arXiv subjects

Wenliang Zhang

Publications and source records attributed to Wenliang Zhang.

At least 19 recordsLinked to original sources

arXiv2026

Keller maps and holonomic $D$-modules

Let $\kk$ be a field of characteristic $p$ and $R=\kk[x_1,\dots,x_n]$. Let $D$ denote the ring of $\kk$-linear differential operators on $R$. Let $φ:R\to R$ be a $\kk$-algebra endomorphism whose Jacobian is a unit in $R$. We show that there is a unique $\kk$-algebra endomorphism $Φ:D\to D$ such that $Φ|_R=φ$ and that the restriction of scalar via $Φ$ preserves holonomicity. We also construct an example of a $\kk$-algebra endomorphism of $D$ that does not preserve holonomicity.

math.AC↗

arXiv2026

Time-delay Control Using a New Nonlinear Adaptive Law for Cable-Driven Robots

Cable-driven manipulators exhibit strong nonlinearities and low structural stiffness, which make precise control challenging under time-varying uncertainties and external disturbances. This paper presents a time-delay-estimation (TDE)-based adaptive fractional-order nonsingular terminal sliding mode (AFONTSM) control strategy for cable-driven robots. A robust controller is constructed within a TDE-based model-free framework by combining fractional-order nonsingular terminal sliding mode error dynamics with a fast terminal sliding mode reaching law. The main contribution is a new adaptive law that introduces an adaptive exponential term into the update gain to form a nonlinear adaptive mechanism. This design improves adaptive regulation under different operating conditions by suppressing noise-induced chattering during smooth tracking while preserving or enhancing the adaptive gain during trajectory reversal. Lyapunov analysis proves the ultimate uniform boundedness of the tracking error. Experimental results show that, compared with the baseline method, the proposed controller reduces RMSE by 34.52% and 31.11%, ITAE by 33.79% and 32.97%, and ISCT by 6.69% and 17.77% for the two joints, respectively. Further comparisons with recently reported adaptive laws demonstrate that the proposed law provides faster adaptive response, more stable gain evolution, and improved chattering suppression. Additional payload tests further verify the robustness and repeatability of the proposed method.

eess.SY↗

arXiv2026

$3d_{z^2}$ orbital delocalization and magnetic collapse in superconducting (La,Pr)$_3$Ni$_2$O$_{7-δ}$ films

The recent discovery of Ruddlesden--Popper (RP) nickelate thin-film superconductors has opened a new frontier in unconventional superconductivity. Its realization requires both compressive epitaxial strain and highly oxidative growth conditions, yet the microscopic pathway from the parent phase to the superconducting phase remains elusive. Here, X-ray absorption spectra and resonant inelastic X-ray scattering are employed to track this evolution by independently tuning strain and oxygen content in (La,Pr)$_3$Ni$_2$O$_{7-δ}$ thin films. We uncover a remarkable two-step narrative. First, signatures of delocalization emerge in the same way upon two independent tunings: Spectral weight transfers from a ''Upper Hubbard''-like peak to the hole-like peak associated with O $2p_z$ state, and in parallel, the initially localized Ni $3d_{z^2}$ orbital becomes more itinerant followed by the broadening and weakening of $dd$ orbital excitations. Second, as itinerancy increases, long-range spin-density-wave (SDW) order is suppressed in both intensity and correlation length, indicating direct competition with superconductivity. Yet, short-range magnons persist: they become damped but their bandwidth stays unchanged. Our results paint a coherent picture that both strain and oxygenation drive the RP bilayer nickelates towards the superconducting instability, where the O $2p_z$ and Ni $3d_{z^2}$ orbitals become delocalized. Concomitantly, the long-range magnetic order loses coherence and gets suppressed. These findings establish an orbital-selective route to RP nickelate superconductivity, in which the delocalization of the $2p_z$ and $3d_{z^2}$ orbitals and the robust short-range magnons upon the melting of SDW order are prerequisites, providing strong constraints for theory and the roadmap for designing nickelate superconductors.

