arXiv subjects

Yu Ye

Publications and source records attributed to Yu Ye.

At least 19 recordsLinked to original sources

arXiv2026

Deriving Newton's Canonical Forms of Cubic Curves via the Center of Polynomials

Existing classifications of real plane cubic curves rely on sophisticated tools and require a lengthy exposition. This paper provides a concise yet elementary treatment of this classical topic. Using the centers of polynomials, we establish a correspondence between the algebraic structure of these centers and geometric properties of binary cubic polynomials, which yields a novel approach to Newton's canonical forms.

math.RA↗

arXiv2026

Excitons probe intrinsic flat band Mottness in a van der Waals heterostructure

Excitons provide a sensitive optical probe of electronic correlations in nearby two-dimensional materials, yet their coupling to intrinsic flat-band Mott systems remains largely unexplored. Here we combine gate-tunable optical spectroscopy with first-principles calculations to study monolayer WSe$_2$ in direct contact with the van der Waals Mott insulator Nb$_3$Cl$_8$. The gate evolution of WSe$_2$ excitonic resonances reveals signatures of a correlation-reconstructed Mott gap in Nb$_3$Cl$_8$ that is absent from the single-particle band picture. In the electron-doped regime, the WSe$_2$ 2s Rydberg exciton undergoes a multistage evolution and develops into interlayer attractive and repulsive polaron branches, showing that a Rydberg exciton can be dressed by strongly correlated flat-band electrons in an adjacent Mott layer. Under an out-of-plane magnetic field, spin-polarized Nb$_3$Cl$_8$ states further induce valley-selective exciton coupling, producing a strongly enhanced circular polarization of the WSe$_2$ exciton emission. These results extend exciton-based sensing and exciton-polaron physics to intrinsic flat-band Mott materials, providing an optical route to probe and engineer correlation-driven interfacial quasiparticles.

cond-mat.mtrl-sci↗

arXiv2026

Direct Measurement of Exciton Dispersion in the Long-Wavelength Limit

Exciton dispersion, which governs the propagation, scattering and radiative decay of electron-hole pairs, is essential to optoelectronics and quantum materials. In two-dimensional systems, weakened dielectric screening and long-range electron-hole exchange are predicted to induce nonanalytic exciton dispersion in the long-wavelength limit. However, direct quantitative characterization of its dimensional evolution remains lacking, especially in the ultralow-q regime (q < 0.02 $\r{A}^{-1}$). Here we employ defocus-engineered momentum-resolved electron energy-loss spectroscopy in scanning transmission electron microscopy, achieving an ultrahigh momentum resolution of 0.0002 $\r{A}^{-1}$. Using freestanding hBN as a prototypical platform, we resolve layer-dependent exciton dispersion and quantify its characteristic crossover momentum and group velocity in the long-wavelength limit. With increasing thickness, the nonanalytic linear-dispersion regime is progressively compressed, manifested by a reduction in characteristic crossover momentum q_c from $1.82 \times 10^{-1} \r{A}^{-1}$ in the monolayer to $3.0 \times 10^{-1} \r{A}^{-1}$ in 25 layers. Meanwhile, the low-q group velocity increases from $2.0 \times 10^{-3} c$ to $2.9 \times 10^{-2} c$, before the dispersion ultimately approaches the bulk-like parabolic limit. We further examine how the exciton band structure of monolayer hBN responds to its surrounding environment, including temperature, adjacent graphene layers, and interlayer twist in BN/graphene heterostructures. These findings uncover the fundamental physics of low-dimensional excitons, deliver valuable guidance for modulating exciton transport, diffusion and quasiparticle coupling in layered quantum materials, and establish a powerful experimental route to explore low-dimensional exciton physics.

