The interplay between bulk critical fluctuations and nontrivial topology can enrich defect physics and give rise to novel defect universality classes. Understanding the fate of such defects therefore constitutes an important open problem. In this work, we studied a particularly simple setting: a (0+1)-dimensional pinning-field defect coupled to a (2+1)-dimensional deconfined quantum critical bulk. Using the fuzzy-sphere regularization, we numerically investigated the defect operator spectrum and extracted several universal quantities characterizing the defect conformal fixed point, including the scaling dimensions of defect-changing(creating) operators and the defect g-function. These results establish the first numerical characterization of line-defect conformal data at deconfined quantum criticality and may stimulate further investigations of defect critical phenomena in topological quantum critical matter.

The deconfined quantum critical point (DQCP), which separates two distinct symmetry-broken phases, was conjectured to be an example of (2+1)D criticality beyond the standard Landau-Ginzburg-Wilson paradigm. However, this hypothesis has been met with challenges and remains elusive. Here, we perform a systematic study of a microscopic model realizing the DQCP with a global symmetry tunable from SO(5) to O(4). Through the lens of fuzzy sphere regularization, we uncover the key information on the renormalization group flow of conformal operators. We reveal O(4) primaries decomposed from original SO(5) primaries by tracing conformal operator content and identifying the "avoided level crossing" in the operator flows. In particular, we find that the existence of a scalar operator, in support of the nature of pseudo-criticality, remains relevant, persisting from SO(5) to O(4) DQCP. This Letter not only uncovers the nature of O(4) DQCP but also demonstrates that the fuzzy sphere scheme offers a unique perspective on the renormalization group flow of operators in the study of critical phenomena.

Recent advancements in ferroelectric domain engineering have provided a promising avenue for nonlinear beam shaping. However, a device enabling continuous manipulation of spatial modes in a parametric way, akin to waveplates used for polarization control, remains absent. In this work, we introduce and demonstrate a novel nonlinear photonic crystal (NPC) capable of simultaneously converting the frequency and orbital angular momentum (OAM) states of structured light. Instead of constructing a nonlinear spiral phase plate, the NPC was designed to perform a nonlinear unitary transformation on the OAM state of the parametric generation, with the resultant state being contingent upon the relative angle between the input state and the crystal. The NPC facilitates a parametric modal interface that enables access to all possible states on the same modal sphere of the input beam. This nonlinear toolkit shows great potential in diverse applications with structured light.

Two-dimensional (2D) macromolecules are atomically thin materials capable of forming crumpled configurations with complex topologies, defining a new paradigm in macromolecular mechanics. Here, we unveil a universal negative size effect, where smaller sheets yield substantially stronger load-bearing capabilities than larger ones. Coarse-grained molecular dynamics simulations demonstrate a negative scaling between compression pressure or modulus and the Föppl-von Kármán number, with the power index determined by crumpling density but independent of material type. Energy analysis indicates that smaller sheets form dense ridge networks with minimal self-folding, enabling efficient load transfer and energy absorption. During densification, a constant ridge-to-vertex increment ratio of 1.5 preserves the superior ridge density of small sheets. Experiments on paper, aluminum foil, polydimethylsiloxane (PDMS), and silicone rubber confirm this behavior across disparate length scales and across material classes. This work reveals the mechanics underlying size-dependent crumpling in 2D macromolecules and provides principles for designing structural metamaterials with tunable load-bearing characteristics.

We investigate the ground states of the S = 1/2 staircase J-Q_3 model in the maximally anisotropic limit by employing projector quantum Monte Carlo simulations. To overcome boundary-induced finite-size ambiguities inherent in the study of spatially modulated structures, we implement a 45^∘ tilted periodic boundary condition that eliminates intermediate phases and provides direct access to winding-sector transitions of the system. By defining a domain wall density to quantify the spatial modulation of the helical valence bond phase, we perform thermodynamic extrapolations and demonstrate that both the domain wall density and the characteristic wavevector evolve continuously with the coupling ratio, exhibiting no commensurate lock-in behavior. Our results establish that the helical valence bond phase is a genuine two-dimensional incommensurate phase with long-range bond-bond order in the thermodynamic limit, clarifying that winding-sector transitions are finite-size effects enforced by boundary commensurability. Furthermore, we determine the phase transition point between columnar valence bond solid phase and helical valence bond phase to be g_c = 0.046(2).

