Recent advances in quantum simulators allow direct experimental access to ensembles of pure states generated by measuring part of an isolated quantum many-body system. These projected ensembles encode fine-grained information beyond thermal expectation values and provide a new window into quantum thermalization. In chaotic dynamics, projected ensembles exhibit universal statistics governed by maximum-entropy principles, known as deep thermalization. At infinite temperature, this universality is characterized by Haar-random ensembles. More generally, physical constraints such as finite temperature or conservation laws lead to Scrooge ensembles, which are maximally entropic distributions of pure states consistent with these constraints. Here, we introduce Scrooge $k$-designs, which approximate Scrooge ensembles, and we use this framework to sharpen the conditions under which Scrooge-like behavior emerges. We first show that global Scrooge designs arise from long-time chaotic unitary dynamics alone, without measurements. Second, we show that measuring a complementary subsystem of a scrambled global state drawn from a global Scrooge $2k$-design induces a local Scrooge $k$-design. Third, we show that a local Scrooge $k$-design arises from an arbitrary entangled state when the complementary system is measured in a scrambled basis induced by a unitary drawn from a Haar $2k$-design. These results show that the resources required to generate approximate Scrooge ensembles scale only with the desired degree of approximation, enabling efficient implementations. Complementing our analytical results, numerical simulations identify coherence, entanglement, nonstabilizerness, and information scrambling as essential ingredients for the emergence of local Scrooge-like behavior. Together, our findings advance theoretical explanations for maximally entropic, information-stingy randomness in quantum many-body systems.

For closed quantum systems, topological orders are understood through the equivalence classes of ground states of gapped local Hamiltonians. The generalization of this conceptual paradigm to open quantum systems, however, remains elusive, often relying on operational definitions without fundamental principles. Here, we fill this gap by proposing an approach based on three axioms: (i) local recoverability, (ii) absence of long-range correlations, and (iii) spatial uniformity. States that satisfy these axioms are fixed points; requiring the axioms only after coarse-graining promotes each fixed point to an equivalence class, i.e., a phase, presenting the first step toward the axiomatic classification of mixed-state phases of matter: the mixed-state bootstrap program. From these axioms, a rich set of topological data naturally emerges; importantly, these data are robust under relaxation of axioms. For example, each topological mixed state supports locally indistinguishable classical and/or quantum logical memories with distinct responses to topological operations. These data label distinct mixed-state phases, allowing one to distinguish them. We further uncover a hierarchy of secret-sharing constraints: In non-Abelian phases, reliable recovery—even of information that looks purely classical—demands a specific coordination among spatial subregions, a requirement different across non-Abelian classes. This originates from non-Abelian fusion rules that can stay robust under decoherence. Finally, we performed large-scale numerical simulations to corroborate stability: Weakly decohered fixed points respect the axioms once coarse-grained. Surprisingly, the axiom violations at different length scales exhibit an exact crossing at the critical point, enabling its identification without any rescaling or data-collapse ambiguities. These results lay the foundation for a systematic classification of topological states in open quantum systems.

