases constitute a new class of quantum state of matter. They are characterized by excitations that exhibit restricted mobility, being either immobile under local Hamiltonian dynamics or mobile only in certain directions. These phases do not wholly fit into any of the existing paradigms but connect to areas including glassy quantum dynamics, topological order, spin liquids, elasticity theory, quantum information theory, and gravity. We begin by discussing gapped fracton phases, which may be described using exactly solvable lattice spin models. We then introduce the framework of tensor gauge theory, which provides a powerful complementary perspective and allows us to access gapless fracton phases. We discuss the basic properties of gapless fracton phases and their connections to elasticity theory and gravity. We also discuss what is known about the dynamics and thermodynamics of fractons at nonzero density before concluding with a brief survey of some open problems.
Abstract Recent theoretical research on tensor gauge theories led to the discovery of an exotic type of quasiparticles, dubbed fractons, that obey both charge and dipole conservation. Here we describe physical implementation of dipole conservation laws in realistic systems. We show that fractons find a natural realization in hole-doped antiferromagnets. There, individual holes are largely immobile, while dipolar hole pairs move with ease. First, we demonstrate a broad parametric regime of fracton behavior in hole-doped two-dimensional Ising antiferromagnets viable through five orders in perturbation theory. We then specialize to the case of holes confined to one dimension in an otherwise two-dimensional antiferromagnetic background, which can be realized via the application of external fields in experiments, and prove ideal fracton behavior. We explicitly map the model onto a fracton Hamiltonian featuring conservation of dipole moment. Manifestations of fractonicity in these systems include gravitational clustering of holes. We also discuss diagnostics of fracton behavior, which we argue is borne out in existing experimental results.
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)U(1)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.
Fracton emerges from strongly interacting many-body systems whose excitations, referred to as sub-dimensional particles, have restricted mobility or kinetic motions. These entities have garnered significant interest due to their interdisciplinary implications spanning topological quantum codes, quantum field theory, emergent gravity, quantum information, and more, revealing unique nonequilibrium behaviors such as nonergodicity and glassy dynamics. This review presents a structured and educational overview of fracton phenomena, specifically focusing on gapless fracton liquids. Noteworthy for their compressibility and gapless excitations, fracton liquids facilitate collective modes reminiscent of those gauge fluctuations found in Maxwell's electromagnetic framework. However, they are distinct due to an additional higher-moment conservation law that restricts the mobility of individual charges and monopoles. Our exploration begins with the theoretical foundation of 3D fracton liquids, presenting a variety of emergent symmetric tensor gauge theories and reviewing their equilibrium and dynamic properties. Following this theoretical groundwork, we discuss the material realization of various fracton liquids in Yb-based breathing pyrochlore lattices, close-packed tiling structures and other synthetic quantum matter platforms. Additionally, we introduce a general protocol to foster and manipulate emergent fracton spin liquids in the realm of frustrated magnetism.
Fractons emerge from many-body systems, featuring subdimensional particles with restricted mobility. These particles have attracted interest for their roles across disciplines, including topological quantum codes, quantum field theory, emergent gravity, and quantum information. They display unique nonequilibrium behaviors such as nonergodicity and glassy dynamics. This review offers a structured overview of fracton phenomena, especially those of gapless fracton liquids, which enable collective modes similar to gauge fluctuations in Maxwell's electromagnetic framework, yet their phenomena are distinguished by a unique conservation law that restricts the mobility of individual charges and monopoles. We delve into the theoretical basis of three-dimensional (3D) fracton liquids, exploring emergent symmetric tensor gauge theories and their properties. We also discuss the material realization of fracton liquids in Yb-based pyrochlore lattices and other synthetic quantum matter platforms.
We review a burgeoning field of "fractons" -- a class of models where quasi-particles are strictly immobile or display restricted mobility that can be understood through generalized multipolar symmetries and associated conservation laws. Focusing on just a corner of this fast-growing subject, we will demonstrate how one class of such theories -- symmetric tensor and coupled-vector gauge theories surprisingly emerge from familiar elasticity of a two-dimensional quantum crystal. The disclination and dislocation crystal defects respectively map onto charges and dipoles of the fracton gauge theory. This fracton-elasticity duality leads to predictions of fractonic phases and quantum phase transitions to their descendants, that are duals of the commensurate crystal, supersolid, smectic, hexatic liquid crystals, as well as amorphous solids, quasi-crystals and elastic membranes. We show how these dual gauge theories provide a field theoretic description of quantum melting transitions through a generalized Higgs mechanism. We demonstrate how they can be equivalently constructed as gauged models with global multipole symmetries. We expect extensions of such gauge-elasticity dualities to generalized elasticity theories provide a route to discovery of new fractonic models and their potential experimental realizations.