Fracton Phases of Matter (2001.01722v1)

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.

Overview of "Fracton Phases of Matter"

The paper "Fracton Phases of Matter" by Michael Pretko, Xie Chen, and Yizhi You provides a comprehensive review of the burgeoning field of fracton phases. Fractons are a type of quasiparticle with unique immobility characteristics, attracting significant interest in modern condensed matter theory. The paper elucidates various physical settings where fractons emerge, like spin liquids and elasticity theory, and explores their associations with higher moment conservation laws and tensor gauge theories. The review serves as a compendium of concepts, developments, and applications of fracton theory, providing insights into their potential roles in quantum information storage and connections to gravitational physics.

Fractons and Tensor Gauge Theories

Fractons exhibit unusual mobility constraints governed by higher moment conservation laws. They are realized as immobile particles in three-dimensional spin models and elasticity theories. The paper highlights how symmetric tensor gauge theories inherently capture these mobility constraints, providing a formalism where fracton phases naturally manifest out of conservation laws like charge and dipole moment conservation. This formulation contrasts with the behaviors observed in conventional quasiparticles and introduces new paradigms in understanding phases of matter.

Prototypical Models and Geometric Constructions

The paper details iconic fracton models such as the X-cube model and Haah's code—prototypical examples of type-I and type-II fracton models, respectively. These exactly solvable spin models are crucial for understanding fracton physics, highlighting immobile fractons and emergent gauge structures. The paper further explores construction techniques, like the coupled layer approach and cage-net models, which provide pathways to understanding how fracton phases arise from stacks of two-dimensional topological orders.

Recent Developments in Fracton Theory

Recent work has expanded fracton theory beyond its original context. One notable development is the identification of fracton phases in elasticity theory, where topological lattice defects in crystals exhibit fracton-like properties. This fracton-elasticity duality suggests potential experimental realizations of fractons in more familiar systems like crystals and Bose condensates. Moreover, theoretical advancements like fractonic Chern-Simons theories and holographic models propose analogies with gravitational systems and offer a new perspective on the AdS/CFT correspondence.

Fracton Phenomenology and Experimental Signatures

The review emphasizes the non-ergodic behavior of fracton systems, stemming from their restricted mobility. Such systems frequently exhibit slow, glassy dynamics or complete non-ergodicity, making them candidates for robust quantum information storage. The paper recommends exploring these traits experimentally, noting that recent developments in ultra-cold atom systems and material platforms like Yb-based compounds could aid in observing and harnessing fracton behaviors.

Classification and Future Directions

The paper rounds out its examination by addressing classification challenges in fracton models and suggesting frameworks based on their fusion and statistical processes. Much work remains in fully characterizing these phases and identifying more experimentally feasible models. The pursuit of understanding fractons in fermionic systems, relating fracton physics to higher-spin theories, and leveraging their properties for technological applications stand out as exciting avenues for future research.

In conclusion, "Fracton Phases of Matter" serves as an authoritative guide, capturing the richness of the field and setting a foundation for future work to further unfold the depth and potential of fracton phases in condensed matter physics. The paper invites researchers to explore this tantalizing field ripe with possibilities for theoretical intrigue and practical innovation.