arXiv subjects

Rui Xiong

Publications and source records attributed to Rui Xiong.

At least 37 records · Page 2Linked to original sources

arXiv2025

Combinatorial Aspects of Elliptic Schubert Calculus

The main goal of this paper is to extend two fundamental combinatorial results in Schubert calculus on flag manifolds from equivariant cohomology and $K$-theory to equivariant elliptic cohomology. The foundations of elliptic Schubert calculus were laid in a few relatively recent papers by Rimányi, Weber, and Kumar. They include the recursive construction of elliptic Schubert classes via generalizations of the cohomology and $K$-theory push-pull operators and the study of the corresponding Demazure algebra. We derive a Billey-type formula for the localization of elliptic Schubert classes (for partial flag manifolds of arbitrary type) and a pipe dream model for their polynomial representatives in the case of type $A$ flag manifolds. The latter extends the pipe dream model for double Schubert and Grothendieck polynomials. We also study the degeneration of elliptic Schubert classes to $K$-theory, which recovers the corresponding classical formulas.

math.CO↗

arXiv2025

ArgusCogito: Chain-of-Thought for Cross-Modal Synergy and Omnidirectional Reasoning in Camouflaged Object Segmentation

Camouflaged Object Segmentation (COS) poses a significant challenge due to the intrinsic high similarity between targets and backgrounds, demanding models capable of profound holistic understanding beyond superficial cues. Prevailing methods, often limited by shallow feature representation, inadequate reasoning mechanisms, and weak cross-modal integration, struggle to achieve this depth of cognition, resulting in prevalent issues like incomplete target separation and imprecise segmentation. Inspired by the perceptual strategy of the Hundred-eyed Giant-emphasizing holistic observation, omnidirectional focus, and intensive scrutiny-we introduce ArgusCogito, a novel zero-shot, chain-of-thought framework underpinned by cross-modal synergy and omnidirectional reasoning within Vision-Language Models (VLMs). ArgusCogito orchestrates three cognitively-inspired stages: (1) Conjecture: Constructs a strong cognitive prior through global reasoning with cross-modal fusion (RGB, depth, semantic maps), enabling holistic scene understanding and enhanced target-background disambiguation. (2) Focus: Performs omnidirectional, attention-driven scanning and focused reasoning, guided by semantic priors from Conjecture, enabling precise target localization and region-of-interest refinement. (3) Sculpting: Progressively sculpts high-fidelity segmentation masks by integrating cross-modal information and iteratively generating dense positive/negative point prompts within focused regions, emulating Argus' intensive scrutiny. Extensive evaluations on four challenging COS benchmarks and three Medical Image Segmentation (MIS) benchmarks demonstrate that ArgusCogito achieves state-of-the-art (SOTA) performance, validating the framework's exceptional efficacy, superior generalization capability, and robustness.

cs.CV↗

arXiv2025

Experimental Realization of the Topologically Nontrivial Phase in Monolayer Si$_2$Te$_2$

The free-standing monolayer Si$_2$Te$_2$ (ML-Si$_2$Te$_2$) has been theoretically predicted to host a room-temperature quantum spin Hall phase. However, its experimental realization remains challenge due to the absence of a three-dimensional counterpart. Here, we demonstrate that HfTe$_2$ serves as an ideal substrate for the epitaxial growth of ML-Si$_2$Te$_2$, preserving its topological phase. Scanning tunneling microscopy and spectroscopy confirm a strain-free ${(1 \times 1)}$ lattice of ML-Si$_2$Te$_2$, along with a sizable band gap, which is well captured by first-principles calculations. Moreover, distinct edge states, independent of step geometry and exhibiting a broad spatial distribution, are observed at ML-Si$_2$Te$_2$ step edges, underscoring its topological nature.

