Papers

Weak interactions at a two-dimensional quadratic band touching (QBT) can generate an exponentially small symmetry-breaking gap, $m\sim e^{-A/V_1}$, that cannot be captured by every finite order of perturbation theory. We show that the singular quantum geometry of the gapped QBT converts this beyond-all-orders scale into an algebraically enhanced response. The quantum metric develops a momentum-space hot spot whose Brillouin-zone integral diverges logarithmically, and therefore grows algebraically when the gap is dynamically generated by interactions. Through the inverse-frequency Souza–Wilkens–Martin optical sum rule, the same amplification appears in the negative-first longitudinal optical moment, even though the ordinary optical conductivity remains $O(e^2/\hbar)$ and its absorption threshold is exponentially small. We establish these results analytically for a massive QBT and verify them microscopically in an interacting kagome lattice model known to develop a spontaneous quantum anomalous Hall mass at its QBT from loop currents order. Our results identify quantum geometry as an asymptotic amplifier of nonperturbative interaction scales.

In the last years, the application of mechanical tensile stress has been shown to trigger unconventional phases in quantum materials. Recently, an orientational transition of the charge density wave (CDW) of TbTe3 was reported under the application of moderate uniaxial tensile stress, associated to the in-plane a/c lattice anisotropy. This leads to the disappearance of the pristine c-oriented CDW (CDWc) and to the appearance of the orthogonal a-oriented one (CDWa). A coexistence phase with a superposition of CDWa and CDWc appears when a=c. Here, we probe the sliding dynamics of both CDWc and CDWa as a function of applied tensile stress, i.e. in the pure CDWc, pure CDWa and coexistence phases, by measuring current-voltage characteristics and associated differential resistances. If the pristine CDWc has been known to display non-linear dynamics and thus sliding for several years, we show here that the strain-induced CDWa phase also displays the same characteristics, proving its incommensurate nature. Moreover, we show that sliding also takes place both for CDWc and CDWa, with reduced threshold currents, in the coexistence phase, which questions the microstructure of these coexisting orthogonal CDWs in real space. Finally, the linearity of the threshold fields is kept for all deformation states, with finite threshold fields at Tc, which is discussed in terms of commensurability and pinning potentials. This work opens new questions for the theoretical description of sliding CDWs in quasi-2D systems.

We investigate the Seebeck coefficient as a probe of collective transport behavior in graphene and quark-gluon plasma using a kinetic-theory approach in the hydrodynamic regime. The Seebeck coefficient is obtained by solving the Boltzmann transport equation in the relaxation-time approximation. At high-charge-carrier density, corresponding to the Fermi-liquid domain, our result approaches the behavior expected from the conventional Mott relation. In contrast, significant deviations from the Mott relation are observed in the low-carrier-density regime, corresponding to the Dirac fluid domain. These facts are in good agreement with experimental Seebeck coefficient data for graphene. This behavior indicates the emergence of collective hydrodynamic transport in graphene. The enthalpy per particle plays a key role for the Seebeck coefficient in the Dirac fluid regime. We extend our formalism to the ultra-relativistic quark-gluon plasma. A similar deviation from the Mott relation is observed, supporting a similar fluid response in the Seebeck coefficient across two markedly different strongly correlated quantum systems - graphene and quark matter.

Excitonic states in two-dimensional semiconductors are sensitive to time-reversal symmetry breaking, yet how interfacial exchange acts on higher-lying exciton Rydberg states remains largely unexplored. Here we show that wavelength-resolved magneto-optical Kerr spectroscopy of a proximity-coupled MoSe$_2$/Fe$_3$GaTe$_2$ van der Waals heterostructure resolves magnetic symmetry breaking across the A- and B-exciton manifolds. Combining reflection, photoluminescence, and photoluminescence excitation spectroscopy with first-principles many-body calculations including screening by the metallic Fe$_3$GaTe$_2$ layer, we assign the strongly enhanced Kerr resonances to the ground and 2s states of both manifolds. Reversing the magnetic field inverts the polarity of every resonance. A field-odd/field-even decomposition confirms a magnetic origin. The opposite Kerr polarities of the A- and B-exciton manifolds can be explained by proximity-induced exchange coupling to the opposite valence-band spins of the two exciton series. Our results establish resonant Kerr spectroscopy as a sensitive probe of magnetically induced symmetry breaking across the excitonic manifold.

