We study weak ergodicity breaking in a one-dimensional, nonintegrable spin-1 XY model. We construct for it an exact, highly excited eigenstate, which despite its large energy density, can be represented analytically by a finite bond-dimension matrix product state (MPS) with area-law entanglement. Upon a quench to a finite Zeeman field, the state undergoes periodic dynamics with perfect many-body revivals, in stark contrast to other generic initial states which instead rapidly thermalize. This dynamics can be completely understood in terms of the evolution of entangled virtual spin-1/2 degrees of freedom, which in turn underpin the presence of an extensive tower of strong-eigenstate thermalization hypothesis (ETH)-violating many-body eigenstates. The resulting quantum many-body scars are therefore of novel origin. Our results provide important analytical insights into the nature and entanglement structure of quantum many-body scars.

Nodal lines inside the momentum space of three-dimensional crystalline solids are topologically stabilized by a $\pi$ flux of Berry phase. Nodal-line rings in $\mathcal{P}\mathcal{T}$-symmetric systems with negligible spin-orbit coupling (here described as “nodal class AI”) can carry an additional “monopole charge,” which further enhances their stability. Here, we relate two recent theoretical advancements in the study of band topology in nodal class AI. On the one hand, cohomology classes of real vector bundles were used to relate the monopole charge of nodal-line rings to their linking with nodal lines formed among the occupied and among the unoccupied bands. On the other hand, homotopy studies revealed that the generalization of the Berry-phase quantization to the case of multiple band gaps defines a non-Abelian topological charge, which governs the possible deformations of the nodal lines. The present work has three aims. First, we present how to efficiently wield the recently discovered non-Abelian topological charge. Second, we apply these methods to present an independent proof of the relation between the monopole charge and the linking structure, including all the fragile-topology exceptions. Finally, we show that the monopole charge flips sign when braided along a path with a nontrivial Berry phase. This facilitates a new type non-Abelian “braiding” of nodal-line rings inside the momentum space, that has not been previously reported. The work begins with a brief review of $\mathcal{P}\mathcal{T}$-symmetric band topology, and the geometric arguments employed in our theoretical analysis are supplemented in the appendices with formal mathematical derivations.

Quantum many-body scar states are many-body states with finite energy density in non-integrable models that do not obey the eigenstate thermalization hypothesis. Recent works have revealed “towers” of scar states that are exactly known and are equally spaced in energy, specifically in the AKLT and spin-1 XY models, and a spin-1/2 model that conserves the number of domain walls. We provide a common framework to understand and prove known exact towers of scars in these systems, by evaluating the commutator of the Hamiltonian and a ladder operator. In particular, we provide a simple proof of the scar towers in the integer-spin 1D AKLT models by studying two-site spin projectors. Through this picture we deduce a family of Hamiltonians that share the scar tower with the AKLT model, and also find common parent Hamiltonians for the AKLT and XY model scars. We also introduce new towers of exact states, organized in a “pyramid” structure, in the spin-1/2 model through the successive application of a nonlocal ladder operator.

We show how a finite number of conservation laws can globally “shatter” Hilbert space into exponentially many dynamically disconnected subsectors, leading to an unexpected dynamics with features reminiscent of both many-body localization and quantum scars. A crisp example of this phenomenon is provided by a “fractonic” model of quantum dynamics constrained to conserve both charge and dipole moment. We show how the Hilbert space of the fractonic model dynamically fractures into disconnected emergent subsectors within a particular charge and dipole symmetry sector. This shattering can occur in arbitrary spatial dimensions. A large number of the emergent subsectors, exponentially many in system volume, have dimension one and exhibit strictly localized quantum dynamics—even in the absence of spatial disorder and in the presence of temporal noise. Other emergent subsectors display nontrivial dynamics and may be constructed by embedding finite-sized nontrivial blocks into the localized subspace. While “fractonic” models provide a particularly clean realization, the shattering phenomenon is more general, as we discuss. We also discuss how the key phenomena may be readily observed in near term ultracold atom experiments. In experimental realizations, the conservation laws are approximate rather than exact, so the localization only survives up to a prethermal timescale that we estimate. We comment on the implications of these results for recent predictions of Bloch/Stark many-body localization.