cond-mat.supr-con↗

arXiv2026

Dissecting superconductivity in the Ruddlesden-Popper nickelates: The role of electron correlation and interlayer magnetic exchange

The discovery of superconductivity in the Ruddlesden-Popper (RP) nickelates has opened a new chapter in the search for high superconducting transition temperatures ($T_\mathrm{c}$) materials. A central and puzzling feature of this family is the wide variation in $T_\mathrm{c}$ despite their common NiO$_2$ building blocks, as highlighted by the recent observation of superconductivity at $\sim$ 30 K in trilayer $\mathrm{La_4Ni_3O_{10}}$, significantly lower than 80 K reported in bilayer $\mathrm{La_3Ni_2O_7}$. Understanding the factors that control $T_\mathrm{c}$ in this family is therefore of paramount importance. Here, we use resonant inelastic x-ray scattering (RIXS) to investigate the electronic and magnetic excitations of $\mathrm{La_4Ni_3O_{10}}$ in direct comparison with its bilayer counterpart. Our results reveal a markedly different landscape. $\mathrm{La_4Ni_3O_{10}}$ exhibits a more itinerant character, evidenced by broader Ni $dd$ orbital excitations and a strong Ni 3$d$ fluorescence continuum, suggesting weaker electronic correlations than in the bilayer. Despite this, well-defined collective spin excitations persist, including dispersive acoustic and optical magnon branches alongside an incommensurate spin density wave. Using linear spin wave theory, we extract the interlayer superexchange interaction ($J_z$) to be $\sim$ 22 meV, much smaller than that in $\mathrm{La_3Ni_2O_7}$. The weaker correlation and reduced interlayer exchange together provide a consistent explanation for the substantially lower $T_\mathrm{c}$ in the trilayer compound. Our findings establish interlayer magnetic coupling and electronic correlation as key parameters governing superconductivity in layered nickelates and offer critical constraints for understanding the pairing mechanism in this emerging family.

cond-mat.supr-con↗

arXiv2026

X-ray magnetic circular dichroism evidence of intrinsic $d$-wave altermagnetism in rutile-structure NiF$_2$

We present the x-ray magnetic circular dichroism (XMCD) at the Ni $L_{2,3}$-edge as an evidence of the $d$-wave altermagnetism in rutile-structure NiF$_2$. Sizable XMCD signal is observed in excellent agreement with theoretical simulations. Owing to a considerable net magnetization due to spin canting, the XMCD spectrum consists of an altermagnetic signal as well as a non-negligible ferromagnetic contribution. We verify experimentally that the XMCD spectrum can be written as a sum of contributions from altermagnetism and weak ferromagnetism. Two experimental methods to isolate the ferromagnetic contribution are shown to yield essentially the same result. These are dependence of XMCD on applied magnetic fields below the Néel temperature and the XMCD measured in applied field above the Néel temperature. Our results demonstrate the utility of XMCD as a probe for altermagnetic materials with the coexisting weak ferromagnetism induced by the relativistic spin-orbit coupling.

cond-mat.str-el↗

arXiv2025

Coexistence of insulator-like paramagnon and metallic spin-orbit exciton modes in SrIrO$_3$

We probe the spectrum of elementary excitations in SrIrO$_3$ by using heterostructured [(SrIrO$_3$)$_m$/(SrTiO$_3$)$_l$] samples to approach the bulk limit. Our resonant inelastic x-ray scattering (RIXS) measurements at the Ir $L_3$-edge reveal a robust low-lying collective magnetic mode with an antiferromagnetic (AF) dispersion similar to the insulators Sr$_2$IrO$_4$ and Sr$_3$Ir$_2$O$_7$, albeit with a large gap and much larger linewidth. At higher energies we find the spin-orbit exciton, also strongly broadened, but with an inverted dispersion and doubled periodicity that are controlled by the charge hopping. These results demonstrate that the AF paramagnon persists, somewhat counterintuitively, far into the metallic regime of the insulator-metal transition driven by the degree of confinement in the heterostructure. We conclude that these two excitations, which are contrasting but coexisting hallmarks of strong AF pseudospin and charge fluctuations in a spin-orbit-coupled Mott-Slater material, are properties intrinsic to the ground state of semimetallic perovskite SrIrO$_3$.

