arXiv subjects

Tianran Chen

Publications and source records attributed to Tianran Chen.

At least 19 recordsLinked to original sources

arXiv2026

Orbital-selective oxygen holes in cuprate ladders beyond the Zhang-Rice paradigm

The electronic structure of the spin-ladder cuprate Sr14Cu24O41 challenges the presumed universality of the Zhang-Rice singlet (ZRS) framework and models based exclusively on Cu-O hybridized orbitals. Combining polarization-dependent resonant soft X-ray scattering at the O K-edge with inelastic neutron scattering, we show that doped holes in the Cu2O3 ladders localize predominantly in planar non-bonding O 2pz (p{\pi}) orbitals of rung oxygen sites rather than forming conventional ZRS states. Polarization-resolved RSXS uniquely identifies this orbital assignment, while lattice and magnetic excitations reveal its coupled consequences, establishing a unified microscopic picture that excludes the conventional {\sigma}-bonded singlet. This oxygen-sublattice charge order produces an anomalous diagonal stretching phonon and explains the absence of incommensurate magnetic fluctuations and anomalous magnon splitting. These findings motivate a reassessment of hole pairing in ladder cuprates and the sufficiency of copper-centric models for cuprate superconductors.

cond-mat.str-el↗

arXiv2026

S2FT: Parameter-Efficient Fine-Tuning in Sparse Spectrum Domain

Parameter Efficient Fine-Tuning (PEFT) is a key technique for adapting a large pretrained model to downstream tasks by fine-tuning only a small number of parameters. Recent methods based on Fourier transforms have further reduced the fine-tuned parameters scale by only fine-tuning a few spectral coefficients. Its basic assumption is that the weight change \delta W is a spatial-domain matrix with a sparse spectrum. However, in this paper, we observe that the spectrum of weight change is not sparse, but instead distributed like power-uniform. This fact implies that fine-tuning only a few spectral coefficients is insufficient to accurately model the weight change with uniform spectrum. To address this issue, we propose to seek an invertible transformation that can transform a latent spatial-domain matrix with sparse spectrum to the weight change, and then perform PEFT on such sparse spectrum domain with few spectral coefficients, called S2FT. To seek such transformation, we first pre-estimate a coarse weight change as a prior. Then, inspired by that sparse spectrum often correspond to locally smooth spatial structures, we regard this transformation as a row and column rearrangement operation on the pre-estimated weight change that smooth spatial structures while keep the structure information of neurons. Finally, we propose to solve the rearrangement search problem in a simple nearest neighbor search manner, thereby obtaining the invertible transformation. Extensive results show our S2FT achieves superior performance by only using 0.08% training parameters.

cs.CV↗

arXiv2026

A New Layered Kagome Strip Structure Na2Co3(AsO4)2(OH)2: Static and Dynamic Magnetic Properties

One-dimensional kagome strip chains share much of the same frustrated structural motif as two-dimensional kagome antiferromagnets, making them valuable for deepening our understanding of kagome lattice magnetism. In this paper, we report the hydrothermal synthesis and detailed structural and property characterization of Na2Co3(AsO4)2(OH)2, a striped kagome system. The crystal structure was characterized using single crystal X-ray diffraction, which reveals that Na2Co3(AsO4)2(OH)2 crystallizes in the monoclinic crystal system C2/m. The structure features a one-dimensional kagome strip lattice built from Co2+ ions and undergoes an antiferromagnetic transition at TN = 14 K. The magnetic ground state at zero field was characterized using neutron powder diffraction. Below the magnetic transition, Na2Co3(AsO4)2(OH)2 orders into an antiferromagnetic structure with a k-vector (0.5, 0.5, 0.5). In the proposed model, the Co1 moment is predominantly confined to the ac-plane while the Co2 moment is primarily aligned along the b-axis. Two flat bands were observed in the inelastic neutron spectra below the magnetic transition at 5 and 10 meV. Inelastic neutron spectra were modeled with a Heisenberg Hamiltonian including three nearest-neighbor exchange interactions (J1, J2, J3) and strong single-ion anisotropy to stabilize the observed magnetic structure. Our study highlights the complexity of the Co2+-based kagome strip magnetic lattice compound Na2Co3(AsO4)2(OH)2, which provides an excellent platform to broaden our understanding of the frustrated kagome magnetic lattice space.

cond-mat.mtrl-sci↗

arXiv2025

Emergent hidden order in ice: frustration and glassiness from slow hydrogen dynamics