cond-mat.mtrl-sci↗

arXiv2025

Strain-induced nonrelativistic altermagnetic spin splitting effect

Recent studies reveal that $\mathcal{T}$-odd spin currents generated via the nonrelativistic altermagnetic spin splitting effect (ASSE) exhibit significant potential for spintronics applications, with both computational and experimental validations. Addressing the scarcity of conductive altermagnets, we propose strain engineering as a reliable method for inducing altermagnetism. Focusing on rutile-structured $\mathrm{OsO}_2$, first-principles calculations show that minor equibiaxial tensile strain ($\mathcal{E}_{\mathrm{ts}}$=3\%) induces nonmagnetic-to-altermagnetic transitions, achieving an ASSE-driven spin-charge conversion ratio ($θ_{\text{AS}}$) of $\sim$7\% -- far surpassing conventional spin Hall angles ($θ_{\text{IS}}$). Calculations reveal that substantial $θ_{\text{AS}}$ persists even in the absence of spin-orbit coupling, with its magnitude positively correlating to nonrelativistic spin splitting magnitude, which further confirms the strain-induced ASSE's nonrelativistic origin. Further investigation reveals that $\mathrm{RuO}_2$ exhibits analogous phenomena, which may resolve recent controversies regarding its magnetic properties. Our research opens new simple pathways for developing next-generation altermagnetic spintronic devices.

cond-mat.mtrl-sci↗

arXiv2025

Strain-Induced Non-alter Compensated Magnet and Its Application to Magnetic Tunnel Junction Device Design

The recent proposal of altermagnetism has drawn widespread attention to antiferromagnet (AFM) exhibiting spin splitting, extending beyond the realm of sign-alternating spin splitting in momentum space protected solely by rotational symmetry. Herrin, we propose a shear-strain strategy that enables significant modulation of d-wave altermagnets into an non-alter compensated magnets. A comprehensive analysis combining the magnetic moment compensation characteristics of opposite spin sublattices with the distribution of spin-resolved conduction channels in momentum space under the [001] crystal orientation reveals that shear strain breaks the rotational symmetry of alternatmagnets. To explore the application potential of non-alter compensated magnets, we designe RuO2/TiO2/RuO2 magnetic tunnel junctions (MTJ) with three crystallographic orientations ((001), (110), (100)) and investigated their transport properties under shear strain. This non-alter electronic structure not only enhances the tunneling magnetoresistance (TMR) in spin-split paths of intrinsic RuO2 (226% to 431%) but also enables substantial TMR in spin-degenerate paths (from 0-88%)). Our work provides guidelines for broadening magnetic materials and device platforms.

cond-mat.mtrl-sci↗

arXiv2025

Graham positivity of triple Schubert calculus

We prove Samuel's conjecture on certain Graham positivity of the expansion coefficient of two double Schubert polynomials in three sets of variables by establishing a refined version of Graham's positivity theorem. As a corollary, we prove Kirillov's conjecture on the positivity of skew divided difference operators applied to Schubert polynomials.

math.CO↗

arXiv2025

Nonreciprocally Boosting Magnetoacoustic Coupling with Surface-Acoustic-Wave-induced Spin Transfer Torque

Strengthening magnetoacoustic coupling is crucial to the improvement of the surface acoustic wave (SAW)-driven spintronics devices. A key challenge in enhancing magnetoacoustic coupling is minimizing the phonon and magnon dissipation of the device, which usually requires complicated techniques for generating shear-horizontal (SH) or standing waves to suppress the phonon dissipation. In this work, we significantly strengthened the magnetoacoustic coupling by suppressing the magnon dissipation via the SAW-induced spin-transfer-torque (STT) in Co/Cu/NiFe multilayer, which is facilitated by the non-parallel magnetization alignment between the two ferromagnetic layers. Also, this STT exhibits the form of Zhang-Li torque due to the SAW-induced spin wave, which gives rise to the unique nonreciprocal SAW transportation under external magnetic field. This finding opens new avenues for non-reciprocally boosting magnetoacoustic coupling, which pays the way for developing on-chip SAW-driven multifunctional devices.

physics.app-ph↗

arXiv2024

Extremely Large Anisotropy of Effective Gilbert Damping in Half-Metallic CrO2

Half-metals are a class of quantum materials with 100% spin-polarization at the Fermi level and have attracted a lot of attention for future spintronic device applications. CrO2 is one of the most promising half-metal candidates, for which the electrical and magnetic properties have been intensively studied in the last several decades. Here, we report the observation of a giant anisotropy (~1600%) of effective Gilbert damping in the single crystalline half metallic (100)-CrO2 thin films, which is significantly larger than the values observed on conventional ferromagnetic Fe and CoFe thin films. Furthermore, the effective Gilbert damping exhibits opposite temperature-dependent behaviors below 50 K with magnetic field along [010] direction and near [001] direction. These experimental results suggest the strong spin-orbit coupling anisotropy of the half-metallic CrO2 and might pave the way for future magnonic computing applications.

cond-mat.mtrl-sci↗

arXiv2024

Field-free current-induced magnetization switching of a room temperature van der Waals magnet for neuromorphic computing