We consider the thermal Hall effect of fermionic matter coupled to emergent gauge fields in $2+1$ dimensions. While the low-temperature thermal Hall conductivity of bulk topological phases can be connected to chiral edge states and a gravitational anomaly, there is no such interpretation at nonzero temperatures above $2+1$-dimensional quantum critical points. In the limit of a large number of matter flavors, the leading contribution to the thermal Hall conductivity is that of the fermionic matter. The next-to-leading contribution is from the gauge fluctuations, and this has a sign which is opposite to that of the matter contribution. We illustrate this by computations on a Dirac Chern-Simons theory of the quantum phase transition in a square-lattice antiferromagnet involving the onset of semion topological order. We find similar results for a model of the pseudogap metal with Fermi pockets coupled to an emergent U(1) gauge field. We note connections to recent observations on the hole-doped cuprates: our theory captures the main trends, but the overall magnitude of the effect is smaller than that observed.

The thermodynamic uncertainty relation (TUR), a trade-off relation between thermodynamic cost (entropy production) and precision (fluctuations), is expected to hold in nanoscale electronic conductors, when the electron transport process is quantum coherent and the transmission probability is constant (energy and voltage independent). We present measurements of the electron current and its noise in gold atomic-scale junctions and confirm the validity of the TUR for electron transport in realistic quantum coherent conductors. Furthermore, we show that it is beneficial to present the current and its noise as a TUR ratio to identify deviations from noninteracting-electron coherent dynamics.

We revisit the problem of classifying topological band structures in non-Hermitian systems. Recently, a solution has been proposed, which is based on redefining the notion of energy band gap in two different ways, leading to the so-called “point-gap” and “line-gap” schemes. However, simple Hamiltonians without band degeneracies can be constructed which correspond to neither of the two schemes. Here, we resolve this shortcoming of the existing classifications by developing the most general topological characterization of non-Hermitian bands for systems without a symmetry. Our approach, which is based on homotopy theory, makes no particular assumptions on the band gap, and predicts significant extensions to the previous classification frameworks. In particular, we show that the one-dimensional invariant generalizes from $\mathbb{Z}$ winding number to the non-Abelian braid group, and that depending on the braid group invariants, the two-dimensional invariants can be cyclic groups ${\mathbb{Z}}_n$ (rather than $\mathbb{Z}$ Chern number). We interpret these results in terms of a correspondence with gapless systems, and we illustrate them in terms of analogies with other problems in band topology, namely, the fragile topological invariants in Hermitian systems and the topological defects and textures of nematic liquids.

In the mixed-valence manganites, a near-infrared laser typically melts the orbital and spin order simultaneously, corresponding to the photoinduced $d^1{d}^0\stackrel{}{\to }{d}^0{d}^1$ excitations in the Mott-Hubbard bands of manganese. Here, we use ultrafast methods—both femtosecond resonant x-ray diffraction and optical reflectivity—to demonstrate that the orbital response in the layered manganite ${\mathrm{Nd}}_{1-x}{\mathrm{Sr}}_{1+x}{\mathrm{MnO}}_4\left(x=2/3\right)$ does not follow this scheme. At the photoexcitation saturation fluence, the orbital order is only diminished by a few percent in the transient state. Instead of the typical $d^1{d}^0\stackrel{}{\to }{d}^0{d}^1$ transition, a near-infrared pump in this compound promotes a fundamentally distinct mechanism of charge transfer, the $d^0\stackrel{}{\to }{d}^{1}L$, where $\mathit{L}$ denotes a hole in the oxygen band. This finding may pave a different avenue for selectively manipulating specific types of order in complex materials of this class.

Chiral nanophotonic components, such as waveguides and resonators coupled to quantum emitters, provide a fundamentally new approach to manipulate light-matter interactions. The recent emergence of topological photonics has provided a new paradigm to realize helical/chiral nanophotonic structures that are flexible in design and, at the same time, robust against sharp bends and disorder. Here we demonstrate such a topologically protected chiral nanophotonic resonator that is strongly coupled to a solid-state quantum emitter. Specifically, we employ the valley-Hall effect in a photonic crystal to achieve topological edge states at an interface between two topologically distinct regions. Our helical resonator supports two counterpropagating edge modes with opposite polarizations. We first show chiral coupling between the topological resonator and the quantum emitter such that the emitter emits preferably into one of the counterpropagating edge modes depending upon its spin. Subsequently, we demonstrate strong coupling between the resonator and the quantum emitter using resonant Purcell enhancement in the emission intensity by a factor of 3.4. Such chiral resonators could enable designing complex nanophotonic circuits for quantum information processing and studying novel quantum many-body dynamics.

