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 of matter

Semiconductor moiré materials

Author(s): Gromov, A | Abstract: We present an effective field theory approach to the fracton phases. The approach is based on the notion of a multipole algebra. It is an extension of space(time) symmetries of a charge-conserving matter that includes global symmetries responsible for the conservation of various components of the multipole moments of the charge density. We explain how to construct field theories invariant under the action of the algebra. These field theories generally break rotational invariance and exhibit anisotropic scaling. We further explain how to partially gauge the multipole algebra. Such gauging makes the symmetries responsible for the conservation of multipole moments local, while keeping rotation and translations symmetries global. It is shown that upon such gauging one finds the symmetric tensor gauge theories, as well as the generalized gauge theories discussed recently in the literature. We refer to all such theories as multipole gauge theories. The outcome of the gauging procedure depends on the choice of the multipole algebra. In particular, we show how to construct an effective theory for the U(1) version of the Haah code based on the principles of symmetry and provide a two-dimensional example with operators supported on a Sierpinski triangle. We show that upon condensation of charged excitations, fracton phases of both types as well as various Symmetry-protected topological phases emerge. Finally, the relation between the present approach and the formalism based on polynomials over finite fields is discussed.

https://link.aps.org/pdf/10.1103/PhysRevX.9.031035

Towards Classification of Fracton Phases: The Multipole Algebra

Quantum anomalous Hall goes intrinsic Quantum anomalous Hall effect—the appearance of quantized Hall conductance at zero magnetic field—has been observed in thin films of the topological insulator Bi2Se3 doped with magnetic atoms. The doping, however, introduces inhomogeneity, reducing the temperature at which the effect occurs. Two groups have now observed quantum anomalous Hall effect in intrinsically magnetic materials (see the Perspective by Wakefield and Checkelsky). Serlin et al. did so in twisted bilayer graphene aligned to hexagonal boron nitride, where the effect enabled the switching of magnetization with tiny currents. In a complementary work, Deng et al. observed quantum anomalous Hall effect in the antiferromagnetic layered topological insulator MnBi2Te4. Science, this issue p. 900, p. 895; see also p. 848 Transport measurements indicate quantized Hall conductance without a magnetic field. The quantum anomalous Hall (QAH) effect combines topology and magnetism to produce precisely quantized Hall resistance at zero magnetic field. We report the observation of a QAH effect in twisted bilayer graphene aligned to hexagonal boron nitride. The effect is driven by intrinsic strong interactions, which polarize the electrons into a single spin- and valley-resolved moiré miniband with Chern number C = 1. In contrast to magnetically doped systems, the measured transport energy gap is larger than the Curie temperature for magnetic ordering, and quantization to within 0.1% of the von Klitzing constant persists to temperatures of several kelvin at zero magnetic field. Electrical currents as small as 1 nanoampere controllably switch the magnetic order between states of opposite polarization, forming an electrically rewritable magnetic memory.

Intrinsic Quantized Anomalous Hall Effect in a Moiré Heterostructure, Part III: Scanning Probe Magnetometry

In condensed-matter systems, higher temperatures typically disfavour ordered phases, leading to an upper critical temperature for magnetism, superconductivity and other phenomena. An exception is the Pomeranchuk effect in 3He, in which the liquid ground state freezes upon increasing the temperature1, owing to the large entropy of the paramagnetic solid phase. Here we show that a similar mechanism describes the finite-temperature dynamics of spin and valley isospins in magic-angle twisted bilayer graphene2. Notably, a resistivity peak appears at high temperatures near a superlattice filling factor of −1, despite no signs of a commensurate correlated phase appearing in the low-temperature limit. Tilted-field magnetotransport and thermodynamic measurements of the in-plane magnetic moment show that the resistivity peak is connected to a finite-field magnetic phase transition3 at which the system develops finite isospin polarization. These data are suggestive of a Pomeranchuk-type mechanism, in which the entropy of disordered isospin moments in the ferromagnetic phase stabilizes the phase relative to an isospin-unpolarized Fermi liquid phase at higher temperatures. We find the entropy, in units of Boltzmann’s constant, to be of the order of unity per unit cell area, with a measurable fraction that is suppressed by an in-plane magnetic field consistent with a contribution from disordered spins. In contrast to 3He, however, no discontinuities are observed in the thermodynamic quantities across this transition. Our findings imply a small isospin stiffness4,5, with implications for the nature of finite-temperature electron transport6–8, as well as for the mechanisms underlying isospin ordering and superconductivity9,10 in twisted bilayer graphene and related systems. An electronic analogue of the Pomeranchuk effect is present in twisted bilayer graphene, shown by the stability of entropy in a ferromagnetic phase compared to an unpolarized Fermi liquid phase at certain high temperatures.