Frustrated systems can host hidden order, in which weak interactions select correlated structure from a highly degenerate manifold. Water ice Ih is the canonical example of such a manifold, yet whether its hydrogen disorder conceals local structure beyond the Bernal-Fowler ice rules has remained controversial. Here, using high-resolution inelastic neutron scattering on single-crystal heavy ice, we identify strongly anisotropic librational phonons dispersing uniaxially along the crystallographic c axis - a spectroscopic signature inaccessible to bulk-averaging probes. A physics-guided analysis reveals that these excitations encode a hidden partial order: correlated polar armchair chains driven by a shallow stereochemical bias that creates an imperfectly flat energy landscape. This bias promotes nanoscale polar domains, yet frustrated topology prevents their straightforward coarsening into the ice XI ground state, trapping the system in a rugged configurational landscape that, within the experimentally constrained model, retains finite residual entropy even in the limit of infinitely slow cooling. These findings show that ice Ih is not a simple disordered solid, but a frustrated, partially ordered hydrogen network with glass-like arrest on a crystalline lattice, providing a microscopic framework that reconciles thermodynamic theory with spectroscopic observations.

cond-mat.mtrl-sci↗

arXiv2024

Green/WeakCoupling: Implementation of fully self-consistent finite-temperature many-body perturbation theory for molecules and solids

The accurate ab initio simulation of molecules and periodic solids with diagrammatic perturbation theory is an important task in quantum chemistry, condensed matter physics, and materials science. In this article, we present the WeakCoupling module of the open-source software package Green, which implements fully self-consistent diagrammatic weak coupling simulations, capable of dealing with real materials in the finite-temperature formalism. The code is licensed under the permissive MIT license. We provide self-consistent GW (scGW) and self-consistent second-order Green's function perturbation theory (GF2) solvers, analysis tools, and post-processing methods. This paper summarizes the theoretical methods implemented and provides background, tutorials and practical instructions for running simulations.

cond-mat.mtrl-sci↗

arXiv2024

Numerical Nonlinear Algebra

Numerical nonlinear algebra is a computational paradigm that uses numerical analysis to study polynomial equations. Its origins were methods to solve systems of polynomial equations based on the classical theorem of Bézout. This was decisively linked to modern developments in algebraic geometry by the polyhedral homotopy algorithm of Huber and Sturmfels, which exploits the combinatorial structure of the equations and led to efficient software for solving polynomial equations. Subsequent growth of numerical nonlinear algebra continues to be informed by algebraic geometry and its applications. These include new approaches to solving, algorithms for studying positive-dimensional varieties, certification, and a range of applications both within mathematics and from other disciplines. With new implementations, numerical nonlinear algebra is now a fundamental computational tool for algebraic geometry and its applications. We survey some of these innovations and some recent applications.

math.AG↗

arXiv2024

The influence of Structural Dynamics in Two-Dimensional Hybrid Organic-Inorganic Perovskites on their Photoluminescence Efficiency -- Neutron scattering analysis

Two-dimensional hybrid organic-inorganic perovskites (HOIPs) have emerged as promising materials for light-emitting diode applications. In this study, by using time-of-flight neutron spectroscopy we identified and quantitatively separated the lattice vibrational and molecular rotational dynamics of two perovskites, butylammonium lead iodide (BA)$_{2}$PbI$_{4}$ and phenethyl-ammonium lead iodide (PEA)$_{2}$PbI$_{4}$. By examining the corresponding temperature dependence, we found that the lattice vibrations, as evidenced by neutron spectra, are consistent with the lattice dynamics obtained from Raman scattering. We revealed that the rotational dynamics of organic molecules in these materials tend to suppress their photoluminescence quantum yield (PLQY) while the vibrational dynamics did not show predominant correlations with the same. Additionally, we observed photoluminescence emission peak splitting for both systems, which becomes prominent above certain critical temperatures where the suppression of PLQY begins. This study suggests that the rotational motions of polarized molecules may lead to a reduction in exciton binding energy or the breaking of degeneracy in exciton binding energy levels, enhancing non-radiative recombination rates, and consequently reducing photoluminescence yield. These findings offer a deeper understanding of fundamental interactions in 2D HOIPs and could guide the design of more efficient light-emitting materials for advanced technological applications.

cond-mat.mtrl-sci↗

arXiv2024

The rheology of ultra-high molecular weight poly(ethylene oxide) dispersed in a low molecular weight carrier