We consider a two-band spinless model describing an excitonic insulator (EI) on the two-dimensional square lattice with anisotropic hopping parameters and electron-phonon (el-ph) coupling, inspired by the EI candidate ${\mathrm{Ta}}_2{\mathrm{NiSe}}_5$. We systematically study the nature of the collective excitations in the ordered phase which originates from the interband Coulomb interaction and the el-ph coupling. When the ordered phase is stabilized only by the Coulomb interaction (pure EI phase), its collective response exhibits a massless phase mode in addition to the amplitude mode. We show that in the BEC regime, the signal of the amplitude mode becomes less prominent and that the anisotropy in the phase-mode velocities is reduced. Through coupling to the lattice, the phase mode acquires a mass and the signal of the amplitude mode becomes less prominent. Importantly, the character of the softening mode at the boundary between the normal semiconductor phase and the ordered phase depends on the parameters. In particular, we point out that even for el-ph coupling smaller than the Coulomb interaction, the mode that softens to zero at the boundary can have a phonon character. We also discuss how the collective modes can be observed in the optical conductivity. Furthermore, we study the effects of nonlocal interactions on the collective modes and show the possibility of realizing a coexistence of an in-gap mode and an above-gap mode split off from the single-amplitude mode in the system with local interactions only.

The realization of mixtures of excitons and charge carriers in van der Waals materials presents a frontier for the study of the many-body physics of strongly interacting Bose-Fermi mixtures. In order to derive an effective low-energy model for such systems, we develop an exact diagonalization approach based on a discrete variable representation that predicts the scattering and bound state properties of three charges in two-dimensional transition metal dichalcogenides. From the solution of the quantum mechanical three-body problem we thus obtain the bound state energies of excitons and trions within an effective mass model which are in excellent agreement with quantum Monte Carlo predictions. The diagonalization approach also gives access to excited states of the three-body system. This allows us to predict the scattering phase shifts of electrons and excitons that serve as input for a low-energy theory of interacting mixtures of excitons and charge carriers at finite density. To this end we derive an effective exciton-electron scattering potential that is directly applicable for quantum Monte Carlo or diagrammatic many-body techniques. As an example, we demonstrate the approach by studying the many-body physics of exciton Fermi polarons in transition-metal dichalcogenides, and we show that finite-range corrections have a substantial impact on the optical absorption spectrum. Our approach can be applied to a plethora of many-body phenomena realizable in atomically thin semiconductors ranging from exciton localization to induced superconductivity.

${\mathrm{H}}_3\mathrm{LiI}{\mathrm{r}}_2{\mathrm{O}}_6$ is the first honeycomb-lattice system without any signs of long-range magnetic order down to the lowest temperatures, raising the hope for the realization of an ideal Kitaev quantum spin liquid. Its honeycomb layers are coupled by interlayer hydrogen bonds. Static or dynamic disorder of these hydrogen bonds was proposed to strongly affect the magnetic exchange and to make Kitaev-type interactions dominant. Using dielectric spectroscopy, here we provide experimental evidence for dipolar relaxations in ${\mathrm{H}}_3\mathrm{LiI}{\mathrm{r}}_2{\mathrm{O}}_6$ and deuterated ${\mathrm{D}}_3\mathrm{LiI}{\mathrm{r}}_2{\mathrm{O}}_6$, which mirror the dynamics of protons and deuterons within the double-well potentials of the hydrogen bonds. The detected hydrogen dynamics reveals glassy freezing, characterized by a strong slowing down under cooling, with a crossover from thermally activated hopping to quantum-mechanical tunneling towards low temperatures. Thus, besides being Kitaev quantum-spin-liquid candidates, these materials also are quantum paraelectrics. However, the small relaxation rates in the mHz range, found at low temperatures, practically realize quasistatic hydrogen disorder, as assumed in recent theoretical works to explain the quantum-spin-liquid ground state of both compounds.