cond-mat.mes-hall↗

arXiv2026

Direct Sum and Direct Product Decompositions of Multivariate Functions

This paper addresses the problem of whether or not a vector-valued multivariate functions can be expressed as a sum or a product of vector-valued functions in disjoint sets of variables through a proper invertible linear change of variables. The crux is an invariant algebra, the so-called center, that we introduce for a set of multivariate functions with second order partial derivatives. We thus provide simple criteria and algorithms for simultaneous additive and multiplicative decompositions of any set of multivariate functions with minor analytic conditions. This is applied to the factorization problem of multivariate homogeneous polynomials, in particular those that are products of linear forms.

math.RA↗

arXiv2026

Direct observation of anisotropic exciton dispersion in the 2D semiconductor CrSBr

We report momentum-resolved measurements of exciton dispersion in multilayer CrSBr using defocus-engineered electron energy-loss spectroscopy, supported by first-principles calculations. A pronounced in-plane anisotropy is observed, with the exciton exhibiting a linear dispersion along $\Gamma$Y within $\lvert \boldsymbol{q} \rvert$ < 0.007 \r{A}$^{-1}$, while remaining nearly dispersionless along $\Gamma$X. The slope reaches 7.02 eV \r{A}, among the largest reported in low-dimensional systems. The calculations reproduce the experimentally observed linear dispersion, confirming its intrinsic origin. We attribute the anisotropic dispersion to the long-range electron--hole exchange interaction, enhanced by strong out-of-plane confinement and governed by the directional selection rules of the transition dipole moment. Comparative measurements across the magnetic phase transition from the paramagnetic to the A-type antiferromagnetic state show that the dispersion remains essentially unchanged, indicating negligible coupling between exciton propagation and magnetic order. These results establish CrSBr as a model system for investigating anisotropic exciton dynamics in low-symmetry layered semiconductors.

cond-mat.mtrl-sci↗

arXiv2026

Layer-parity-dependent interfacial coupling in Nb$_3$Cl$_8$/graphene van der Waals heterostructures

Strongly correlated two-dimensional systems provide compelling platforms for investigating exotic quantum phenomena. Niobium chloride (Nb$_3$Cl$_8$), a single-band Mott insulator, exhibits a remarkable out-of-plane polarization in its topmost layer that oscillates with layer parity, manifesting as an odd-even effect. Using atomic force microscopy (AFM) and Kelvin probe force microscopy (KPFM), this layer-parity-dependent polarization can be effectively characterized through surface morphology and potential mapping, enabling the unambiguous identification of different surface phases. We then fabricated dual-gate Hall devices by coupling different surface phases of Nb$_3$Cl$_8$ with monolayer graphene to investigate how the topmost-layer out-of-plane polarization influences interfacial coupling and the resulting transport behavior. Our results reveal significant phase-dependent variations in charge transfer, carrier densities, and hybridization gaps (25.2 meV for Phase 1 and 30.0 meV for Phase 2). Density functional theory calculations corroborate these experimental findings, showing that distinct out-of-plane polarizations in the topmost layer lead to different orbital overlaps and interfacial coupling strengths. These findings highlight the critical importance of surface polarization and orbital orientation in engineering the properties of strongly correlated van der Waals heterostructures.

cond-mat.mtrl-sci↗

arXiv2026

Layer-parity-defined surface polarization in Nb$_3$Cl$_8$ for excitonic modulation at van der Waals interfaces

