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arXiv:2009.05577 · npj Quantum Materials

Fractons from frustration in hole-doped antiferromagnets

John Sous, Michael Pretko

Published Nov 5, 2020• 17 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1038/s41535-020-00278-2

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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 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.
We design a set of classical macroscopic electric circuits in which charge exhibits the mobility restrictions of fracton quasiparticles. The crucial ingredient in these circuits is a transformer, which induces currents between pairs of adjacent wires. For an appropriately designed geometry, this induction serves to enforce conservation of the dipole moment. We show that a network of capacitors connected via ideal transformers will forever remember the dipole moment of its initial charge configuration. Relaxation of the dipole moment in realistic systems can only occur via flux leakage in the transformers, which will lead to violations of fracton physics at the longest times. We propose a concrete diagnostic for these ``fractolectric'' circuits in the form of their characteristic equilibrium charge configurations, which we verify using simple circuit simulation software. These circuits not only provide an experimental testing ground for fracton physics, but also serve as DC filters. We outline extensions of these ideas to circuits featuring other types of higher moment conservation laws, as well as to higher-dimensional circuits which act as fracton ``current ice.'' While our focus is on classical circuits, we discuss how these ideas can be straightforwardly extended to realize quantized fractons in superconducting circuits.
The objective of the present work -- a literature review on both gapped and gapless fractonic theories -- is to pedagogically fill in the gaps between the research on fractons, and an undergraduate physics education (particularly quantum and statistical mechanics). Some familiarity with classical field theory is assumed. We will begin this work by reviewing the gauging of the Ising model to obtain the toric code. Then, following the chronological order of fracton research, we will establish the gauged spin model picture of gapped fracton theories. Next (after introducing lattice gauge theory) we will cover the developments on the tensor gauge theory front in describing gapless fracton theories. We then explain how conservation of dipole moment is key in the development of field-theoretic descriptions of fracton models, and conclude by providing future plans for work on gauging such field theories. Finally, we point out two more future plans: one being an established theoretical advance which in fact inspired this work, and the other being exciting experimental advances in ultracold atomic physics which could lead to the physical realization of fracton physics. Highlights of this work include: a derivation of the gauge field dynamics (field strength/curvature) term in the gauging of a spin system to obtain the toric code, a reduction of the 3 terms of the Kogut-Susskind lattice QED Hamiltonian to the 2 terms of the toric code, a proof of the correspondence between the invariance of a gauge field and a particular Gauss's law constraint in a tensor gauge theory context, a demonstration that conservation of dipole moment accounts for the same immobility/fractalization phenomenology that we also show from a gauged spin model perspective, and proof of the necessity for polynomial shift symmetries and higher-order spatial derivatives in a Lagrangian in order to have dipole moment conservation.
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.
Fractons, as a new exotic quasiparticle, have attracted immense attention due to their unique properties. Here, the authors construct a connection between fractons and polarons. This allows them to derive explicitly microscopic models, in which polarons and their two-body bound states, known as bipolarons, map exactly on to fractons and their two-body counterparts, dipoles. As a specific example, the authors show how fractons and dipoles arise from magnetic polarons and bipolarons in hole-doped antiferromagnets, thus providing a route towards their physical realization.
Fracton phases of matter feature a variety of exciting phenomena stemming from the restricted mobility of their quasiparticles. Here we consider a model of interacting electrons in one dimension that describes hopping of spin-singlet pairs and obeys both charge and dipole conservation laws. The model contains Bethe ansatz integrable sectors which allow us to solve the ground state and calculate the exact spin and single-electron excitation gaps. We observe hallmarks of fractonic behavior, including localization of single-electron excitations and propensity to clustering. Our results demonstrate the important role of the dipole moment conservation law in a simple model of spin-1/2 fermions.