We distinguish two Casimir observables associated with a conformal surface defect. A circular cylinder embedded in flat space has a logarithmic contribution to its Casimir energy, $-d_1\log(R/\epsilon)/(24R)$, fixed by the displacement anomaly. A great cylinder obtained by radial quantization of the ambient theory instead has Casimir energy $-b/(12R)$ in the conformal defect vacuum with a fixed local anomaly convention. Free-field and holographic calculations provide checks of the proposed relations in both embeddings.

Ce$_2$Zn$_6$Ge$_3$ is a rare example of the Ce-based honeycomb ferromagnet. Here, we report its Fermi surface and topological properties by quantum oscillations via the magnetoresistance and tunnel diode oscillator (TDO) based measurements, in combination with the density functional theory (DFT) calculations. Four fundamental frequencies are observed in the quantum oscillations, and their angle dependence is more compatible with the DFT calculations assuming that the 4$f$-electrons are localized, suggesting a localized nature of ferromagnetism in Ce$_2$Zn$_6$Ge$_3$. Furthermore, the observations of negative longitudinal magnetoresistance and non-zero Berry phase, as well as the existence of two pairs of Weyl points near the Fermi level as revealed from the calculated electronic structures, provide strong evidence for nontrivial topology in Ce$_2$Zn$_6$Ge$_3$. These findings suggest that Ce$_2$Zn$_6$Ge$_3$ could provide a unique platform to study magnetism, topology, quantum criticality and their interplay.

This thesis studies how disorder and fluctuations shape large-scale growth phenomena in three related settings: fluctuating interfaces, random spring chains, and random multiplicative growth. The first part concerns interface growth and a phenomenon denoted anomalous scaling, where local and global exponents differ.To clarify its origin, we study two models in which this mismatch has different causes. The first is a heterogeneous elastic line, where we show that the apparent anomaly is a purely statistical effect. The second is the stochastic porous medium equation, a strongly nonlinear model in which the anomaly is genuine. The second part concerns Anderson localization, which appears here through the spectral properties of the heterogeneous elastic lines. We study chains with both random masses and random spring constants, with particular emphasis on the strong-disorder regime, where standard weak-disorder expansions break down. We develop a new combinatorial method to probe this regime. The last part concerns random multiplicative growth with redistribution. In such models, changes in wealth, population, or mass, for instance, are proportional to the amount already present, so that small differences are amplified over time. This naturally generates broad distributions and provides a simple mechanism for the emergence of inequality and concentration, with applications to population dynamics, wealth distribution, city growth, and ecology. We in particular study models in which each site has its own quenched growth rate, representing a persistent advantage or disadvantage, and is also subject to transient fluctuations. Redistribution competes with these mechanisms by homogenizing the system. This competition leads to rich phase diagrams.

Near-field radiative heat transfer between two objects has been theoretically predicted and experimentally demonstrated to exceed far-field blackbody limit across nanoscale vacuum gap distance enabled by evanescent surface waves coupling, while significant enhancement by more than 100 times usually requires sub-50-nm vacuum gaps around room temperature. This is challenging for parallel-plate configuration with millimeter sample sizes due to intrinsic wafer bow and contaminant particles. Sphere-plate configuration with a microsphere attached to bimaterial cantilevers or micro-thermocouple tips has been used to experimentally demonstrate near-field radiative heat transfer down to 30-nm gaps, but it is much less developed because of the challenges in the sophisticated sensor fabrication, low sensitivity and weak signals. In this work, we overcome these challenges by an annular micro-thermocouple junction fabricated at the end of a glass fiber with straightforward thin-film deposition to achieve high measurement accuracy with large Seebeck coefficient 25 uV/K and thermal resistance 8.7e6 K/W. With a silica microsphere attached underneath the micro-thermocouple junction, we report experimental observation of colossal near-field radiation heat transfer over blackbody limit down to 10-nm gap up to 2600 times with quartz and 900 times with doped silicon. Upon phase transition of VO2 thin film emitter, tunable near-field heat transfer up to 430-fold enhancement is experimentally demonstrated at 15-nm gap with 64% reduction. Experimental data agrees well with rigorous modeling based on fluctuational electrodynamics and Derjaguin approximation, and underlying mechanism is understood by energy transmission calculations. The results will advance the experimental study and fundamental understanding of energy transport at nanoscale gaps.