Isospin Pomeranchuk effect in twisted bilayer graphene

Utilizing a dual description of two-dimensional elasticity theory as a rank-2 tensor gauge theory, the authors show that zero-temperature quantum melting of a two-dimensional crystal differs crucially from the Halperin-Nelson thermal melting scenario. This is due to the particle number conservation symmetry enforced dislocation glide constraint, or fractonicity. The authors show that quantum crystal fluctuations favor a supersolid phase before melting can occur and, furthermore, discuss applications to the quantum melting of a vortex-lattice and charge-stripe order in a metal.

Symmetry-enforced fractonicity and two-dimensional quantum crystal melting

Strong coupling between light and elementary excitations is emerging as a powerful tool to engineer the properties of solid-state systems. Spin-correlated excitations that couple strongly to optical cavities promise control over collective quantum phenomena such as magnetic phase transitions, but their suitable electronic resonances have yet to be found. Here we report strong light-matter coupling in $\textrm{NiPS}_3$, a van der Waals antiferromagnet with highly correlated electronic degrees of freedom. A previously unobserved class of polaritonic quasiparticles emerges from the strong coupling between its spin-correlated excitons and the photons inside a microcavity. Detailed spectroscopic analysis in conjunction with a microscopic theory provides unique insights into the origin and interactions of these exotic magnetically coupled excitations. Our work introduces van der Waals magnets to the field of strong light-matter physics and provides a path towards the design and control of correlated electron systems via cavity quantum electrodynamics. 

/pdf/spin-correlated-exciton-polaritons-in-a-van-der-waals-magnet-1uv046xq.pdf

Spin-correlated exciton–polaritons in a van der Waals magnet

Utilizing a time-dependent mean-field approximation, the authors calculate collective particle-hole modes in a correlated insulating phase of magic-angle twisted bilayer graphene. They find that the low-energy modes are well described by a model with a local pseudospin composed of spin, valley, and orbital degrees of freedom in each moir\'e unit cell. They further show that the intra-flavor collective mode couples strongly to terahertz light, giving a significant signature in the system's optical response.

Lattice Collective Modes from a Continuum Model of Magic-Angle Twisted Bilayer Graphene

A hitherto unobserved three-body coupled composite of excitons, photons and spins is created by strong light-matter coupling in a van der Waals magnetic insulator hosting spin-correlated excitonic excitations [1].

Strong exciton-photon-spin coupling in a van der Waals antiferromagnet

Nascent platforms for programmable quantum simulation offer unprecedented access to new regimes of far-from-equilibrium quantum many-body dynamics in (approximately) isolated systems. Here, achieving precise control over quantum many-body entanglement is an essential task for quantum sensing and computation. Extensive theoretical work suggests that these capabilities can enable dynamical phases and critical phenomena that exhibit topologically-robust methods to create, protect, and manipulate quantum entanglement that self-correct against large classes of errors. However, to date, experimental realizations have been confined to classical (non-entangled) symmetry-breaking orders. In this work, we demonstrate an emergent dynamical symmetry protected topological phase (EDSPT), in a quasiperiodically-driven array of ten $^{171}\text{Yb}^+$ hyperfine qubits in Honeywell's System Model H1 trapped-ion quantum processor. This phase exhibits edge qubits that are dynamically protected from control errors, cross-talk, and stray fields. Crucially, this edge protection relies purely on emergent dynamical symmetries that are absolutely stable to generic coherent perturbations. This property is special to quasiperiodically driven systems: as we demonstrate, the analogous edge states of a periodically driven qubit-array are vulnerable to symmetry-breaking errors and quickly decohere. Our work paves the way for implementation of more complex dynamical topological orders that would enable error-resilient techniques to manipulate quantum information.

Realizing a dynamical topological phase in a trapped-ion quantum simulator

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