cond-mat.str-el↗

arXiv2025

Remarks on effective uniform Briançon-Skoda

Let $R$ be a noetherian commutative ring. Of great interest is the question whether one can find an explicit integer $k$ such that $\overline{I^{k+n}}\subseteq I^n$ for each ideal $I$ and each integer $n\geq 1$ (the notation $\overline{I^{k+n}}$ denotes the integral closure of $I^{k+n}$). In this article, we investigate this question and obtain optimal values of $k$ for $F$-pure (or dense $F$-pure type) rings and Cohen-Macaulay $F$-injective (or dense $F$-injective type) rings.

math.AC↗

arXiv2025

Koszul cohomology and support of local cohomology modules of complete intersections

Let $R$ be a noetherian commutative ring and $f_1,\dots,f_c$ be a regular sequence in $R$. We introduce a framework to study $Supp(H^j_I(R/(f_1,\dots,f_c)))$ by linking the Koszul cohomology of $H^j_I(R)$ on the sequence $f_1,\dots,f_c$ and local cohomology modules $H^j_I(R/(f_1,\dots,f_c))$. As an application, we prove that if $R$ is a noetherian regular ring of prime characteristic $p$ and $f_1,f_2$ form a regular sequence in $R$ then $Supp(H^j_I(R/(f_1,f_2)))$ is Zariski-closed for each integer $j$ and each ideal $I$.

math.AC↗

arXiv2025

Persistent quantum vibronic dynamics in a $5d^1$ double perovskite oxide

Quantum entanglement between the spin, orbital, and lattice degrees of freedom in condensed matter systems can emerge due to an interplay between spin-orbit and vibronic interactions. Heavy transition metal ions decorated on a face-centered cubic lattice, for example, in $5d^1$ double perovskites, are particularly suited to support these quantum entangled states, but direct evidence has not yet been presented. In this work, we report additional peaks in the low-energy spectra of a $5d^1$ double perovskite, Ba$_2$CaReO$_6$, which cannot be explained by adopting a purely classical description of lattice vibrations. Instead, our theoretical analysis demonstrates that these spectroscopic signatures are characteristic of orbital-lattice entangled states in Ba$_2$CaReO$_6$. Crucially, both theory and experiment demonstrate that these quantum-entangled states persist to low temperatures, despite the onset of multipolar order.

cond-mat.str-el↗

arXiv2025

Applications of perverse sheaves in commutative algebra

The goal of this paper is to explain how basic properties of perverse sheaves sometimes translate via Riemann-Hilbert correspondences (in both characteristic $0$ and characteristic $p$) to highly non-trivial properties of singularities, especially their local cohomology. Along the way, we develop a theory of perverse $\mathbf{F}_p$-sheaves on varieties in characteristic $p$, expanding on previous work by various authors, and including a strong version of the Artin vanishing theorem.

math.AG↗

arXiv2025

Local cohomology and Segre products

We prove a Künneth formula for local cohomology of a Segré product of graded modules supported in a Segré product of ideals. In order to apply our formula to the study of cohomological dimension, we also investigate asymptotic behaviors of Eulerian graded $\scr{D}$-modules.

math.AC↗

arXiv2025

The Second Vanishing Theorem for Local Cohomology Modules

We prove the Second Vanishing Theorem for local cohomology modules of an unramified regular local ring in its full generality and provide a new proof of the Second Vanishing Theorem in prime characteristic $p$. As an application of our vanishing theorem for unramified regular local rings, we extend our topological characterization of the highest Lyubeznik number of an equi-characteristic local ring to the setting of mixed characteristic. An upper bound of local cohomological dimension in mixed characteristic is also obtained by partially extending Lyubeznik's vanishing theorem in prime characteristic $p$ to mixed characteristic.