Gel spinning is the industrial method of choice for combining hydrophilic ultra-high molecular weight (UHMW) polymer resins with a hydrophobic support polymer to produce composite filaments for cytapheresis. Cytapheresis is a medical technique for removal of leukocytes from blood. Gel spinning is used to avoid high melt viscosity and thermal sensitivity of UHMW resins and the high melt temperature of the substrate resin but requires the recovery of toxic solvents. The UHMW resin is used because it forms a stable gel phase in the presence of water; a lower molecular weight resin (LMW) simply dissolves. UHMW and LMW resins were both poly(ethylene oxide) (PEO) and the substrate was polyarylsulfone (PAS). The literature indicated PEO undergoes non-oxidative thermal degradation above 200 °C and PAS is processed up to 350 °C. Dynamic oscillatory shear rheometry was used to study 0, 25, 40, 50, 60, and 75 wt. % UHMW PEO in LMW PEO to take advantage of the sensitivity of viscosity to changes in molecular weight and material configuration, indicating degradation. Samples were exposed to 220 °C, 230 °C, 240 °C, 250 °C, 275 °C, and 300 °C temperatures for 5 min to explore conditions that could result in sample degradation. The viscosity decreased less with increasing UHMW PEO content for samples exposed to the same temperature and the viscosity decreased more with increasing exposure temperature for samples with the same UHMW PEO content. Parameters were regressed from observed data to predict the change in molecular weight via empiricisms relating the viscosity to molecular weight, shear rate, temperature, and time.

physics.flu-dyn↗

arXiv2023

A geometric criterion on the equality between BKK bound and intersection index

The Bernshtein-Kushnirenko-Khovanskii theorem provides a generic root count for system of Laurent polynomials in terms of the mixed volume of their Newton polytopes (i.e., the BKK bound). A recent and far-reaching generalization of this theorem is the study of birationally invariant intersection index by Kaveh and Khovanskii. This short note establishes a simple geometric condition on the equality between the BKK bound and the intersection index for a system of vector spaces of Laurent polynomials. Applying this, we show that the intersection index for the algebraic Kuramoto equations equals their BKK bound.

math.AG↗

arXiv2023

A stratified polyhedral homotopy method for sampling positive-dimensional zero sets of polynomial systems

Numerical algebraic geometry revolves around the study of solutions to polynomial systems via numerical methods. The polyhedral homotopy of Huber and Sturmfels for computing isolated solutions and the concept of witness sets as numerical representations of non-isolated solution components, put forth by Sommese and Wampler, are two pillars of this field. In this paper, we show that a modified polyhedral homotopy places the computation of isolated solutions and sample sets for non-isolated components into a single, unified framework. In certain cases, this method also leads to a natural decomposition of the BKK bound into a sum of its local contributions.

math.AG↗

arXiv2022

Facets and facet subgraphs of symmetric edge polytopes

Symmetric edge polytopes, a.k.a. PV-type adjacency polytopes, associated with undirected graphs have been defined and studied in several seemingly independent areas including number theory, discrete geometry, and dynamical systems. In particular, the authors are motivated by the study of the algebraic Kuramoto equations of unmixed form whose Newton polytopes are the symmetric edge polytopes. The interplay between the geometric structure of symmetric edge polytopes and the topological structure of the underlying graphs has been a recurring theme in recent studies. In particular, ``facet/face subgraphs'' have emerged as one of the central concepts in describing this symmetry. Continuing along this line of inquiry we provide a complete description of the correspondence between facets/faces of a symmetric edge polytope and maximal bipartite subgraphs of the underlying connected graph.

math.CO↗

arXiv2022

On the typical and atypical solutions to the Kuramoto equations

The Kuramoto model is a dynamical system that models the interaction of coupled oscillators. There has been much work to effectively bound the number of equilibria to the Kuramoto model for a given network. By formulating the Kuramoto equations as a system of algebraic equations, we first relate the complex root count of the Kuramoto equations to the combinatorics of the underlying network by showing that the complex root count is generically equal to the normalized volume of the corresponding adjacency polytope of the network. We then give explicit algebraic conditions under which this bound is strict and show that there are networks where the Kuramoto equations have infinitely many equilibria.

math.AG↗

arXiv2022

Computing Volumes of Adjacency Polytopes via Draconian Sequences

Adjacency polytopes appear naturally in the study of nonlinear emergent phenomena in complex networks. The "PQ-type" adjacency polytope, denoted $\nabla^{\mathrm{PQ}}_G$ and which is the focus of this work, encodes rich combinatorial information about power-flow solutions in sparse power networks that are studied in electric engineering. Of particular importance is the normalized volume of such an adjacency polytope, which provides an upper bound on the number of distinct power-flow solutions. In this article we show that the problem of computing normalized volumes for $\nabla^{\mathrm{PQ}}_G$ can be rephrased as counting $D(G)$-draconian sequences where $D(G)$ is a certain bipartite graph associated to the network. We prove recurrences for all networks with connectivity at most $1$ and, for $2$-connected graphs under certain restrictions, we give recurrences for subdividing an edge and taking the join of an edge with a new vertex. Together, these recurrences imply a simple, non-recursive formula for the normalized volume of $\nabla^{\mathrm{PQ}}_G$ when $G$ is part of a large class of outerplanar graphs; we conjecture that the formula holds for all outerplanar graphs. Explicit formulas for several other (non-outerplanar) classes are given. Further, we identify several important classes of graphs $G$ which are planar but not outerplanar that are worth additional study.