ABSTRACT Mechanical force redistributes reactivity through anisotropic, topology‐dependent load transmission. Predicting which covalent bond in a complex molecule ruptures first under tension remains a central problem in mechanochemistry, biomaterials and chemically recyclable polymers. Bond dissociation energy is an incomplete proxy because it describes zero‐force thermodynamic stability, whereas mechanochemical site selectivity is governed more directly by the peak force sustained along a prescribed loading path. Here we introduce covalent‐bond peak force network (CBPFNet), a graph‐attention model that predicts covalent‐bond peak force (CBPForce) from relaxed molecular structures through a virtual‐stretching workflow and avoids the hundreds of constrained geometry optimisations typically required for each candidate bond. In the CHON benchmark studied here, CBPFNet reproduces bond‐ranking trends from density functional theory (DFT) and can be used for bond‐level screening. Post hoc attribution analyses indicate that rupture selectivity depends on both bond identity and local stiffness contrast, with relatively rigid segments concentrating tensile stress on softer adjacent bonds. In oligopeptides, the model recovers the DFT weakest bond and highlights a serine‐containing motif as a possible topology‐dependent weak point under the same protocol. CBPFNet therefore extends screening beyond equilibrium bond stability toward bond‐resolved peak‐force ranking in sustainable polymer design and biomaterials.

Unlike common materials, van der Waals (vdW) materials are vulnerable to buckling under basal plane compression regardless of their slenderness. Understanding their post-buckling configurations is fundamental to preparing large-size high-quality samples, modulating physical properties, and revealing the strengthening and toughening mechanism in layered crystalline phases. Nevertheless, due to their unique features, such as layered crystalline lattice, decoupled intralayer and bending deformation mechanisms, and extreme anisotropy, vdW materials exhibit unique post-buckling behaviors that remain poorly understood. In this paper, we propose a general layered model, incorporating both the layered structure and interlayer tension-compression asymmetry, which can well capture the post-buckling evolvement behaviors for both bulk and finite-thickness vdW materials. The analytical expression of initial buckling strain is derived, only depending on two dimensionless parameters, reflecting the competition among intralayer compression, monolayer bending and interlayer shearing modes. For bulk vdW materials, the kink band configuration forms during the post-buckling deformation. Further analysis indicates that it is energetically driven by the release of intralayer and interlayer compression energies, stemming from the extreme anisotropy of layered crystalline structure, while the transformation from a sinusoidal configuration to a kink band configuration is induced by high interlayer pressure during post-buckling. In finite-thickness systems, three distinct post-buckling configurations are identified. i.e., internal kink, internal fold, global buckling, arising from the impaired lateral constraint as the slenderness increases. Phase diagrams for these three post-buckling configurations are presented. This work advances our understanding of the buckling and post-buckling evolvement behaviors in vdW materials, offering valuable insights for high-quality sample preparation and strengthening and toughening design of layered crystalline phases.

Two-dimensional (2D) materials exhibit diverse thermal expansion coefficients (TECs) spanning from negative to positive values, yet a unified theoretical framework connecting TECs to geometrical and interfacial factors remains elusive. Herein, we develop a statistical mechanics model to predict the TECs of multilayer 2D materials by incorporating the effects of layer number, lateral size, and substrate interaction. The total TEC is decomposed into positive bond-anharmonicity and negative fluctuation-induced contributions, with the latter governed by a dimensionless parameter coupling bending rigidity, interlayer shear, and substrate constraint. The theory predicts logarithmic size dependence for freestanding monolayers, progressive suppression of negative thermal expansion with increasing layer number, and substrate-mediated transitions from negative to positive thermal expansion. These predictions are validated by molecular dynamics simulations. Phase diagrams constructed in the parameter space of size, thickness, and substrate interaction delineate the boundaries between thermal expansion regimes. This theoretical framework offers predictive guidelines for engineering thermal expansion of 2D materials.

