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arXiv:1904.08424 · Physical review. B./Physical review. B

Fractons from polarons

John Sous, Michael Pretko

Published Dec 28, 2020• 36 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.102.214437

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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.
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.
Phases of matter have always attracted great interest within the scientific community, as they represent emergent phenomena arising from the collective behavior of a large number of interacting degrees of freedom. Their macroscopic properties, often impossible to predict directly from the microscopic scale, can be effectively captured in terms of quasiparticles, \textit{i.e.} particle-like low-energy excitations that emerge from interactions among the underlying microscopic constituents and may exhibit properties entirely different from those of any fundamental particle, reflecting the rich structure of the many-body system. In this Thesis, we investigate two classes of quasiparticles that arise in distinct exotic phases of matter. The first class appears in antiferromagnetic quantum spin chains with discrete symmetries and frustrated boundary conditions, namely periodic boundary conditions with an odd number of sites. In this setting, the competition between global and local orders produces exotic gapless, non-relativistic excitations above the ground state, which can dramatically modify the physics even in the thermodynamic limit. In particular, we focus on how this specific choice of boundary conditions profoundly modifies the phase diagram of one of the most famous integrable models, the XY chain. The second class consists of subdimensional quasiparticles, excitations whose mobility is restricted to lower-dimensional subspaces and which characterize the low-energy sector of emerging fracton phases of matter. Quasiparticles with restricted mobility first appeared in exactly solvable quantum spin models, and it was later realized that they can also emerge from higher-rank gauge theories. In this part of the Thesis, we develop Lorentz-covariant gauge field theories for fractons in 2+12+12+1 dimensions, starting from the first principles of Quantum Field Theory (fields and symmetries), with the aim of embedding the features observed in the condensed matter literature into a more formal field theoretical framework.
When dressed particles (polarons) exchange quantum phonons, the resulting interactions are generally attractive. If the particles have hard-core statistics and the coupling to phonons is through the kinetic energy terms, phonon-mediated interactions are repulsive. Here, we show that such repulsive phonon-mediated interactions bind dressed particles into bipolarons with unique properties. These bipolaron states appear in the gap between phonon excitations, above the two-polaron continuum. While thermodynamically unstable, the bipolaron is protected by energy and momentum conservation and represents a quasiparticle with a large dispersion and a negative effective mass near zero momentum. We discuss possible experimental implementation of the conditions for the formation of such repulsively bound bipolarons.
Fracton phases of matter are gapped phases of matter that, by dint of their sensitivity to UV data, demand non-standard quantum field theories to describe them in the IR. Two such approaches are foliated quantum theory and exotic field theory. In this paper, we explicitly construct a map from one to the other and work out several examples. In particular, we recover the equivalence between the foliated and exotic fractonic BF theories recently demonstrated at the level of operator correspondence. We also demonstrate the equivalence of toric code layers and the anisotropic model with lineons and planons to the foliated BF theory with one and two foliations, respectively. Finally, we derive new exotic field theories that provide simple descriptions of hybrid fracton phases from foliated field theries known to do so. Our results both provide new examples of exotic field theories and pave the way toward their systematic construction from foliated field theories.
Mobile impurities in a Bose-Einstein condensate form quasiparticles called polarons. Here, we show that two such polarons can bind to form a bound bipolaron state. Its emergence is caused by an induced nonlocal interaction mediated by density oscillations in the condensate, and we derive using field theory an effective Schrödinger equation describing this for an arbitrarily strong impurity-boson interaction. We furthermore compare with quantum Monte Carlo simulations finding remarkable agreement, which underlines the predictive power of the developed theory. It is found that bipolaron formation typically requires strong impurity interactions beyond the validity of more commonly used weak-coupling approaches that lead to local Yukawa-type interactions. We predict that the bipolarons are observable in present experiments, and we describe a procedure to probe their properties.