The intrinsic symmetry breaking in the breathing kagome lattice of layered Nb$_3$Cl$_8$ provides a unique mechanism for realizing electrically polar surfaces. In each monolayer, the trimerization of Nb atoms breaks inversion and mirror symmetries, generating an out-of-plane electric dipole. The AB-stacked $\alpha$ phase arranges adjacent layer dipoles antiferroelectrically, leaving the uncompensated surface polarization strictly governed by layer parity. Here, using atomic force microscopy operated in Kelvin probe force microscopy mode, we directly visualize layer-dependent polarization states in exfoliated Nb$_3$Cl$_8$ flakes and resolve a pronounced odd-even oscillation of the surface electrostatic potential. Beyond this parity-locked antiferroelectric order, we further identify intralayer polar domains in which local atomic reconstructions of the breathing kagome network reverse the out-of-plane dipole of the surface layer, producing ferroelectric-like stacking configurations. By interfacing monolayer MoSe$_2$ with Nb$_3$Cl$_8$, we demonstrate that these surface-polarization textures effectively modulate adjacent excitonic emission through domain-dependent interfacial band alignment and charge transfer. Our findings establish Nb$_3$Cl$_8$ as an intrinsic layer-polarized van der Waals platform and show that layer parity provides powerful structural degree of freedom for programming excitonic and optoelectronic responses at van der Waals interfaces.

cond-mat.mtrl-sci↗

arXiv2026

In-situ operation of amorphous circuits under heavy-ion irradiation

Radiation-hardened electronics using semiconductors beyond silicon are essential for computation and control in extreme environments. Yet complex digital circuits based on such material platforms operating in situ under heavy-ion irradiation remain largely unexplored. Here, we show a timing circuit based on amorphous thin-film semiconductors at the 100-transistor scale, and demonstrate its robust operation through a functional "Hello World" ASCII output sequence. Beyond static device characterization, we evaluate the circuit under powered heavy-ion irradiation using tantalum ions, providing an operationally relevant assessment of radiation tolerance at the system level. Under a high particle flux of 2.5 x 10^3 ions cm^-2 s^-1, the circuit maintains stable operation during the irradiation test, achieving a total fluence of 1 x 10^6 ions cm^-2, establishing a milestone of prolonged powered digital operation under extreme conditions. Our work expands the design space of radiation-tolerant electronics, highlighting amorphous semiconductors as a promising foundation for digital circuits deployed in harsh environments.

cond-mat.mtrl-sci↗

arXiv2026

Point varieties and point-exactness of Koszul algebras

In this paper, we introduce the point-exact condition for a Koszul algebra $A$, which is useful for characterizing the (G1) condition of $A$ in the sense of Mori. Let $B = A/(f)$, where $f \in A_2$ is a regular normal element. We show that if $A$ satisfies the (G1) condition and is point-exact up to degree $\ell \geq 2$, then $B$ also satisfies the (G1) condition and is point-exact up to degree $\ell$. Moreover, we show that skew polynomial algebras satisfy the point-exact condition.

math.RA↗

arXiv2026

Benchmarking Multimodal Large Language Models for Missing Modality Completion in Product Catalogues

Missing-modality information on e-commerce platforms, such as absent product images or textual descriptions, often arises from annotation errors or incomplete metadata, impairing both product presentation and downstream applications such as recommendation systems. Motivated by the multimodal generative capabilities of recent Multimodal Large Language Models (MLLMs), this work investigates a fundamental yet underexplored question: can MLLMs generate missing modalities for products in e-commerce scenarios? We propose the Missing Modality Product Completion Benchmark (MMPCBench), which consists of two sub-benchmarks: a Content Quality Completion Benchmark and a Recommendation Benchmark. We further evaluate six state-of-the-art MLLMs from the Qwen2.5-VL and Gemma-3 model families across nine real-world e-commerce categories, focusing on image-to-text and text-to-image completion tasks. Experimental results show that while MLLMs can capture high-level semantics, they struggle with fine-grained word-level and pixel- or patch-level alignment. In addition, performance varies substantially across product categories and model scales, and we observe no trivial correlation between model size and performance, in contrast to trends commonly reported in mainstream benchmarks. We also explore Group Relative Policy Optimization (GRPO) to better align MLLMs with this task. GRPO improves image-to-text completion but does not yield gains for text-to-image completion. Overall, these findings expose the limitations of current MLLMs in real-world cross-modal generation and represent an early step toward more effective missing-modality product completion.