Cold metals possess an intrinsic energy gap located close to the Fermi level, which enables cold-carrier injection for steep-slope transistors and is therefore promising for low-power electronics. High-throughput screening has revealed 252 three-dimensional (3D) cold metals in the Materials Project database, but database searches are inherently limited to known compounds. Here we present an inverse-design workflow that generates 3D cold metals using MatterGPT, a conditional autoregressive Transformer trained on SLICES, an invertible and symmetry-invariant crystal representation. We curate a training set of 26,309 metallic structures labeled with energy above hull and a unified band-edge distance descriptor that merges p-type and n-type features to address severe label imbalance. Property-conditioned generation targeting thermodynamic stability and 50–500  meV band-edge distances produces 148,506 unique candidates; 92.1 % are reconstructed into 3D structures and down-selected by symmetry, uniqueness and novelty filters, followed by high-throughput DFT validation. We identify 257 cold metals absent from the Materials Project database, all within the targeted 50–500  meV window. First-principles phonon, electronic-structure, and work-function calculations for representative candidates confirm dynamical stability and contact-relevant work functions. Our results demonstrate that SLICES-enabled generative transformers can expand the chemical space of cold metals beyond high-throughput screening, providing a route to low-power electronic materials discovery.

The development of high-performance nonlinear optical (NLO) crystals for the short-wave ultraviolet (UV) region remains a significant challenge. In this work, four novel organic-inorganic metal halides, (3-QUO)2MX4 (3-QUO = 1-azabicyclo[2.2.2]octan-3-one; M = Zn, Cd; X = Br, I), were developed. Our initial efforts with the iodide compounds, (3-QUO)2ZnI4 and (3-QUO)2CdI4, yielded materials with modest second-harmonic generation (SHG) responses and, critically, they were non-phase-matchable. To overcome this, we employed a halogen-substitution strategy, replacing iodine with bromine, guided by the principle of bandgap widening. This approach successfully yielded (3-QUO)2ZnBr4 and (3-QUO)2CdBr4, which exhibit superior short-wave UV transparency and achieve phase-matchable SHG. Specifically, (3-QUO)2ZnBr4 shows a wide bandgap of 5.10 eV (UV cutoff: 220 nm) and a phase-matchable SHG response of 1.5 times that of KH2PO4 (KDP). Similarly, (3-QUO)2CdBr4 possesses a bandgap of 4.55 eV (UV cutoff: 245 nm) and an SHG response of 1.8 × KDP. Furthermore, these materials exhibit yellowish-white fluorescence under blue light excitation. This work demonstrates an effective approach to simultaneously tune bandgap, SHG response, and phase-matching capabilities for short-wave UV NLO applications.

In this work, we propose a one-dimensional t-J-K-U model, where itinerant spin-1/2 fermions are coupled to a spin-1/2 Heisenberg chain via a Kondo interaction Jk. Depending on the sign of Jk, the system realizes either a high-spin or low-spin ground state. Using the density matrix renormalization group (DMRG) calculations, we demonstrate the emergence of a pairing density wave (PDW) with wave vector Q = pi in this model. In the low-spin state, the ground state of the system is identified as a Luther-Emery liquid. In the high-spin state, superconducting pairing correlations are suppressed, and a quasi-long-range (QLR) spin density wave (SDW) emerges. In addition to the Kondo coupling JK, strong correlations among the itinerant electrons also play a significant role in stabilizing these density wave orders. We suggest that this model may be realized in a Ni2+ chain with Ni in the d8 configurations. Although superconductivity has not yet been observed in these materials, charge and spin ordering phenomena have been widely reported. Our results provide a potential pairing mechanism, indicating the possible existence of these intertwined orders in nickelates.