math.CO↗

arXiv2021

Lattice and magnetic dynamics in YVO$_{3}$ Mott insulator studied by neutron scattering and first-principles calculations

The Mott insulator YVO$_{3}$ with $T_{N}$ = 118 K is revisited to explore the role of spin, lattice and orbital correlations across the multiple structural and magnetic transitions observed as a function of temperature. Upon cooling, the crystal structure changes from orthorhombic to monoclinic at 200 K, and back to orthorhombic at 77 K, followed by magnetic transitions. From the paramagnetic high temperature phase, C-type ordering is first observed at 118 K, followed by a G-type spin re-orientation transition at 77 K. The dynamics of the transitions were investigated via inelastic neutron scattering and first principles calculations. An overall good agreement between the neutron data and calculated spectra was observed. From the magnon density of states, the magnetic exchange constants were deduced to be $J_{ab}$ = $J_{c}$ = -5.8 meV in the G-type spin phase, and $J_{ab}$ = -3.8 meV, $J_{c}$ = 7.6 meV at 80 K and $J_{ab}$ = -3.0 meV, $J_{c}$ = 6.0 meV at 100 K in the C-type spin phase. Paramagnetic scattering was observed in the spin ordered phases, well below the C-type transition temperature, that continuously increased above the transition. Fluctuations in the temperature dependence of the phonon density of states were observed between 50 and 80 K as well, coinciding with the G-type to C-type transition. These fluctuations are attributed to optical oxygen modes above 40 meV, from first principles calculations. In contrast, little change in the phonon spectra is observed across $T_{N}$.

cond-mat.str-el↗

arXiv2021

GPU-accelerated path tracker for polyhedral homotopy

The polyhedral homotopy method of Huber and Sturmfels is a particularly efficient and robust numerical method for solving system of (Laurent) polynomial equations. A central component in an implementation of this method is an efficient and scalable path tracker. While the implementation issues in a scalable path tracker for computer clusters or multi-core CPUs have been solved thoroughly, designing good GPU-based implementations is still an active research topic. This paper addresses the core issue of efficiently evaluate a multivariate system of Laurent polynomials together with all its partial derivatives. We propose a simple approach that maps particularly well onto the parallel computing architectures of modern GPUs. As a by-product, we also simplify and accelerate the path tracker by consolidating the computation of Euler and Newton directions.

math.AG↗

arXiv2021

Volume of convex polytopes equals mixed volume of simplices

This note provides a simple proof for the equality between the normalized volume of a convex polytope with $m$ vertices and the mixed volume of $m$ simplices and thus shows the seemingly restrictive problem of computing mixed volume of simplices is still at least as hard as computing volumes of convex polytopes.

math.MG↗

arXiv2020

Temporally-decoherent and spatially-coherent vibrations in metal halide perovskite

The long carrier lifetime and defect tolerance in metal halide perovskites (MHPs) are major contributors to the superb performance of MHP optoelectronic devices. Large polarons were reported to be responsible for the long carrier lifetime. Yet microscopic mechanisms of the large polaron formation including the so-called phonon melting, are still under debate. Here, time-of-flight (TOF) inelastic neutron scattering (INS) experiments and first-principles density-functional theory (DFT) calculations were employed to investigate the lattice vibrations (or phonon dynamics) in methylammonium lead iodide ($\rm{MAPbI_3}$), a prototypical example of MHPs. Our findings are that optical phonons lose temporal coherence gradually with increasing temperature which vanishes at the orthorhombic-to-tetragonal structural phase transition. Surprisingly, however, we found that the spatial coherence is still retained throughout the decoherence process. We argue that the temporally decoherent and spatially coherent vibrations contribute to the formation of large polarons in this metal halide perovskite.

cond-mat.mtrl-sci↗

arXiv2020

Graph edge contraction and subdivisions for adjacency polytopes

Adjacency polytopes, a.k.a. symmetric edge polytopes, associated with undirected graphs have been defined and studied in several seemingly independent areas including number theory, discrete geometry, and dynamical systems. In particular, the authors are motivated by the tropical intersections problem derived from the Kuramoto equations. Regular subdivisions of adjacency polytopes are instrumental in solving these problems. This paper explores connections between the regular subdivisions of an adjacency polytope and the contraction of the underlying graph along an edge. We construct a special regular subdivision whose cells are in one-to-one correspondence with facets of an adjacency polytope associated with an edge-contraction of the original graph. Moreover, this subdivision induces a decomposition of the original graph into ``cell subgraphs''. We explore the combinatorial, graph-theoretic, and matroidal aspects of this connection.

math.CO↗