cs.MM↗

arXiv2026

The Waring Problem of Harmonic Polynomials

This paper investigates the Waring problem of harmonic polynomials. By characterizing the annihilating ideal of a homogeneous harmonic polynomial, i.e., a real binary form that is in the kernel of the Laplacian, we show that its Waring rank equals its degree. Moreover, we show that any linear form can appear in a minimal Waring decomposition of a homogeneous harmonic polynomial, implying that the forbidden locus is empty. We also provide an explicit algorithm for computing the minimal Waring decompositions.

math.NT↗

arXiv2025

The Hurwitz existence problem and the prime-degree conjecture: A computational perspective

We investigate the Hurwitz existence problem from a computational viewpoint. Leveraging the symmetric-group algorithm by Zheng and building upon implementations originally developed by Baroni, we achieve a complete and non-redundant enumeration of all non-realizable partition triples for positive integers up to $31$. These results are further categorized into four types according to their underlying mathematical structure; it is observed that nearly nine-tenths of them can be explained by known theoretical results. As an application, we verify the prime-degree conjecture for all primes less than $32$. In light of the exponential memory growth inherent in existing computational approaches -- which limits their feasibility at higher degrees -- we propose a novel software architecture designed to stabilize memory usage, thereby facilitating further detection of exceptional cases in the Hurwitz existence problem. The complete dataset of non-realizable partition triples, along with our implementation, will been made public on GitHub.

math.GR↗

arXiv2025

The Waring Problem of Complex Binary Forms

The Waring problem of forms concerns the expression of homogeneous multivariate polynomials as sums of powers of linear forms. This paper focuses on complex binary forms, and we solve the Waring problem for them using basic tools in algebra and analysis. In particular, we present elementary treatments of the Apolarity Lemma and Sylvester's 1851 Theorem, which are easily accessible and will provide an ideal approach for future extension to the general case.

math.NT↗

arXiv2025

Are Multimodal Embeddings Truly Beneficial for Recommendation? A Deep Dive into Whole vs. Individual Modalities

Multimodal recommendation has emerged as a mainstream paradigm, typically leveraging text and visual embeddings extracted from pre-trained models such as Sentence-BERT, Vision Transformers, and ResNet. This approach is founded on the intuitive assumption that incorporating multimodal embeddings can enhance recommendation performance. However, despite its popularity, this assumption lacks comprehensive empirical verification. This presents a critical research gap. To address it, we pose the central research question of this paper: Are multimodal embeddings truly beneficial for recommendation? To answer this question, we conduct a large-scale empirical study examining the role of text and visual embeddings in modern multimodal recommendation models, both as a whole and individually. Specifically, we pose two key research questions: (1) Do multimodal embeddings as a whole improve recommendation performance? (2) Is each individual modality - text and image - useful when used alone? To isolate the effect of individual modalities - text or visual - we employ a modality knockout strategy by setting the corresponding embeddings to either constant values or random noise. To ensure the scale and comprehensiveness of our study, we evaluate 14 widely used state-of-the-art multimodal recommendation models. Our findings reveal that: (1) multimodal embeddings generally enhance recommendation performance - particularly when integrated through more sophisticated graph-based fusion models. Surprisingly, commonly adopted baseline models with simple fusion schemes, such as VBPR and BM3, show only limited gains. (2) The text modality alone achieves performance comparable to the full multimodal setting in most cases, whereas the image modality alone does not. These results offer foundational insights and practical guidance for the multimodal recommendation community.

cs.IR↗

arXiv2025

Anderson Lattice in Incommensurate $\bf{Nb_3Cl_8}$/Graphene van der Waals Heterostructures