We examine the spectral dissipation-coherence trade-off inequality conjectured by Oberreiter et al. [Phys. Rev. E 106, 014106 (2022)], stating that the coherent number, defined from the second largest eigenvalue, provides a lower bound on the stationary entropy production per unit oscillation. We disprove this conjecture by explicitly constructing a counterexample, which accompanies finite coherent number with vanishing stationary entropy production. This model also excludes a wide class of thermodynamic bound with the real and imaginary parts of the second largest eigenvalue of the transition rate matrix. Our result implies that the second largest eigenvalue does not necessarily characterize the degree of coherent oscillation.

We report a three-month autonomous research-agent program testing five solid-state-physics-inspired compression mappings on pretrained language models, with predictions committed to git before any pilot data and a 3-sigma gate deciding PASS or SHELVE. The common anchor – area-law / Kohn-nearsighted decay of the one-particle density matrix – has a distance face (P001 Wannier, P002 tight-binding) and a rank face (P003 DMRG-truncated MLPs, P005 Wilson-RG, P011 tensor-train embeddings). P005 was pre-empted at Phase 1; three of four Phase-3 pilots were falsified. On the attention face, GPT-2-medium attention-versus-distance is best fit by a stretched exponential in 12 of 16 median-layer heads once probe padding is excluded, and a tight-binding cutoff costs +96% perplexity (P002); on Pythia-160M the Wannier sparsity 0.054 +/- 0.004 is indistinguishable from PCA, random-Haar and identity baselines (P001). On the rank face, per-token tensor-train bond dimension does not track surprisal (r = 0.016 vs a pre-registered 0.65) and the format inflates rather than compresses (P011). P003 is mixed: its scaling claim shelved (r = -0.434), its MPO premise died at stage-0, and its cross-paper check, r = 0.523 as first written, collapses to 0.047 under the same correction, leaving both cross-paper checks null. The results invert the pre-registered prediction that most attention heads behave like Kohn-nearsighted insulators, pointing instead to critical, glassy or heavy-tailed regimes; the inversion is specific to the <= 350M scale tested, while the rank-face no-gain result held to 7-8B. We contribute the pre-registration + 3-sigma + cluster-framing + append-only-catalogue discipline – including why our own enforcement gate was designed but not deployed – four pre-registered negative results with full data release, and the inversion. The catalogue holds eighteen concluded studies, seventeen negative.

We establish an exact correspondence between renormalization-group (RG) evolution and real-time quantum dynamics in the anisotropic current-current perturbed $SU(2)_1$ Wess-Zumino-Witten (WZW) model. Using its integrable fermionic representation, we construct the exact time-dependent many-body wavefunction by means of the generalized Bethe ansatz and show that periodic boundary conditions lead to quantum Knizhnik-Zamolodchikov equations associated with the XXZ trigonometric $R$-matrix, which corresponds to the quantum affine algebra $\mathcal{U}_q(\widehat{\mathfrak{sl}_2})$ evaluated in its spin-$1/2$ evaluation representation. Consistency of these equations constrains the temporal evolution of the longitudinal and transverse interaction strengths. In the universal regime, these integrability conditions are exactly equivalent to the Berezinskii-Kosterlitz-Thouless RG flow equations upon identifying physical time with the logarithmic RG scale. Consequently, the RG limit cycles of the anisotropic current-current perturbed $SU(2)_1$ WZW model are realized as periodic real-time evolution of its interaction strengths. Our results provide an exact dynamical realization of RG limit cycles and establish a direct connection between cyclic RG flows, quantum integrability, and periodically driven interacting quantum field theories.