The parkerite-type ternary chalcogenide ${\mathrm{Bi}}_2{\mathrm{Rh}}_3{\mathrm{Se}}_2$ was discovered to be a charge-density wave (CDW) superconductor. However, there was a debate on whether the observed phase transition at 240 K could be attributed to the formation of CDW order. To address the issue, we performed optical spectroscopy and ultrafast pump-probe measurements on single-crystal samples of ${\mathrm{Bi}}_2{\mathrm{Rh}}_3{\mathrm{Se}}_2$. Our optical conductivity measurement clearly reveals the formation of an energy gap with associated spectral change only at low energies, yielding strong evidence for a CDW phase transition at 240 K. Time-resolved pump-probe measurements provide further support for the CDW phase transition. The amplitude and relaxation time of quasiparticles extracted from the photoinduced reflectivity show strong enhancement near transition temperature, yielding further evidence for the CDW energy gap formation. Additionally, a collective mode is identified from the oscillations in the pump-probe time delay at low temperatures. This mode, whose frequency decreases gradually at elevated temperatures, could be naturally attributed to the amplitude mode of the CDW state.

Non-Hermiticity alters band topology in the presence of loss and/or gain in topological systems, which not only introduces new definitions in topological classifications, topological invariants, and the bulk-boundary correspondence, but also gives rise to unprecedented applications such as topological insulator lasers. Most existing non-Hermitian topological systems derive their topological phases from Hermitian components, rather than being driven by non-Hermiticity itself. Here we report on the experimental observation of topological edge states induced solely by non-Hermiticity in an acoustic crystal. The acoustic crystal consists of a periodic one-dimensional chain of coupled acoustic resonators with tunable loss. In the Hermitian limit, or when the loss is negligible, the crystal exhibits no band gap and hosts no topological edge states. By introducing loss, we show that a band gap is induced, which can be either topological or trivial, depending on the loss configuration. In the topological case, topological edge modes are found inside the band gap. These results demonstrate that non-Hermiticity is able to drive a topological phase transition from a trivial system to a topological one, offering the possibilities for actively steerable topological wave manipulations in applications ranging from acoustics to photonics.

The sulfur-substituted FeSe system, ${\mathrm{FeSe}}_{1-x}{\mathrm{S}}_x$, provides a versatile platform for studying the relationship among nematicity, antiferromagnetism, and superconductivity. Here, by nuclear magnetic resonance (NMR) and resistivity measurements up to 4.73 GPa on ${\mathrm{FeSe}}_{0.91}{\mathrm{S}}_{0.09}$, we established the pressure- ($p$-) temperature ($T$) phase diagram in which the nematic state is suppressed with pressure showing a nematic quantum phase transition (QPT) around $p=0.5\mathrm{GPa}$, two superconductivity (SC) regions separated by the QPT appear, and antiferromagnetic (AFM) phase emerges above $\sim 3.3\mathrm{GPa}$. From the NMR results up to 2.1 GPa, AFM fluctuations are revealed to be characterized by the stripe-type wave vector which remains the same for the two SC regions. Furthermore, the electronic state is found to change in character from non-Fermi liquid to Fermi liquid around the nematic QPT and persists up to $\sim 2.1\mathrm{GPa}$. In addition, although the AFM fluctuations correlate with $T_{\mathrm{c}}$ in both SC states, demonstrating the importance of the AFM fluctuations for the appearance of SC in the system, we found that, when nematic order is absent, $T_{\mathrm{c}}$ is strongly correlated with the AFM fluctuations whereas $T_{\mathrm{c}}$ weakly depends on the AFM fluctuations when nematic order is present. Our findings on ${\mathrm{FeSe}}_{0.91}{\mathrm{S}}_{0.09}$ were shown to be applied to the whole ${\mathrm{FeSe}}_{1-x}{\mathrm{S}}_x$ system and provide an insight into the relationship between AFM fluctuations and SC in Fe-based superconductors.

The recently reported magnetic ordering in insulating two-dimensional (2D) materials, such as chromium triiodide (${\mathrm{CrI}}_3$) and chromium tribromide (${\mathrm{CrBr}}_3$), opens new possibilities for the fabrication of magnetoelectronic devices based on 2D systems. Inevitably, the magnetization and spin dynamics in 2D magnets are strongly linked to Joule heating. Therefore, understanding the coupling between spin, charge, and heat, i.e., spin caloritronic effects, is crucial. However, spin caloritronics in 2D ferromagnets remains mostly unexplored, due to their instability in air. Here we develop a fabrication method that integrates spin-active contacts with 2D magnets through hBN encapsulation, allowing us to explore the spin caloritronic effects in these materials. The angular dependence of the thermal spin signal of the ${\mathrm{CrBr}}_3/\mathrm{Pt}$ system is studied, for different conditions of magnetic field and heating current. We highlight the presence of a significant magnetic proximity effect from ${\mathrm{CrBr}}_3$ on Pt revealed by an anomalous Nernst effect in Pt, and suggest the contribution of the spin Seebeck effect from ${\mathrm{CrBr}}_3$. These results pave the way for future magnonic devices using air-sensitive 2D magnetic insulators.