ABSTRACT Lattice structures enable tailored mechanical properties for aerospace, biomedical, and energy applications, yet navigating their vast design space while meeting complex performance requirements remains challenging. Here, we introduce DeepSeek‐Lattice‐KG, an intelligent framework synergistically integrating a domain‐adapted 14B‐parameter large language models with knowledge graphs for lattice structure design. The model was fine‐tuned on 2500 peer‐reviewed articles and integrated with a knowledge graph containing 658,623 entities from 50,000 publications, enabling both generative reasoning and graph‐based knowledge validation. Evaluation on 2100 expert‐curated questions across six technical domains demonstrates 94.8% accuracy, surpassing DeepSeek‐R1‐670B (88.2%) and conventional fine‐tuning approaches, while ensuring data privacy and computational efficiency. Through dynamic knowledge augmentation, the framework maintains 93% accuracy on 2025 emerging topics versus 77% for static systems, enabling real‐time updates without retraining. Engineering case studies demonstrate the framework's capability to synthesize knowledge across thousands of publications for design exploration. This work establishes a paradigm that domain‐specialized small models combined with structured knowledge provide an efficient alternative to large general‐purpose systems for specialized engineering domains.

The hydrogen evolution reaction represents a critical bottleneck in renewable energy conversion, with transition state (TS) identification being essential for rational catalyst design. While strain engineering offers powerful pathways to modulate catalytic activity in high-entropy alloys (HEAs), conventional density functional theory (DFT) calculations face prohibitive computational costs due to inherent atomic-level disorder and expanded configurational space. Here, we present a fine-tuned graph neural network EquiformerV2 (eqV2) framework that dramatically accelerates TS discovery in strain-engineered Ir-Pt-Rh-Pd-Ru HEA catalysts. Our lightweight 31-million-parameter model achieves pathway prediction from hours-scale DFT calculations to second-scale predictions while maintaining exceptional accuracy: mean absolute errors below 0.1 eV for reaction energies and structural predictions within 0.1 & Aring; root mean square deviation for 88.8% of configurations across Volmer, Heyrovsky, and Tafel pathways under biaxial strain. This methodology establishes a scalable computational framework that overcomes traditional limitations in high-dimensional catalyst screening, offering a generalizable strategy for artificial intelligence-accelerated next-generation electrocatalyst discovery.

We develop an experimental protocol based on Floquet-engineered ultracold fermions in optical lattices, enabling the emulation of pair-hopping and competing singlet/triplet pairing interactions. Through large-scale density matrix renormalization group (DMRG) simulations, we uncover three emergent topological phases: (i) A Majorana-enabled spin-density-wave (MS) phase featuring exponentially localized edge charges, non-local fermionic edge correlations, and doubly degenerate entanglement spectra; (ii) A z-axis polarized triplet superconducting (TS) phase exhibiting fractionalized edge spins (S=1/4 per edge), two-fold ground state degeneracy and a bulk single-particle gap; (iii) A hybrid x-directional triplet superconducting (XTS) phase that uniquely combines fractional spin textures and Majorana-type edge correlations, defining a new universality class of hybrid orders in number-conserving systems. These findings establish a universal framework for engineering non-Abelian topological matter, crucially bypassing the need for external pairing fields while maintaining experimental feasibility with current cold-atom techniques.

Inverse design of solid-state materials with desired properties remains a central challenge in materials science, requiring exploration of vast chemical spaces containing potentially 10100 possible structures. Current generative approaches face limitations in computational efficiency, multi-property targeting precision and mechanistic interpretability. Here, we introduce MatterGPT, an autoregressive Transformer-decoder architecture that leverages SLICES (Simplified Line-Input Crystal-Encoding System) representation to generate novel crystals through conditional next-token prediction. Trained on 306,533 crystal structures, MatterGPT achieves > 99% structural validity, > 99% structural uniqueness and > 50% novelty rates while targeting both specific lattice-insensitive and lattice-sensitive properties. Critically, MatterGPT enables direct multi-property generation without post-generation filtering. Interpretability analysis reveals clear property-guided generation mechanisms and systematic chemical space exploration. The comprehensive open-source release, including MatterGPT Hub integration platform, establishes sequence-based autoregressive generation as a computationally efficient and interpretable paradigm for inverse crystal design, accelerating materials discovery across energy storage, electronics, and functional applications.