Current understanding of alloy grain boundaries is limited by the incompleteness of atomistic simulation techniques, which either neglect entropy or artificially constrain the atomic density. This study introduces Monte Carlo simulations that simultaneously sample all the microscopic degrees of freedom in complex interfaces: position, configuration, and atom number. The method enables rigorous predictions of finite-temperature grain boundary structures, phase transformations, and diagrams in multicomponent materials. Simulations of W-V alloys demonstrate the necessity of the approach by uncovering a range of previously inaccessible phase transitions including condensation of interstitial solutes and transformation of dislocation structure.

Coupled-cluster theory is the method of choice for weakly correlated systems, but in strongly correlated systems where the mean-field reference is qualitatively poor, it can break down badly. These failures can be ameliorated by using symmetry-broken mean-field references. For systems that spontaneously break spin symmetry, we might favor an unrestricted reference. In systems that instead break number symmetry, we turn to Bogoliubov coupled cluster theory. In this work, we apply Bogoliubov coupled-cluster to Hamiltonians with an underlying su(2) algebra to study the pairing Hamiltonian and the spin XXZ and J1-J2 models by exploiting the correspondence between fermionic-pair operators and spin-1/2 operators. For the pairing problem, the reference is the usual Bardeen–Cooper–Schrieffer (BCS) quasiparticle vacuum, while for spin systems we use the analogous spin-BCS reference, which breaks Sz symmetry and provides a flexible starting point for strongly correlated regimes. Correlation is incorporated through a hierarchy of coupled-cluster approximations. Beyond energies, we compute the response density matrices for the evaluation of spin–spin correlation functions for the XXZ and J1-J2 Heisenberg models, and the pairing parameter and particle-number variance for the pairing Hamiltonian. We also derive the corresponding relaxed density matrices, including the effects of orbital relaxation. Benchmark calculations for the half-filled pairing Hamiltonian and spin models demonstrate that Bogoliubov coupled cluster provides a systematically improvable wave-function-based approach for su(2) Hamiltonians, including geometrically frustrated spin systems requiring complex and noncollinear BCS references.

Symmetry-protected topological (SPT) phases in quantum spin chains are distinguished by topological indices. Ogata's operator-algebraic indices apply to a broad range of symmetry classes without requiring continuous symmetry, whereas the elementary twist index of Tasaki requires $\mathrm{U}(1)$ symmetry. We prove their equivalence in the common setting of integer-spin chains with on-site $\mathrm{U}(1)\rtimes\mathbb{Z}_2$ symmetry and a symmetric locally-unique gapped ground state, without assuming translation invariance or a matrix product representation. A charge-fluctuation estimate yields a strong-limit construction of half-chain rotations with their phases fixed. An exact group commutator identity then identifies the Ogata index with the limit of local twist expectations and gives an explicit error bound. This provides a computable formula for the index when a lower bound on the gap and the relevant ground-state expectations are available. Combining the equivalence with a recent boundary-field gap theorem of OpenAI and our earlier twist-index calculation, we obtain a spin-rotation-invariant locally-unique gapped ground state of the infinite $S=1$ antiferromagnetic Heisenberg chain with both indices equal to $-1$, without assuming infinite-volume uniqueness. The author formulated the problem and proposed the basic strategy, while ChatGPT Astra made substantial contributions to the development of the proof.

Fairness, as a fundamental social norm, continues to pose a longstanding puzzle regarding its emergence. Traditional game-theoretic models largely rely on the assumption of Homo economicus, wherein individuals are purely rational and self-interested, acting solely to maximize material payoffs. Such accounts, however, overlook the multidimensional nature of human decision-making, which is often shaped also by other considerations beyond economic incentives. To address this gap, we propose a multi-objective reinforcement learning framework that models the evolution of fairness as a dynamic trade-off between material payoff maximization and fairness-driven moral behavior, regulated by a fairness pressure coefficient. Using simulations of a two-objective Q-learning ultimatum game, we find that increased fairness pressure promotes fair outcomes, as expected. Strikingly, however, under moderate pressure, responder behavior reverses: responders become “forgiving" by accepting low offers – a pattern in line with our daily experience. Microscopic analyses reveal that this strategy reversal stems from competition between payoff-maximizing and fairness-oriented preferences. We further extend our framework to an asymmetric setting, where proposers and responders assign different weights to the two objectives. Overall, our work expands the reinforcement learning paradigm from a single-objective to a multi-objective formulation, offering a versatile tool for elucidating a broader range of human social behaviors.