A spin nematic order, analogous to a nematic liquid crystal, characterizes the spontaneous breaking of spin-space rotational symmetry while preserving time-reversal ($T$) symmetry. On the other hand, the order parameter characterizing the $T$-symmetry breaking is the composite three-spin order, i.e., the scalar spin chirality (SSC) ${\chi }_{ijk}=⟨S_i·(S_j\times S_k)⟩$, where $S_i$, $S_j$, $S_k$ are spins at neighboring sites $i$, $j$, $k$, respectively, and nonzero SSC is known to induce anomalous Hall effect (AHE). Although a spin nematic phase has been suggested in the frustrated magnets and the square-lattice iridate, how a spin nematic phase might affect magneto-transport properties is unknown. Here we use polarized neutron scattering to show that tetragonal lattice $A{\mathrm{MnBi}}_2$ ($A=\mathrm{Ca}$, Yb) is a strictly $c$-axis-aligned collinear antiferromagnet ($C$-type) with $T_N\approx 270$ and 290 K. On cooling from 450 K to $T_N$, low-energy spin excitations in ${\mathrm{YbMnBi}}_2$ spontaneously change from isotropic to anisotropic in spin space within the tetragonal plane, forming a dynamic spin nematic phase around 400 K due to heavy Yb-induced spin-orbit coupling, before gapping out below $T_N$. Similar polarized neutron scattering measurements on ${\mathrm{CaMnBi}}_2$ reveal isotropic paramagnetic scattering without a spin nematic phase above $T_N$. Under an in-plane external magnetic field, the ${\mathrm{Yb}}^{3+}$ moments may interact with the dynamic spin nematic phase to induce nonzero SSC, giving rise to AHE and anomalous Nernst effect (ANE) in ${\mathrm{YbMnBi}}_2$ that is absent in ${\mathrm{CaMnBi}}_2$ above $T_N$. Theoretical analysis of Ginzburg-Landau theory based on the symmetry indicates that the coupling terms between the nematic order and SSC of 5 order in the spin operators are allowed under an external magnetic field $B$. This could explain the rapid increase of AHE as a function of $B$ in ${\mathrm{YbMnBi}}_2$. Our results, therefore, provide compelling evidence for dynamic SSC-induced AHE and ANE in the paramagnetic phase of a compensated collinear antiferromagnet, opening a new avenue for the physics of composite orders of multiple spins for room-temperature spintronics without magnetic order.

We experimentally and theoretically study the thermodynamically optimal control of interacting multiparticle systems, focusing on collections of colloidal particles individually confined in optical traps. We investigate protocols that transport the system between prescribed trap configurations within a fixed time in the most energy efficient way. For Markovian systems with conservative pairwise interactions, we establish a general result in the low-noise limit: optimal particle trajectories are linear in space and time, corresponding to steady straight-line motion, irrespective of the specific interaction potential, even for nonlinear forces. Thus, conservative interactions do not modify the geometry of the optimal paths. This property breaks down in the presence of strong noise or nonconservative interactions. For the paradigmatic case of hydrodynamic coupling, we demonstrate experimentally that optimal control can involve curved trajectories that significantly reduce the energetic cost by exploiting collectively generated fluid flows. The emergence of curved paths as optimal solutions highlights a fundamental distinction between noninteracting and interacting systems and reveals a cooperative mechanism for energy-efficient control.

Quasicrystals extend topological concepts beyond periodic systems, but their exploration in mechanical wave systems remains elusive. Here, we experimentally realize two-dimensional quasicrystal water waves with fivefold rotational symmetry via the interference of multiple quasiplane waves. Although topologically indistinguishable in real space, these patterns are uniquely classified by higher-dimensional topological charge vectors that obey an angular-momentum-like conservation law. Using the water-wave amplitude and its in-plane gradient, we construct a synthetic three-dimensional vector field and demonstrate the emergence of skyrmions in water-wave quasicrystals. These skyrmions exhibit dynamically evolving boundaries and orientations, i.e., deformation and propagation due to phasonlike motion during the evolution of the quasicrystal water-wave field. Remarkably, the associated phase singularities can generate forces and torques that stably trap and drive the rotation of floating particles. We demonstrate in experiments the simultaneous manipulation of particles at multiple trapping sites in different ways, opening a path toward programmable control of particle dynamics. By bridging higher-dimensional topology with water-wave quasicrystals and skyrmions, our work not only advances the physics of topological hydrodynamics but also establishes a platform for on-demand particle control in aqueous environments, which is promising for applications in biomedicine, microfluidics, and lab-on-a-chip technologies.

We introduce a variational method for simulating the dynamics of interacting open quantum bosonic systems deep in the quantum regime. The method is based on a multidimensional Wigner phase-space representation and employs a variational multi-Gaussian Ansatz, whose accuracy is systematically controlled by the number of Gaussian components. The variational equations of motion are derived from the Dirac-Frenkel principle and evaluated efficiently by combining the analytical structure of Gaussian functions with automatic differentiation. As a key physical application, we study a driven-dissipative two-dimensional Bose-Hubbard lattice with two-boson coherent driving and two-body losses. Using our dynamical approach, we compute the finite-size scaling of the Liouvillian spectral gap—extracted from the relaxation dynamics—which vanishes in the thermodynamic limit. Our results reveal critical slowing down with dynamical exponents of the 2D quantum Ising universality class, demonstrating the power of our method to capture complex quantum dynamics in large open systems.