The periodic Anderson model}, traditionally realized in rare-earth compounds with limited tunability, have hindered systematic exploration of correlated quantum phenomena. Here, we introduce a strategy for {realizing and }engineering {this model} in incommensurate van der Waals heterostructures by coupling a Mott insulator (Nb$_3$Cl$_8$) with itinerant electrons (from monolayer graphene), circumventing strict lattice-matching requirements. Through magnetotransport and slave spin mean-field calculations, we demonstrate the hybridization gap ($\Delta\approx30$ meV), gate-tunable metal-insulator transition, and band-selective electron effective mass enhancement, hallmarks of Kondo coherence. The heterostructure exhibits a nearly order-of-magnitude enhancement in the effective electron mass between hybridized and conventional graphene-like regimes, alongside in-plane magnetic field-induced metal-insulator transitions. Top gate-temperature phase mapping reveals competing correlated states, including insulating and hidden-order phases. This work establishes an electrically tunable van der Waals platform for studying correlated states generated by coupling a Mott-insulating layer to an itinerant-electron system, providing a materials route for exploring low-dimensional correlated quantum phases.

cond-mat.str-el↗

arXiv2025

Polarized electroluminescence with magnetic spectral tuning in van der Waals magnet CrSBr

Polarized wavelength-tunable electroluminescence (EL) represents a critical on-demand functionality for next-generation optoelectronics. While conventional van der Waals (vdW) EL devices offer discrete wavelength switching constrained by fixed emission states, we report a novel platform enabling continuous spectral tuning combined with intrinsically polarized emission. By leveraging exciton-assisted inelastic tunneling in the anisotropic magnet CrSBr, our devices achieve uniform EL with a near unity degree of linear polarization ($\approx$ 94.3$\%$). The strong magneto-electronic coupling in CrSBr facilitates continuous magnetic-field-controlled spectral tuning through spin canting-induced band renormalization. This work establishes vdW magnets as a versatile platform for developing reconfigurable polarized light sources with simultaneous spectral and polarization control.

cond-mat.mtrl-sci↗

arXiv2025

A composition theory for upward planar orders

An upward planar order on an acyclic directed graph $G$ is a special linear extension of the edge poset of $G$ that satisfies the nesting condition. This order was introduced to combinatorially characterize upward plane graphs and progressive plane graphs (commonly known as plane string diagrams). In this paper, motivated by the theory of graphical calculus for monoidal categories, we establish a composition theory for upward planar orders. The main result is that the composition of upward planar orders is an upward planar order. This theory provides a practical method to calculate the upward planar order of a progressive plane graph or an upward plane graph.

math.CO↗

arXiv2025

Reconfigurable Room Temperature Exchange Bias through N\'eel Order Switching in van der Waals Heterostructures

Exchange bias effect plays a crucial role in modern magnetic memory technology. Recently, van der Waals magnetic materials have emerged and shown potential in spintronic devices at atomic scale. Owing to their tunable physical properties and the flexibility in fabrication, the van der Waals heterostructures offer more possibilities for investigating potential mechanisms of the exchange bias effect. However, due to low magnetic ordering temperatures for most van der Waals magnets, to establish exchange bias in van der Waals antiferromagnet/ferromagnet heterostructures at room temperature is challenging. In this study, we fabricate (Fe$_{0.56}$Co$_{0.44}$)$_{5}$GeTe$_{2}$(FCGT)/Fe$_{3}$GaTe$_{2}$(FGaT) heterostructures with magnetic ordering temperatures of each component well above room temperature to achieve a room temperature exchange bias effect. It is found that the sign and magnitude of the exchange bias field can be efficiently controlled by manipulating the N\'eel order of FCGT with magnetic field. The manipulation of N\'eel order shows significant magnetic field dependence. A strong pre-set field induces a switch in the N\'eel order of FCGT, which aligns the interfacial magnetization at the FCGT/FGaT interface, leading to robust exchange bias, as revealed by both transport measurements and macro-spin model calculations. Our findings demonstrate the intrinsic manipulation and switchable of room-temperature exchange bias in all-van der Waals heterostructures and further promote the development of novel two-dimensional spintronic devices.

cond-mat.mtrl-sci↗