Stimulated Brillouin Scattering (SBS) couples light to acoustic waves and underpins applications ranging from sensing and signal processing to quantum photonics. In solids, this interaction is generally attributed to photoelasticity and the motion of dielectric boundaries. Here we show that piezoelectricity opens an additional, previously unrecognized pathway that can substantially reshape Brillouin gain. This contribution arises from the combined action of linear electro-optic “Pockels” scattering and its reciprocal $\chi^{(2)}$-mediated optical drive, which couple optical fields to the electric fields that accompany mechanical motion in piezoelectrics. We formally incorporate these effects into the modern theory of SBS and apply it to monolithic lithium niobate waveguides. In addition to large enhancement and suppression of the Brillouin gain, we surprisingly find occurrences of large gain where conventional theory would otherwise have predicted zero Brillouin interaction. These instances are the first identification of purely electro-optic SBS, a process we term stimulated electro-optic scattering, as it only involves interactions between electromagnetic fields even though a mechanical excitation is present. Our results establish the electro-optic tensor as a key governing parameter for Brillouin interactions in piezoelectric media and provide a new degree of freedom for engineering photon-phonon coupling independent of photoelasticity and index contrast.

Spectral fingerprints in optical absorption and emission have typically been used as a signature of exciton localization in twisted moiré bilayers. However, the mechanism by which excitons become confined to specific stacking sites and their associated optical signature is experimentally unresolved. Here, we directly visualize in real space how tuning the change in extent of structural reconstruction leads to localization and delocalization of moiré excitons in the WSe2/WS2 moiré superlattice. Using cryogenic monochromated electron energy loss spectroscopy, together with first-principles GW-Bethe Salpeter equation calculations and optical spectroscopy, we uncover the physical mechanism that drives the correlation between twist-angle-dependent structural transformations, the real-space localization of moiré excitons, and their optical signatures. Surprisingly, and in contrast to the prevailing understanding, we show that the emergence of new moiré exciton resonances in the optical spectra alone is insufficient to establish exciton localization. Instead, the extent of structural reconstruction and external strain drives exciton localization, leading to new design principles for engineering moiré excitons and strain-aware quantum optoelectronic devices.

Understanding local electric fields at oxide interfaces is essential for linking interfacial electrostatics to device functionality, yet conventional electrical measurements infer these fields only indirectly. Here, we combine operando scanning transmission electron microscope electron-beam-induced current (STEM-EBIC) with four-dimensional-STEM (4D-STEM) to quantitatively reconstruct the bias-dependent electric field spatial distribution across an oxide Schottky junction at nanometer scale. Using La0.67Sr0.33MnO3/Nb:SrTiO3 (LSMO/NSTO) as a model system, we fabricate an electron-transparent junction on a MEMS biasing platform and verify that it retains the rectifying transport behavior. STEM-EBIC provides complementary information addressing several key limitations in quantitative 4D-STEM field mapping for heterojunctions. The reconstructed electric field profiles show a pronounced nonlinear decay within the depletion region and an extended penetration into the LSMO. These results directly reveal the deviations of oxides Schottky junction from the ideal conventional Schottky depletion model, providing experimental signatures of non-classical interfacial electrostatics. Our correlative approach enables quantitative nanoscale electric field mapping in operating oxide heterojunctions, providing a basis for linking interfacial electrostatics to macroscopic transport and guiding oxide devices design.

Long-horizon micromagnetic simulation remains expensive because conventional and learned solvers typically propagate Landau–Lifshitz–Gilbert (LLG) dynamics step by step. Existing learned approaches generally retain stepwise integration or model deterministic evolution, leaving full-field, direct-horizon stochastic prediction largely unexplored. We propose FLARE, a flow-matching framework that recasts stochastic finite-time magnetization prediction as conditional transport over anchor-relative local axis-angle rotations. This rotation-space formulation respects the intrinsic geometry of magnetization dynamics and preserves pointwise unit norm by construction. By explicitly conditioning on the physical prediction horizon, FLARE directly generates full-field stochastic endpoints across multiple target times without stepwise integration. Against the strongest single-checkpoint external baseline on each metric, FLARE achieves 29.9% lower angular energy distance ($15.30^\circ$), and a 37.3% lower fair energy score (0.393). On a representative composed 5-ns two-segment protocol, FLARE achieves a $3{,}062\times$ best-batch speedup over the widely used GPU micromagnetic solver MuMax$^3$ on a single GPU.