Spin orbit torque (SOT) has become a promising approach to efficiently manipulate the magnetization switching in spintronic devices. As a main factor to impact the device performance, the high quality interface is essentially desired, which can be readily acquired by using the two-dimensional (2D) van der Waals (vdW) materials. Recently, a 2D ferromagnetic material Fe3GaTe2 has been discovered to possess the above-room-temperature Curie temperature and strong perpendicular magnetic anisotropy (PMA), providing an excellent candidate to build spintronic devices. On the other hand, an external magnetic field is necessary for the SOT-driven deterministic switching of perpendicular magnetization, which has become a block for the real applications. Here, we realize the field-free SOT switching of Fe3GaTe2 at room temperature based on the Fe3GaTe2/MnPt heterostructure. In addition, inspired by the superiority of 2D materials in 3D heterogeneous integration, we explore the potential of our device in the computing in memory (CIM). With the application of the current pulses, the gradual switching of our device at zero field imitates the function of artificial synapse in the convolutional neural network (CNN), achieving a high accuracy (~92.8%) pattern recognition. Our work proposes a feasible solution for field-free SOT switching in 2D vdW spintronic devices, which paves the way for applications in magnetic memory and neuromorphic computing.

physics.app-ph↗

arXiv2024

Non-Hermitian quasicrystalline topological insulators

In recent years, the interplay between non-Hermiticity and band topology is expected to uncover numerous novel physical phenomena. However, the majority of research has focused on periodic crystalline structures, with comparatively fewer studies exploring quasicrystalline systems. In this paper, we delve into the influence of asymmetric hopping on the topological insulators, specifically focusing on quantum spin Hall insulators and higher-order topological insulators in an octagonal Ammann-Beenker quasicrystalline lattice. We demonstrate that asymmetric hopping can significantly alter the distribution of edge states, leading to a uniform distribution across all boundaries or localizing them at a single edge, depending on the symmetry adjustments. Furthermore, we explore the robustness of higher-order topological corner states under perturbations, showing that these states can maintain their distribution even in the presence of non-Hermiticity. Our findings not only expand the current understanding of topological states in quasicrystals under non-Hermitian conditions, but also provide valuable theoretical guidance for manipulating corner state distributions in non-Hermitian quasicrystalline higher-order topological insulators.

cond-mat.mes-hall↗

arXiv2024

Hybrid Pipe Dreams for Key Polynomials

We develop a family of new combinatorial models for key polynomials. It is similar to the hybrid pipe dream model for Schubert polynomials defined recently by Knutson and Udell.

math.CO↗

arXiv2024

Equivariant log-concavity and equivariant Kähler packages

We show that the exterior algebra $Λ_{R}\left[α_{1}, \cdots, α_{n}\right]$, which is the cohomology of the torus $T=(S^{1})^{n}$, and the polynomial ring $\mathbb{R}\left[t_{1}, \ldots, t_{n}\right]$, which is the cohomology of the classifying space $B (S^{1})^{n}=\left(\mathbb{C} \mathbb{P}^{\infty}\right)^{n}$, are $S_{n}$-equivariantly log-concave. We do so by explicitly giving the $S_{n}$-representation maps on the appropriate sequences of tensor products of polynomials or exterior powers and proving that these maps satisfy the hard Lefschetz theorem. Furthermore, we prove that the whole Kähler package, including algebraic analogies of the Poincaré duality, hard Lefschetz, and Hodge-Riemann bilinear relations, holds on the corresponding sequences in an equivariant setting.

math.RT↗

arXiv2024

Motivic Lefschetz theorem for twisted Milnor hypersurfaces

We show that the Grothendieck-Chow motive of a smooth hyperplane section $Y$ of an inner twisted form $X$ of a Milnor hypersurface splits as a direct sum of shifted copies of the motive of the Severi-Brauer variety of the associated cyclic algebra $A$ and the motive of its maximal commutative subfield $L\subset A$. The proof is based on the non-triviality of the (monodromy) Galois action on the equivariant Chow group of $Y_L$.

