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Abstract The Dicke model describes the cooperative interaction of an ensemble of twolevel atoms with a singlemode photonic field and exhibits a quantum phase transition as a function of light–matter coupling strength. Extending this model by incorporating shortrange atom–atom interactions makes the problem intractable but is expected to produce new physical phenomena and phases. Here, we simulate such an extended Dicke model using a crystal of ErFeO_{3}, where the role of atoms (photons) is played by Er^{3+}spins (Fe^{3+}magnons). Through terahertz spectroscopy and magnetocaloric effect measurements as a function of temperature and magnetic field, we demonstrated the existence of a novel atomically ordered phase in addition to the superradiant and normal phases that are expected from the standard Dicke model. Further, we elucidated the nature of the phase boundaries in the temperature–magneticfield phase diagram, identifying both firstorder and secondorder phase transitions. These results lay the foundation for studying multiatomic quantum optics models using wellcharacterized manybody solidstate systems.

The hallmark of highly frustrated systems is the presence of many states close in energy to the ground state. Fluctuations between these states can preclude the emergence of any form of order and lead to the appearance of spin liquids. Even on the classical level, spin liquids are not all alike: they may have algebraic or exponential correlation decay, and various forms of long wavelength description, including vector or tensor gauge theories. Here, we introduce a classification scheme, allowing us to fit the diversity of classical spin liquids (CSLs) into a general framework as well as predict and construct new kinds. CSLs with either algebraic or exponential correlationdecay can be classified via the properties of the bottom flat band(s) in their softspin Hamiltonians. The classification of the former is based on the algebraic structures of gapless points in the spectra, which relate directly to the emergent generalized Gauss's laws that control the low temperature physics. The second category of CSLs, meanwhile, are classified by the fragile topology of the gapped bottom band(s). Utilizing the classification scheme we construct new models realizing exotic CSLs, including one with anisotropic generalized Gauss's laws and charges with subdimensional mobility, one with a network of pinchline singularities in its correlation functions, and a series of fragile topological CSLs connected by zerotemperature transitions.more » « lessFree, publiclyaccessible full text available May 30, 2024

Classical spin liquids (CSL) lack longrange magnetic order and are characterized by an extensive ground state degeneracy. We propose a classification scheme of CSLs based on the structure of the flat bands of their Hamiltonians. Depending on absence or presence of the gap from the flat band, the CSL are classified as algebraic or fragile topological, respectively. Each category is further classified: the algebraic case by the nature of the emergent Gauss's law at the gapclosing point(s), and the fragile topological case by the homotopy of the eigenvector winding around the Brillouin zone. Previously identified instances of CSLs fit snugly into our scheme, which finds a landscape where algebraic CSLs are located at transitions between fragile topological ones. It also allows us to present a new, simple family of models illustrating that landscape, which hosts both fragile topological and algebraic CSLs, as well as transitions between themmore » « lessFree, publiclyaccessible full text available April 29, 2024

Abstract Magnetic order in most materials occurs when magnetic ions with finite moments arrange in a particular pattern below the ordering temperature. Intriguingly, if the crystal electric field (CEF) effect results in a spinsinglet ground state, a magnetic order can still occur due to the exchange interactions between neighboring ions admixing the excited CEF levels. The magnetic excitations in such a state are spin excitons generally dispersionless in reciprocal space. Here we use neutron scattering to study stoichiometric Ni 2 Mo 3 O 8 , where Ni 2+ ions form a bipartite honeycomb lattice comprised of two triangular lattices, with ions subject to the tetrahedral and octahedral crystalline environment, respectively. We find that in both types of ions, the CEF excitations have nonmagnetic singlet ground states, yet the material has magnetic order. Furthermore, CEF spin excitons from the tetrahedral sites form a dispersive diffusive pattern around the Brillouin zone boundary, likely due to spin entanglement and geometric frustrations.more » « lessFree, publiclyaccessible full text available December 1, 2024

We study the nature of the debated thermal Hall effect in the candidate Kitaev material αRuCl3. Without assuming the existence of a gapped spin liquid, we show that a realistic minimal spin model in the canted zigzag phase suffices, at the level of linear spinwave theory, to qualitatively explain the observed temperature and magnetic field dependence of the nonquantized thermal Hall conductivity κ_xy, with its origin lying in the Berry curvature of the magnon bands. The magnitude of the effect is however too small compared to the measurement by Czajka et al. [Nat. Mater. 22, 3641 (2023)], even after scanning a broad range of model parameters so as to maximize κ_xy/T. Recent experiments suggest that phonons play an important role, which we show couple to the spins, endowing phonons with chirality. The resulting intrinsic contribution, from both magnons and phonons, is however still insufficient to explain the observed magnitude of the Hall signal. After careful analysis of the extrinsic phonon mechanisms, we use the recent experimental data on thermal transport in αRuCl3 by Lefrançois et al. [Phys. Rev. X 12, 021025 (2022)] to determine the phenomenological ratio of the extrinsic and intrinsic contributions η≡κ_E/κ_I. We find η=1.2±0.5, which when combined with our computed intrinsic value, explains quantitavely both the magnitude and detailed temperature dependence of the experimental thermal Hall effect in αRuCl3.more » « less

Electronic spins can form longrange entangled phases of condensed matter named quantum spin liquids. Their existence is conceptualized in models of two or threedimensional frustrated magnets that evade symmetrybreaking order down to zero temperature. Quantum spin ice (QSI) is a theoretically wellestablished example described by an emergent quantum electrodynamics, with excitations behaving like photon and matter quasiparticles. The latter are fractionally charged and equivalent to the `spinons' emerging from coherent phases of singlets in one dimension, where clear experimental proofs of fractionalization exist. However, in frustrated magnets it remains difficult to establish consensual evidence for quantum spin liquid ground states and their fractional excitations. Here, we use backscattering neutron spectroscopy to achieve extremely high resolution of the timedependent magnetic response of the candidate QSI material Ce2Sn2O7. We find a gapped spectrum featuring a threshold and peaks that match theories for pair production and propagation of fractional matter excitations (spinons) strongly coupled to a background gauge field. The observed peaks provide evidence for a QSI through spectroscopic signatures of spacetime symmetry fractionalization, while the threshold behavior corroborates the regime of strong lightmatter interaction predicted for the emergent universe in a QSI.more » « lessFree, publiclyaccessible full text available May 16, 2024

Unlike ordinary topological quantum phases, fracton orders are intimately dependent on the underlying lattice geometry. In this work, we study a generalization of the Xcube model, dubbed the Ycube model, on lattices embedded in H2×S1 space, i.e., a stack of hyperbolic planes. The name `Ycube' comes from the Yshape of the analog of the Xcube's Xshaped vertex operator. We demonstrate that for certain hyperbolic lattice tesselations, the Ycube model hosts a new kind of subdimensional particle, treeons, which can only move on a fractalshaped subset of the lattice. Such an excitation only appears on hyperbolic geometries; on flat spaces treeons becomes either a lineon or a planeon. Intriguingly, we find that for certain hyperbolic tesselations, a fracton can be created by a membrane operator (as in the Xcube model) or by a fractalshaped operator within the hyperbolic plane.more » « less

Free, publiclyaccessible full text available January 1, 2025