We implement the machine-learned Skala exchange-correlation (XC) functional natively in CP2K using its Gaussian and plane-wave (GPW) and Gaussian and augmented-plane-wave (GAPW) methods. A joint one-centre reconstruction of density, density gradients, and kinetic-energy density before functional evaluation preserves mixed gradient terms and nonlocal couplings between smooth and atom-local contributions in all-electron and pseudopotential calculations. An XC-specific GAPW representation resolves rapidly varying local contributions on atom-centred grids, reducing plane-wave requirements for pseudopotential calculations. The implementation includes Brillouin-zone sampling and point-group symmetry reduction. With sufficiently flexible orbital bases, it retains the molecular benchmark accuracy of our earlier GauXC formulation. All-electron Skala-D3(BJ) calculations yield a mean absolute error (MAE) of 1.54 kJ mol$^{-1}$ against diffusion Monte Carlo for crystalline CO$_2$, NH$_3$, and urea, spanning dispersion, quadrupolar electrostatics, and hydrogen bonding. For all thirteen DMC-ICE13 phases, the MAEs are 1.16 kJ mol$^{-1}$ for absolute lattice energies and 0.82 kJ mol$^{-1}$ for the twelve relative energies to ice Ih. At fixed experimental geometries, all-electron/mixed-core calculations give a band-gap MAE of 0.43 eV on a 15-material set, substantially below commonly used semilocal functionals and comparable to widely used hybrid functionals. The LC10 benchmark nevertheless reveals systematically underestimated equilibrium lattice constants, indicating structural overbinding. This framework connects molecular Skala to condensed-phase electronic structure and enables future development using periodic many-body reference data.

Polymer informatics has matured from isolated property-prediction studies into an integrated discipline that couples data, models, and decision-making across the polymer design cycle. Yet it still falls short of a true intelligent system capable of inverse design on demand, causal reasoning across chemistry, processing, and performance, and closed-loop autonomous experimentation. This article traces a roadmap toward that goal, grounded in experience developing two complementary agentic and informatics platforms. Central to this vision is a modular, agent-directed architecture in which a polymer super-intelligence layer interprets a researcher's design question in natural language and coordinates domain-specialized tools, matched to the available data, for neat polymers, composites and formulations, solvents, and synthesis and processing. The resulting system spans the full chain from molecular design through processing to product-level performance and human perception. Orchestrated together, its generative design, synthesis-feasibility reasoning, and practicality assessment already form the decision-making core of a self-driving polymer laboratory, leaving autonomous, closed-loop experimentation as the principal step that remains. We survey emerging capabilities along this roadmap, including automated extraction of property data from the literature, chemistry-aware representation, property prediction for membranes and sustainable plastics, solubility and green-solvent recommendation, and computer-guided retrosynthetic planning, exposing the remaining gaps and the research and infrastructure investments needed to move from today's orchestrated tool ecosystem toward a genuinely super-intelligent polymer design partner.

Nonlinear oscillators exhibit rich collective phenomena including synchronization, bifurcation, and chaos. Experimentally accessing multimode nonlinear dynamics, however, remains challenging because low-order internal resonances readily induce mode locking and suppress stable multimode oscillation. Here, we demonstrate a transverse-mode-coupled optomechanical platform that combines engineered collective mechanical modes with optically controllable nonlinear interactions. The engineered transverse mechanical modes enable stable two- and three-mode self-sustained oscillations while suppressing trivial low-order internal resonances. By varying the laser frequency, we observe successive beat-frequency fractionalization ({\Delta}f/2 and {\Delta}f/3), followed by a broadband state exhibiting enhanced trajectory divergence consistent with deterministic chaos. These results establish transverse-mode-coupled optomechanical resonators as a scalable and tunable platform for exploring high-dimensional nonlinear dynamics in interacting mechanical networks.