We study chaotic many-body quantum dynamics in a minimal model with spatial structure and local interactions. It has a time-independent Hamiltonian, in contrast to quantum circuits and Brownian models, and is simple at the single-site level, in contrast to Sachdev-Ye-Kitaev chains. It is analytically tractable for large local Hilbert space dimension and weak intersite coupling. In this limit, we show that energy dynamics is described by a classical master equation and is diffusive. We also show that the spectral form factor can be expressed exactly in terms of the solution to this master equation. For a two-site system, we obtain closed-form expressions for both the two-point correlator of energy density and the spectral form factor, in essentially perfect agreement with numerical simulations. For an $L$-site system we show at late times how a linear ramp emerges in the spectral form factor, as universally expected from level repulsion in chaotic quantum systems. Conversely, at earlier times we identify two distinct mechanisms for an increase of the spectral form factor above its ramp value. One of these is associated with energy diffusion and is effective until the Thouless time, which varies as $L^2$. The other involves contributions like those that would appear if the system were composed of many uncoupled subsystems: They generate a large enhancement of the spectral form factor and are suppressed on a timescale varying as $(\ln L{)}^2$. Besides being exact for the limit considered, we believe our approach provides the natural approximation even for small local Hilbert space dimension and strong intersite coupling. We present a numerical study of a spin-half chain, finding an early-time enhancement of the spectral form factor which is qualitatively similar to that in our solvable model.

Topology can imbue lattice systems with special properties, notably, the presence of robust eigenstates living at their boundary. Through dimensional reduction, the robust bulk band topology of, e.g., the integer quantum Hall system can be mapped onto similarly robust charge-pumping dynamics of a topological pump living in one lower dimension. Recent studies have uncovered a rich influence of interactions on the dynamics of topological pumps in nonlinear systems, including the robust pumping of self-bound solitons. These striking observations in classical nonlinear photonics have raised a number of questions, chiefly if and how this phenomenology persists in strongly correlated quantum systems and in the few-body limit. Here, using few- and many-atom arrays, we explore how dipolar interactions impact the dynamics of topological population pumping along a Rydberg synthetic dimension. In the few-body limit, we find that dipolar interactions lead to self-bound states that are efficiently pumped along the synthetic dimension, described by an emergent pair-state topological pump. We find that this interaction-assisted pumping persists in many-atom arrays, with a sharpened dependence on the dipolar interaction strength that stems from the enhanced spatial connectivity. These Rydberg-based studies on interaction-assisted topological pumping help connect observations from classical nonlinear photonics to the few-body quantum limit and pave the way for studies of new strongly correlated topological phenomena.

Fractional quantum Hall states are promising platforms for topological quantum computation due to their capacity to encode quantum information in topologically degenerate ground states and in the fusion space of non-Abelian anyons. We investigate how the information encoded in two paradigmatic states, the Laughlin and Moore-Read states, is affected by density decoherence—coupling of local charge density to nonthermal noise. We identify a critical filling factor ${\nu }_c$, above which the quantum information remains fully recoverable for arbitrarily strong decoherence. The $\nu =1/3$ Laughlin state and $\nu =1/2$ Moore-Read state both lie within this range. Below ${\nu }_c$ both classes of states undergo a decoherence-induced Berezinskii-Kosterlitz-Thouless (BKT) transition into a critical decohered phase. For Laughlin states, information encoded in the topological ground state manifold degrades continuously with decoherence strength inside this critical phase, vanishing only in the limit of infinite decoherence strength. On the other hand, quantum information encoded in the fusion space of non-Abelian anyons of the Moore-Read states remains fully recoverable under arbitrarily strong decoherence even beyond the BKT transition. These results lend further support to the promise of non-Abelian FQH states as platforms for topological quantum computation. They reveal how the interplay between chiral topological order and global symmetry can give rise to novel mixed-state phases under decoherence, distinguished by their capacity for storing quantum information.