math.AG↗

arXiv2024

Structural disorder-induced topological phase transitions in quasicrystals

Recently, the structural disorder-induced topological phase transitions in periodic systems have attracted much attention. However, in aperiodic systems such as quasicrystalline systems, the interplay between structural disorder and band topology is still unclear. In this work, we investigate the effects of structural disorder on a quantum spin Hall insulator phase and a higher-order topological phase in a two-dimensional Amman-Beenker tiling quasicrystalline lattice, respectively. We demonstrate that the structural disorder can induce a topological phase transition from a quasicrystalline normal insulator phase to an amorphous quantum spin Hall insulator phase, which is confirmed by bulk gap closing and reopening, robust edge states, quantized spin Bott index and conductance. Furthermore, the structural disorder-induced higher-order topological phase transition from a quasicrystalline normal insulator phase to an amorphous higher-order topological phase characterized by quantized quadrupole moment and topological corner states is also found. More strikingly, the disorder-induced higher-order topological insulator with eight corner states represents a distinctive topological state that eludes realization in conventional crystalline systems. Our work extends the study of the interplay between disorder effects and topologies to quasicrystalline and amorphous systems.

cond-mat.mes-hall↗

arXiv2024

A Pieri type formula for motivic Chern classes of Schubert cells in Grassmannians

We prove a Pieri formula for motivic Chern classes of Schubert cells in the equivariant K-theory of Grassmannians, which is described in terms of ribbon operators on partitions. Our approach is to transform the Schubert calculus over Grassmannians to the calculation in a certain affine Hecke algebra. As a consequence, we derive a Pieri formula for Segre motivic classes of Schubert cells in Grassmannians. We apply the Pieri formulas to establish a relation between motivic Chern classes and Segre motivic classes, extending a well-known relation between the classes of structure sheaves and ideal sheaves. As another application, we find a symmetric power series representative for the class of the dualizing sheaf of a Schubert variety.

math.CO↗

arXiv2023

On the formal Peterson subalgebra and its dual

In the present notes, we study a generalization of the Peterson subalgebra to an oriented (generalized) cohomology theory which we call the formal Peterson subalgebra. Observe that by recent results of Zhong the dual of the formal Peterson algebra provides an algebraic model for the oriented cohomology of the affine Grassmannian. Our first result shows that the centre of the formal affine Demazure algebra generates the formal Peterson subalgebra. Our second observation is motivated by the Peterson conjecture. We show that a certain localization of the formal Peterson subalgebra for the extended Dynkin diagram of type $\hat A_1$ provides an algebraic model for `quantum' oriented cohomology of the projective line. Our last result can be viewed as an extension of the previous results on Hopf algebroids of structure algebras of moment graphs to the case of affine root systems. We prove that the dual of the formal Peterson subalgebra (an oriented cohomology of the affine Grassmannian) is the $0$th Hochshild homology of the formal affine Demazure algebra.

math.RA↗

arXiv2023

Antiferromagnetic to Ferrimagnetic Phase Transition and Possible Phase Coexistence in Polar Magnets (Fe$_{1-x}$Mn$_x$)$_2$Mo$_3$O$_8$

In the present work, magnetic properties of single crystal (Fe$_{1-x}$Mn$_x$)$_2$Mo$_3$O$_8$ ($0 0.3$. Meanwhile, sizeable electric polarization of spin origin is commonly observed in all samples, no matter what the magnetic state is. For the samples hosting a ferrimagnetic state, square-like magnetic hysteresis loops are revealed, while the remnant magnetization and coercive field can be tuned drastically by simply varying the Mn-content or temperature. Possible coexistence of the antiferromagnetic and ferrimagnetic phases is proposed to be responsible for the remarkable modulation of magnetic properties in the samples.

cond-mat.mtrl-sci↗

arXiv2023

Bumpless pipe dreams meet Puzzles

Knutson and Zinn-Justin recently found a puzzle rule for the expansion of the product $\mathfrak{G}_{u}(x,t)\cdot \mathfrak{G}_{v}(x,t)$ of two double Grothendieck polynomials indexed by permutations with separated descents. We establish its triple Schubert calculus version in the sense of Knutson and Tao, namely, a formula for expanding $\mathfrak{G}_{u}(x,y)\cdot \mathfrak{G}_{v}(x,t)$ in different secondary variables. Our rule is formulated in terms of pipe puzzles, incorporating both the structures of bumpless pipe dreams and classical puzzles. As direct applications, we recover the separated-descent puzzle formula by Knutson and Zinn-Justin (by setting $y=t$) and the bumpless pipe dream model of double Grothendieck polynomials by Weigandt (by setting $v=\operatorname{id}$ and $x=t$). Moreover, we utilize the formula to partially confirm a positivity conjecture of Kirillov about applying a skew operator to a Schubert polynomial.

math.CO↗