math.AC↗

arXiv2024

On the injective dimension of unit Cartier and Frobenius modules

Let $R$ be a regular $F$-finite ring of prime characteristic $p$. We prove that the injective dimension of every unit Frobenius module $M$ in the category of unit Frobenius modules is at most $\operatorname{dim}(\operatorname{Supp}_R(M))+1$. We further show that for unit Cartier modules the same bound holds over any noetherian $F$-finite ring $A$ of prime characteristic $p$. This shows that $\dim A+1$ is a uniform upper bound for the injective dimension of any unit Cartier module over a noetherian $F$-finite ring $A$.

math.AC↗

arXiv2024

Emergence of interfacial magnetism in strongly-correlated nickelate-titanate superlattices

Strongly-correlated transition-metal oxides are widely known for their various exotic phenomena. This is exemplified by rare-earth nickelates such as LaNiO$_{3}$, which possess intimate interconnections between their electronic, spin, and lattice degrees of freedom. Their properties can be further enhanced by pairing them in hybrid heterostructures, which can lead to hidden phases and emergent phenomena. An important example is the LaNiO$_{3}$/LaTiO$_{3}$ superlattice, where an interlayer electron transfer has been observed from LaTiO$_{3}$ into LaNiO$_{3}$ leading to a high-spin state. However, macroscopic emergence of magnetic order associated with this high-spin state has so far not been observed. Here, by using muon spin rotation, x-ray absorption, and resonant inelastic x-ray scattering, we present direct evidence of an emergent antiferromagnetic order with high magnon energy and exchange interactions at the LaNiO$_{3}$/LaTiO$_{3}$ interface. As the magnetism is purely interfacial, a single LaNiO$_{3}$/LaTiO$_{3}$ interface can essentially behave as an atomically thin strongly-correlated quasi-two-dimensional antiferromagnet, potentially allowing its technological utilisation in advanced spintronic devices. Furthermore, its strong quasi-two-dimensional magnetic correlations, orbitally-polarized planar ligand holes, and layered superlattice design make its electronic, magnetic, and lattice configurations resemble the precursor states of superconducting cuprates and nickelates, but with an $S \rightarrow 1$ spin state instead.

cond-mat.str-el↗

arXiv2024

Spin waves and orbital contribution to ferromagnetism in a topological metal

Special arrangements of atoms with more than one atom per unit cell, including honeycomb or kagome (woven bamboo mat) lattices, can host propagating excitations with non-trivial topology as defined by their evolution along closed paths in momentum space. Excitations on such lattices can also be momentum-independent, meaning that they are localized notwithstanding strong hopping of the underlying disturbances between neighbouring sites. The associated flat bands are interesting because the interactions between the heavy quasiparticles inhabiting them will become much more important than for strong dispersion, resulting in novel quantum solid and liquid states. Different stackings of two-dimensional lattices, for example twisted graphene bilayers, provide routes to further engineer topology and many-body effects. Here, we report the discovery, using circularly polarized x-rays for the unambiguous isolation of magnetic signals, of a nearly flat spin wave band and large (compared to elemental iron) orbital moment for the metallic ferromagnet Fe3Sn2, built from compact AB-stacked kagome bilayers and which has a topologically non-trivial electronic band structure controllable by modest external magnetic fields. As a function of out-of-plane momentum, the nearly flat optical mode and the global rotation symmetry-restoring acoustic mode are out of phase, consistent with a bilayer exchange coupling that is larger than the already large in-plane couplings. The defining units of this topological metal are therefore a triangular lattice of octahedral iron clusters rather than weakly coupled kagome planes. The spin waves are strongly damped when compared to elemental iron, opening the topic of interactions of topological bosons (spin waves) and fermions (electrons) with the very specific target of explaining boson lifetimes.