Mechanical memory and computing are gaining significant traction as potential means to complement traditional electronics for robust and energy efficient performance in extreme environments. However, progress has largely focused on bistable metamaterials, while traditional constitutive memory phenomena have been largely overlooked—primarily due to the absence of compelling experimental demonstrations in elastically recoverable materials. Here, we report constitutive return point memory (RPM) in elastically recoverable, vertically aligned carbon nanotube (VACNT) foams, analogous to magnetic hysteresis-based RPM utilized in hard drives. Unlike viscoelastic fading memory, VACNTs exhibit nonvolatile memory arising from rate-independent nanoscale friction. We find that the interplay between RPM and frictional dissipation enables independent tunability of the VACNTs’ dynamic modulus, allowing for both on-demand softening and stiffening. We leverage this property to experimentally demonstrate tunable wave speed in a VACNT array with elastic interlayers, paving the way for novel shock limiters, elastodynamic lensing, and wave-based analog mechanical computing.

The discovery of 80 K superconductivity in pressurized bilayer Ruddlesden-Popper (RP) nickelate ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ has established a new high-temperature superconductor family [1]. The quest to understand the governing principles of RP nickelate superconductivity has become a central focus in condensed matter physics. Here, we report a critical advance by synthesizing and investigating a distinct structural polymorph of the same compound: the monolayer-trilayer (1313) phase of ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$. Under high pressure, synchrotron x-ray diffraction and Raman spectroscopy reveal a structural transition from the orthorhombic $Cmmm$ to the tetragonal $P4/mmm$ space group at 13 GPa. Above 19 GPa, the phase shows a clear superconducting transition, confirmed by a zero-resistance state, albeit at a much lower temperature of 3.6 K. The stark contrast with the 80 K transition in the bilayer phase provides a uniquely clean experimental comparison. Our results not only expand the family of RP nickelate superconductors but also deepen the understanding of the superconducting mechanism that governs the transition temperature in these materials.

In single-particle tracking experiments measuring anomalous diffusion dynamics, understanding ergodicity is crucial, as it ensures that the time average of an observable matches the ensemble average—and can thus be fitted with known ensemble-averaged observables. A commonly used criterion for assessing the ergodicity of a stochastic process is based on the comparison of the mean-squared displacement (MSD) with the time-averaged MSD (TAMSD). This approach has been widely applied and proves effective in cases of weak ergodicity breaking across various systems in both theoretical and experimental studies. However, there is relatively little discussion regarding the theoretical justification and limitations of this definition. Here, we demonstrate that this widely accepted criterion to some extent contradicts the classical definition of ergodicity as well as physical intuition, leading to spurious (non-)ergodicity results when applied to several well-known stochastic models. To address this limitation, we propose using the mean-squared increment (MSI) instead of the MSD for comparison of ensemble- and time-averaged observables. For processes with stationary increments, the results for MSI and MSD coincide. However, if the increments of the process reach stationarity at long times only, they differ, and the MSI-TAMSD comparison still provides the test for ergodicity. Several well-established examples demonstrate, through both trajectory simulations and theoretical analysis, that our MSI-TAMSD criterion provides a more accurate characterization of the genuine (non-)ergodicity of systems where the MSD-TAMSD method fails. Additionally, for systems exhibiting “ultraweak” ergodicity breaking, the MSI can reveal the asymptotic stationarity and ergodic nature of the process’s increments. Our findings emphasize the important role of the MSI observable for SPT experiments and anomalous diffusion studies.

Pyrochlore magnets are a paradigmatic example of three-dimensional frustrated systems and provide an excellent platform for studying a variety of exotic many-body phenomena, including spin liquids, nematic phases, fragmentation, and order by disorder. In recent years, increasing attention has been devoted to bilinear spin models on this lattice, where multiple magnetic phases can be degenerate in energy, often stabilizing unconventional magnetic states. In this work, we focus on one such model, parametrized by the interaction coupling $J_{z\pm }$, which defines a line in parameter space corresponding to the phase boundary between three distinct magnetic phases. Using a combination of analytical and numerical methods, we show that this model exhibits an order-by-disorder mechanism at low temperatures, giving rise to a mixed magnetic phase. This realizes a $\mathbf{q}=0$ long-range-ordered phase in a pyrochlore magnet characterized by two distinct order parameters, which we denote as the $A_2\oplus {\psi }_2$ phase. Furthermore, at $J_{z\pm }=1/\sqrt{2}$, the model acquires a subextensive number of discrete symmetries, which preclude the stabilization of conventional long-range order and instead lead to the emergence of a novel nematic phase. We characterize this nematic phase, describe how its ground-state configurations are constructed, and analyze its stability at higher temperatures and under small deviations from $J_{z\pm }=1/\sqrt{2}$.