Nonlinear frequency conversion provides a powerful tool to generate and manipulate structured light at new wavelengths. In this work, to meet the demands of applications such as high-capacity optical communications and high-dimensional entanglement generation, we use ferroelectric domain engineering to generate frequency-doubled light beams carrying orbital angular momentum (OAM) superposition states and with adjustable radial intensity distribution. Angular and radial phase modulations were introduced into the modulation function of the second-order nonlinear coefficient distribution of lithium tantalate nonlinear photonic crystals, achieving simultaneous tailoring of the OAM spectrum and the radial intensity profile of the second harmonic (SH) waves. As a representative example, we demonstrate the generation of a SH wave that carries a comb-like OAM spectrum, with the radial intensity distribution concentrating on a ring with a specific radius. In addition, the nonlinear photonic devices developed in this work feature polarization insensitivity and broadband characteristics.

Motivated by the recently discovered bilayer nickelate superconductor, the pressurized La3Ni2O7, we present a renormalized mean-field theory of a bilayer single-orbital t-J model, highlighting the interplay between magnetism and superconductivity. We analyze the pairing symmetry and magnetic properties of the system, predicting two distinct states in which magnetism and superconductivity coexist. As hole doping increases, the magnetic order is rapidly suppressed. The interlayer hopping t perpendicular to and coupling J perpendicular to promote a transition from intralayer d-wave pairing to s-wave pairing, which is accompanied by a shift from antiferromagnetic order to a double spin stripe configuration. The latter has been extensively observed in ambient and high-pressure experiments. Our study offers theoretical insights into the coexistence of spin density waves and superconductivity.

Aerogels are known for their high porosity and very low density and can be made from a range of materials, but are limited by structural instability under extreme thermomechanical conditions. We report on 194 types of dome-celled ultralight aerogels that maintain superior elasticity spanning from 4.2 kelvin (K) to 2273 K, realized by a two-dimensional channel–confined chemistry method. Such aerogels exhibit superelasticity under 99% strain for 20,000 cycles and thermal shock resistance at 2273 K over 100 cycles. The high-entropy carbide aerogel achieves a thermal conductivity of 53.4 mW·m −1 ·K −1 at 1273 K and 171.1 mW·m −1 ·K −1 at 2273 K. The combination of temperature-invariant elasticity and chemical diversity makes such aerogels highly promising for extreme thermomechanics, from heat-insulated industries to deep space exploration.

Geometric frustration in quantum spin systems can lead to exotic ground states. In this study, we investigate the $\mathrm{SU}(3)$ spin model on the checkerboard lattice to explore the effects of frustration arising from its point-connected $(N+1)$-site local structure. We employ density matrix renormalization group (DMRG) and exact diagonalization (ED) techniques to determine the ground state properties. Our results reveal the absence of both 3-sublattice antiferromagnetic order and valence cluster solid order. Instead, we identify ground states with bond stripe patterns sensitive to boundary conditions and system size, comprising staggered singlet arrays and uniform flat stripes. Notably, these stripes are relatively decoupled, and similar patterns can be reconstructed in quasi-one-dimensional ladders. These findings suggest that geometric frustration drives the system toward a mixed phase, combining characteristics of spin-liquid and valence cluster solid states, providing new insights into the behavior of frustrated quantum spin systems.

The behavior of strongly interacting electrons in bands with Berry curvature is a problem of wide interest. In this paper, we study this problem by numerically studying a fluxed Hubbard-type model on square lattice. Using this model, we demonstrate a metallic ferromagnet in electron bands equipped with Berry curvature can develop non-coplanar spin order in which spin polarization axes at different position span finite solid angles. We find spin chirality can emerge in this setting by doping or adding gauge flux on top of a collinear ferromagnet. This result supports the prediction of spin chirality occurring through an emergent spin orbital interaction. Meanwhile, our result shows that, on top a ferromagnetic background, the spin chirality emerges at a finite threshold value of orbital magnetization, resembling the predicted behavior in theory.