Fractons from frustration in hole-doped antiferromagnets

John Sous,Michael Pretko

doi:10.1038/s41535-020-00278-2

John Sous, Michael Pretko

Open Access

https://doi.org/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.

Highlights

The concept of exotic emergent quasiparticles has played a prominent role in the theory of strongly correlated quantum many-body systems for several decades, appearing in contexts ranging from fractional quantum Hall systems[1] to quantum spin liquids[2]
While the 2D AFM exhibits only approximate fracton behavior, we investigate a sharp realization of fracton behavior, specializing to the case of holes confined to one dimension of an otherwise 2D antiferromagnetic background, a setup that can be achieved in experiments[43]
A hallmark of fracton behavior is the presence of a universal attraction between fractons that can be regarded as an emergent gravitational force[12], which we show leaves its signatures in holedoped AFMs

Summary

INTRODUCTION

The concept of exotic emergent quasiparticles has played a prominent role in the theory of strongly correlated quantum many-body systems for several decades, appearing in contexts ranging from fractional quantum Hall systems[1] to quantum spin liquids[2]. I.e. within a bipolaron, move together preserving their relative moment: sDep1⁄4arPatiioðhnyi, and σzi hiÞxi whence the bound PThis theory manifestly state gives dipole rise to a dipole conservation law, i ρixi 1⁄4 constant, i.e. a parametric regime of fractonic behavior, only violated at the sixth order in perturbation theory when a single hole becomes mobile. This eliminates the undesirable motion of the hole along closed loops, while preserving spin frustration induced by hole motion, the mechanism behind string-mediated localization of the hole In this mixed dimensionality limit, a single hole always creates magnons first before absorbing them in the reverse order. To leading (second) order, the polaron energy is Ep(k) = −4t2/3J, reflecting a process in which the hole hops from site ix to ix ± 1 via one application of the hoping operator with amplitude t, creating a magnon with energy 3J/2 at ix ± 1, which it absorbs and moves back to ix. Since one hole of spin σ always first emits a string of magnons before they are absorbed by the second hole of spin −σ, this propagator is computed exactly self-consistently, see

DISCUSSION

METHODS