Materials hosting flat bands at the vicinity of the Fermi level promote exotic symmetry broken states. Common to many of these are Van Hove singularities at saddle points of the dispersion or even higher-order Van Hove singularities (HOVHSs) where the dispersion is flattened further. The band structure of kagome metals hosts both a flat band and two regular saddle points flanking a Dirac node. We investigate the kagome ferromagnetic metal ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$ using scanning tunneling spectroscopy. We identify a new mechanism by which a triangular distortion on its kagome ${\mathrm{Co}}_3\mathrm{Sn}$ surface termination considerably flattens the saddle point dispersion and induces an isolated HOVHS with algebraically divergent density of states pinned to the Fermi energy. The distortion-induced HOVHS precipitates a Pomeranchuk instability of the Fermi surface, resulting in the formation of a series of nematic electronic states. We visualize the nematic order across an energy shell of about 100 meV in both real, reciprocal, and momentum spaces, as a cascade of wave function distributions which spontaneously break the remaining rotational symmetry of the underlying distorted kagome lattice, without generating any additional translational symmetry breaking. It signifies the spontaneous removal of a subset of saddle points from the Fermi energy to lower energies. By tracking the electronic wave function structure across the deformed Fermi surface, we further identify a charge pumpinglike evolution of the wave function center of mass. The mechanism we find for the generation of higher-order saddle points under a kagome distortion may be common to other kagome materials, and potentially other lattice structures, suggesting a generic new avenue for inducing unconventional electronic instabilities toward exotic states of matter.

Magnons, the quanta of spin waves, have significant potential for use in modern technologies, especially when they are strongly coupled to another mode for readout and control. Although magnons strongly interact with microwave photons via the magnetic-dipole interaction to form hybrid cavity-magnon polariton modes, the magnon-phonon interaction in micrometer-sized ferromagnetic spheres is typically weak, which is further aggravated by the large polariton linewidths dominated by the magnon dissipation. The material-limited magnon dissipation rate in particular has been regarded as an unavoidable limitation in these systems. Here, we surpass this long-standing limitation by implementing an active microwave feedback loop to suppress the linewidth of cavity-magnon polaritons and reduce their effective decay rate below the magnon-limited linewidth, thereby enhancing the polariton-phonon cooperativity from $C\simeq 1$ to $C\simeq 300$. As a key milestone, we achieved normal-mode splitting between a cavity-magnon polariton and a mechanical mode, providing direct evidence of three-mode hybridization among photons, magnons, and phonons. Our results establish feedback as a general route to accessing strong-coupling regimes in systems previously thought to be limited by material properties and hence open new opportunities for coherent control in hybrid quantum systems.

The dynamics of flexible filaments in flow underpin a broad range of biological and soft-matter phenomena, yet their response to time-dependent forcing remains poorly understood. Here, we investigate the long-time dynamics of Brownian inextensible elastic filaments subjected to strong oscillatory shear by combining microfluidic experiments on actin filaments with numerical simulations based on a fluctuating Euler-Bernoulli elastica model in a viscous fluid. As the oscillation period increases, the interplay of flow-induced buckling and thermal fluctuations drives a transition away from reversible rigid-body dynamics. Remarkably, the time-glide symmetry of oscillatory shear gives rise to two coexisting symmetry-related dynamical attractors, between which stochastic fluctuations induce intermittent switching events. These attractors correspond to cyclic states in which filaments become nearly straight and flow aligned at full periods while adopting buckled conformations at half periods. Individual filaments spontaneously select one attractor but intermittently hop to the other, producing alternating episodes of ordered and chaotic dynamics. Our results establish periodically driven Brownian flexible filaments as an experimentally accessible realization of stochastic symmetry breaking, attractor hopping, and intermittency in a minimal nonequilibrium system, and present novel opportunities for the design and control of soft materials under time-dependent flows.