cond-mat.str-el↗

arXiv2024

Dynamic Jahn-Teller effect in the strong spin-orbit coupling regime

Exotic quantum phases, arising from a complex interplay of charge, spin, lattice and orbital degrees of freedom, are of immense interest to a wide research community. A well-known example of such an entangled behavior is the Jahn-Teller effect, where the lifting of orbital degeneracy proceeds through lattice distortions, often accompanied by ordering of spins and metal-insulator transitions. Static distortions, including cooperative behavior, have been associated with colossal magneto-resistance, multiferroicity, high-$T_\mathrm{C}$ superconductivity and other correlated phenomena. Realizations of the dynamic Jahn-Teller effect, on the other hand, are scarce since the preservation of vibronic symmetries requires subtle tuning of the local environment. Here we demonstrate that a highly-symmetrical 5d$^1$ double perovskite Ba$_2$MgReO$_6$, comprising of a 3D array of isolated ReO$_6$ octahedra, fulfils these requirements, resulting in a unique case of a dynamic Jahn-Teller system with strong spin-orbit coupling. Thermodynamic and resonant inelastic x-ray scattering experiments undoubtedly show that the Jahn-Teller instability leads to a ground-state doublet, invoking a paradigm shift for this family of compounds. The restoration of vibronic degrees of freedom arises from a quantum-mechanical zero-point motion, as revealed by detailed quantum chemistry calculations. The dynamic state of ReO$_6$ octahedra persists down to the lowest temperatures, where a multipolar order sets in, allowing for investigations of the interplay between a dynamic JT effect and strongly correlated electron behavior.

cond-mat.str-el↗

arXiv2024

Spin-orbital excitations encoding the magnetic phase transition in the van der Waals antiferromagnet FePS$_{3}$

In the rich phases of van der Waals (vdW) materials featuring intertwined electronic order and collective phenomena, characterizing elementary dynamics that entail the low-energy Hamiltonian and electronic degrees of freedom is of paramount importance. Here we performed resonant inelastic X-ray scattering (RIXS) to elaborate the spin-orbital ground and excited states of the vdW antiferromagnetic insulator FePS$_{3}$, as well as their relation to magnetism. We observed the spectral enhancement of spin-orbital multiplet transitions about $\sim$ 100 and $\sim$ 220 meV, as well as quasielastic response, when entering the zig-zag antiferromagnetic phase, where the spectral changes develop an order-parameter-like evolution with temperature. By comparing with ligand field theory calculations, we discovered the essential role of trigonal lattice distortion and negative metal-ligand charge-transfer to account for these emergent excitations. Such spectral profiles are further examined upon confinement by mechanical exfoliation. We reveal their spectral robustness down to the few atomic layer limit, in accordance with the persistent antiferromagnetic state previously reported in optical measurements. Our study demonstrates the versatile RIXS capability that resolves magneto-crystalline anisotropy and charge-transfer energetics. These provide the crucial insight to understand how the spontaneous magnetic symmetry-breaking stabilizes in the quasi-two-dimensional limit for the vdW magnet FePS$_{3}$.

cond-mat.str-el↗

arXiv2024

Spectral evidence for Dirac spinons in a kagome lattice antiferromagnet

Emergent quasiparticles with a Dirac dispersion in condensed matter systems can be described by the Dirac equation for relativistic electrons, in analogy with Dirac particles in high-energy physics. For example, electrons with a Dirac dispersion have been intensively studied in electronic systems such as graphene and topological insulators. However, charge is not a prerequisite for Dirac fermions, and the emergence of Dirac fermions without charge degree of freedom has been theoretically predicted to be realized in Dirac quantum spin liquids. These quasiparticles carry a spin of 1/2 but are charge-neutral, and so are called spinons. Here we show that the spin excitations of a kagome antiferromagnet, YCu$_3$(OD)$_6$Br$_2$[Br$_{0.33}$(OD)$_{0.67}$], are conical with a spin continuum inside, which is consistent with the convolution of two Dirac spinons. The predictions of a Dirac spin liquid model with a spinon velocity obtained from the spectral measurements are in agreement with the low-temperature specific heat of the sample. Our results thus provide spectral evidence for the Dirac quantum spin liquid state emerging in this kagome lattice antiferromagnet. However, the locations of the conical spin excitations differ from those calculated by the nearest neighbor Heisenberg model, suggesting the Dirac spinons have an unexpected origin.

cond-mat.str-el↗