Magnetic singularities, also known as magnetic monopoles or Bloch points, represent intriguing phenomena in nanomagnetism. We show that a pair of coupled Bloch points—a dipole string—may appear as a stable state in cubic chiral magnets. Analysis of the thermodynamic stability of such objects in the interior of crystals and in geometrically confined systems is presented. Employing advanced Monte Carlo simulations, we reveal an effect of spontaneous nucleation of dipole strings with characteristic size on the order of the helix pitch at temperature close to the paramagnetic phase transition. Such behavior of chiral magnets at elevated temperature drastically distinguishes them from ordinary ferromagnets and may provide a significant contribution to the topological Hall effect even in the absence of skyrmions.

We uncover the properties of complex tensor ($d$-wave) superconducting order in three-dimensional Rarita-Schwinger-Weyl semimetals that host pseudospin-$\frac{3}{2}$ fermions at a fourfold linear band-crossing point. Although the general theory of $d$-wave order was originally developed for materials displaying quadratic band touching, it directly applies to the case of semimetals with linear dispersion, several candidate compounds of which have been discovered experimentally very recently. The spin-$\frac{3}{2}$ nature of the fermions allows for the formation of spin-2 Cooper pairs which may be described by a complex second-rank tensor order parameter. In the case of linear dispersion, for the chemical potential at the Fermi point and at strong coupling, the energetically preferred superconducting state is the uniaxial nematic state, which preserves time-reversal symmetry and provides a full (anisotropic) gap for quasiparticle excitations. In contrast, at a finite chemical potential, we find that the usual weak-coupling instability is toward the “cyclic state,” well known from the studies of multicomponent Bose-Einstein condensates, which breaks time-reversal symmetry maximally, has vanishing average value of angular momentum, and features 16 small Bogoliubov-Fermi surfaces. The Rarita-Schwinger-Weyl semimetals provide therefore the first example of weakly coupled, three-dimensional, isotropic $d$-wave superconductors where the $d$-wave superconducting phase is uniquely selected by the quartic expansion of the mean-field free energy, and is not afflicted by the accidental degeneracy first noticed by Mermin over 40 years ago. We discuss the appearance and stability of the Bogoliubov-Fermi surfaces in absence of inversion symmetry in the electronic Hamiltonian, as in the case at hand.

The Dzyaloshinskii-Moriya interaction (DMI), which only exists in noncentrosymmetric systems, is responsible for the formation of exotic chiral magnetic states. The absence of DMI in most two-dimensional (2D) magnetic materials is due to their intrinsic inversion symmetry. Here, using first-principles calculations, we demonstrate that significant DMI can be obtained in a series of Janus monolayers of manganese dichalcogenides $\mathrm{Mn}\mathit{XY}$ ($X,Y$= S, Se, Te, $X\ne Y$) in which the difference between $X$ and $Y$ on the opposite sides of Mn breaks the inversion symmetry. In particular, the DMI amplitudes of MnSeTe and MnSTe are comparable to those of state-of-the-art ferromagnet/heavy metal heterostructures. In addition, by performing Monte Carlo simulations, we find that at low temperatures the ground states of the MnSeTe and MnSTe monolayers can transform from ferromagnetic states with wormlike magnetic domains into the skyrmion states by applying an external magnetic field. At increasing temperature, the skyrmion states start fluctuating above 50 K before an evolution to a completely disordered structure at higher temperature. The present results pave the way for new device concepts utilizing chiral magnetic structures in specially designed 2D ferromagnetic materials.

We present a theory of competing ferromagnetic and superconducting orders in twisted double bilayer graphene. In our theory, ferromagnetism is induced by Coulomb repulsion, while superconductivity with intervalley equal-spin pairing can be mediated by electron-acoustic phonon interactions. We calculate the transition temperatures for ferromagnetism and superconductivity as a function of moiré band filling factor, and find that superconducting domes can appear on both the electron and hole sides of the ferromagnetic insulator at half filling. We show that the ferromagnetic insulating gap has a dome shape dependence on the layer potential difference, which provides an explanation to the experimental observation that the ferromagnetic insulator only develops over a finite range of external displacement field. We also verify the stability of the half filled ferromagnetic insulator against two types of collective excitations, i.e., spin magnons and valley magnons.