We demonstrate the emergence of altermagnetism at the surfaces of antiferromagnets, vastly expanding the number of material candidates with altermagnetic characteristics and establishing a route towards two-dimensional altermagnetism through surface-induced symmetry breaking. We do so by developing a surface spin group formalism that fully classifies all surface magnetic states and identifies altermagnetic surface spin groups that can arise at the surfaces of antiferromagnets. We use this formalism to identify over 150 antiferromagnetic entries from the MAGNDATA database with at least one altermagnetic surface, often times with multiple such surfaces in the same material, and clarify the role of surface roughness and terraces. We illustrate this emergent phenomenon in a realistic Lieb lattice-based minimal model and present ab initio calculations on two representative material candidates, $\text{NaMnP}$ and ${\text{FeGe}}_2$, exhibiting $d$-wave and $g$-wave surface altermagnetism, respectively. Our theory naturally resolves the contradiction of recent experimental reports of $d$-wave spin splitting from ARPES measurements on metallic Lieb lattice compounds such as ${\mathrm{KV}}_2{\mathrm{Se}}_2\mathrm{O}$ that have been shown to be antiferromagnetic in the bulk. Hence, we establish a new paradigm for generating effectively two-dimensional altermagnetism by functionalizing the abundant material class of collinear antiferromagnets as viable platforms for controlled surface altermagnetism.

As an instance of geometrical frustration with nonmagnetic degrees of freedom, we explore the physics of local spin $S\ge 1$ moments on the pyrochlore lattice that interact via pure quadrupolar couplings. In the presence of spin-orbit coupling, there are nine allowed couplings between nearest-neighbor quadrupoles. We determine the semiclassical phases and survey the phase diagram of the model. One may view the Hamiltonian as being composed of two copies of the well-studied dipolar model with couplings between the copies, and we find that each easy-plane dipolar phase has two quadrupolar counterparts. As geometrical frustration is important over broad swathes of the parameter space, there are many classical quadrupolar liquids and regions with order-by-disorder selection of discrete states. Order by disorder with quadrupoles admits cubic terms in the Landau theory whose effects appear in Monte Carlo simulations and flavor-wave calculations for fixed spin $S$. We showcase a number of examples of quadrupolar spin liquids, including one realizing a rank-3 symmetric tensor gauge theory exhibiting sixfold pinch point singularities. We discuss remarkable differences between the quadrupolar physics of different spin quantum number. We also discuss connections to the non-Kramers rare earth pyrochlore materials.

In order to understand the unexpected similarity and the correlated behavior in kagome superconductor families $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ ($A=\mathrm{K},\mathrm{Rb},\mathrm{Cs}$) and $A{\mathrm{Ti}}_3{\mathrm{Bi}}_5$ ($A=\mathrm{Rb},\mathrm{Cs}$), we investigate the Hartree-scale local electronic structure of these systems. Our result indicates that V and Ti ions are both of $2+$ valence such that the corresponding itinerant carrier densities are similar, and the difference in electron count is instead reflected in their quantum fluctuating ionic magnetic moments. However, due to the frustrated lattice geometry of these materials, such local moments are difficult to experimentally observe via standard probes. For verification, we systematically introduce nonmagnetic Sn impurities to locally relieve the geometric frustration and experimentally demonstrate the existence of well-defined local magnetic moments via magnetic susceptibility and muon spin rotation or relaxation ($\mu \mathrm{SR}$) measurements. All experiments discover a systematic increase of magnetic susceptibility upon increasing nonmagnetic impurity level. Our discovered ionic moments suggest a paradigm shift from the existing itinerant carrier-only picture to one incorporating strong correlation from local ionic spins. The associated interatomic and local-itinerant correlations offer a solid ground for the emergence of the observed rich correlated behavior in this new family of superconducting materials.