We study a charged particle moving outside a spiral (screw) dislocation in a uniform magnetic field. Although the geometry is locally Euclidean, its global screw identification couples the conserved axial and azimuthal quantities through the combination \(\mathcal{J}=\ell-\beta k\) After eliminating the cyclic coordinates, the radial motion is governed by an inverse-square term determined by $\mathcal{J}$ and a harmonic confining term generated by the magnetic field. The corresponding reduced quantum problem is exactly solvable for $q\mathcal{B}_0\neq0$, yielding an equally spaced spectrum with an orientation-dependent energy shift. The radial probability density depends on $\mathcal{J}$, and opposite values of the screw-modified quantum number have identical spatial profiles but different energies for a fixed magnetic-field orientation. The radial size scales as \(\sqrt{\langle r^2\rangle_n}\propto |q\mathcal{B}_0|^{-1/2}\), with the magnetic length setting the localization scale. At $q\mathcal{B}_0=0$, the confining term vanishes, and the problem reduces to a scale-free inverse-square system. Thus, the screw parameter enters the dynamics through the global coupling of the conserved axial and azimuthal quantities, whereas the magnetic field provides radial confinement and its orientation determines the spectral asymmetry.

A charge-$r$ coupling vortex can remain as one fused order-$r$ zero or split into $r$ nearby unit-charge zeros after weak symmetry breaking. The two configurations have the same total winding and the same number of dark states in the lowest-Landau-level projection, so neither the imposed orbital angular momentum nor the total winding number distinguishes their local geometry. We study this distinction in a two-component Haldane-sphere model coupled by a Raman field. For monopole flux $N$, the detuning $\tau_{\rm c}$ at which a defect branch crosses zero energy scales as $|\tau_{\rm c}|\sim N^{-(r+1)}$ for a fused zero and $N^{-2}$ for resolved unit zeros. A Feshbach reduction establishes these asymptotic laws for the full multiband Hamiltonian, and numerical calculations in a monopole-harmonic basis confirm the fused-vortex scaling for $r=1,2,3$. For a partially split cluster of diameter $d$, the scaling crosses over when $d$ is comparable to the magnetic length $\ell_B$, allowing $d$ to be inferred spectroscopically even below the spatial resolution of direct imaging.

We study the Ising spin glass with independent, identically distributed couplings on the diamond hierarchical lattice with $n$ branches, of effective dimension $1+\log_2 n$; $n=4$ is the Migdal-Kadanoff lattice of $\mathbb{Z}^3$. For $n\ge4$ and every coupling law with a bounded density we prove that at sufficiently low temperature $T>0$, uniformly in the level of the lattice, the poles are ordered, every spin has Edwards-Anderson parameter $1-O(T)$ when the poles are fixed, and the overlap of two free-boundary replicas has second moment $1-O(T)$. For standard Gaussian couplings, $n=3,4,5,7,8$ and every $T\le T^*(n)=4/15,\,6/7,\,6/5,\,7/4,\,2$ ($0.89$ to $0.98$ times numerical estimates of $T_c$), a computer-assisted proof gives pole order and, as the level tends to infinity, site-overlap order and the blue-cluster statements below; likewise for every larger $n$ at these temperatures. Previously, spin-glass order on these lattices with frustrated independent couplings had been proved only for more than $10^{18}$ branches (Collet and Eckmann, 1984). The key step is growth of the effective coupling under the exact renormalization map: for $n\ge4$, by a one-step contraction, via Rogozin's inequality, of a density bound on an event of high probability; near $T_c$, by interval-arithmetic bounds in the peakedness order. A transfer theorem following the ancestor-chain argument of Collet and Eckmann turns this growth into bulk statements. In the Chayes-Machta-Redner representation the same input gives a blue cluster that contains both poles with probability tending to one and whose expected density is bounded away from zero, while the largest other blue cluster has density tending to zero in probability and in $L^1$; hence blue-cluster density imbalance. To our knowledge this is the first proof of such an imbalance for a spin glass on a graph other than the complete graph.

Does the spatial organization of particle mobility in a glass predict future motion beyond what local structure knows? In leakage-free simulations of an aging Kob–Andersen liquid ($N=2028$; 200 trajectories; three temperatures), mobility-network topology raises the out-of-fold $R^2$ by $\dRtwo=0.0049$–$0.0122$, monotonically with quench depth, retaining $\ge 98\%$ atop softness-class baselines. Giant mobile components are dense hotspots whose members subsequently quiet down: exhaustion zones of cooperative motion — a spatial anticorrelation channel invisible to single-particle descriptors.

Complex oxides possess a wide range of electric, magnetic, and optical properties that can be precisely tuned by chemical doping. The atomic-scale analysis of the property-controlling dopants, however, becomes increasingly difficult towards low doping levels. Atom probe tomography (APT) offers chemical sensitivity and spatial resolution to image individual dopant atoms down to a few parts per million. To reliably extract such information, detailed knowledge about the atom-specific field evaporation processes is required. Here we demonstrate a first insight into the APT-measured atomic position of dopant atoms and the field evaporation conditions, using Zr-doped ErMnO3 as a model system. Our analysis reveals a substantial preferential retention of both matrix and dopant atoms which strongly affects the dopant site determination and can lead to an incorrect interpretation. The retention effect is determined by intrinsic and extrinsic parameters, such as the dopant's evaporation field and concentration and the analysis temperature, respectively, as we explain based on field-evaporation simulations. Our results are important for the APT-based analysis of individual dopant atoms in solid systems and the understanding of field evaporation dynamics at the atomic level in general.

Chiral edge modes in topological states of matter are routinely found inside band gaps, which may be deformed and shifted as a function of the lattice momentum. Here we show that they can exist inside a bulk band instead, i.e., in the continuum. These chiral edge modes in the continuum (CEMICs) are induced by introducing an imaginary magnetic flux to an otherwise topologically trivial two-dimensional system, realized by imposing asymmetric couplings along the edge. While the stronger couplings provide a preferred circulation direction, we find that the edge localization of CEMICs does not originate from the non-Hermitian skin effect, which is typically associated with systems featuring asymmetric couplings and the open boundary condition. Instead, this edge localization is due to the energy exchange between the system and the environment at the asymmetric coupling junctions, which leads to a parity-time (PT) transition in the Brillouin zone. Intriguingly, the onset of CEMICs is independent of the system size in the macroscopic limit, which is given by the golden ratio between the asymmetric couplings and their geometric average.

Quantum annealing is a promising form of quantum computation, but it slows down at a small energy gap $\Delta$ during the anneal, and the errors it makes there remain undetected. We introduce cavity quantum annealing, in which a cavity mode of frequency $O(1)\gg\Delta$, coupled mid-schedule, swaps these errors into photons. In the $p$-spin model, this reduces the annealing time to nearly the square root of that required without the cavity. Moreover, counting the photons certifies the result: high-photon runs, with an $O(1)$ yield, reach a ground-state fidelity above $99.99\%$ orders of magnitude sooner, a gain that grows exponentially with system size. A pre-loaded photon instead runs the swap in reverse, preparing an excited state. More broadly, our work shows that cavities can enhance computations performed with qubits, paving the way toward high-fidelity quantum state preparation by quantum annealing.

The one-dimensional swarmalator model is usually understood through three macroscopic states: synchrony, the phase wave, and asynchrony. We show that the identical model also contains a much larger set of hidden stable equilibria - families of q-twisted and m-clustered states - which random initial conditions almost never reach, because many are embedded in a degenerate neutral manifold of vanishing global basin. They are nonetheless locally robust: under Gaussian perturbations of per-coordinate amplitude {\epsilon} their survival radii shrink only algebraically, as 1/q and 1/m, in sharp contrast to the Gaussian basins and winding ceiling of twisted states on a nearest-neighbour Kuramoto ring, both removed by mean-field coupling. A block-circulant Jacobian fixes the stability in closed form, and far-kick experiments indicate the basins are compact cores rather than tentacled sets. Several patterns reported in extended swarmalator models thus already exist, stable or neutrally stable, in the minimal one.