arXiv subjects

Jiyu Fan

Publications and source records attributed to Jiyu Fan.

6 recordsLinked to original sources

arXiv2026

Modeling Bond-Dependent Kitaev-like interaction in 2D Edge-Sharing Tetrahedral Magnets: FeX (X=Te, Se)

Bond-dependent magnetic interactions, exemplified by the Kitaev model, are known to arise from the interplay between spin-orbit coupling (SOC) and specific coordination geometries, but have so far been almost exclusively identified in edge-sharing octahedral systems. Whether such interactions persist in edge-sharing tetrahedral environments, characteristic of the parent compounds of iron-based superconductors, remains an open question. Here, we construct a Kitaev-like model for monolayer FeTe and FeSe and demonstrate the presence of a previously unrecognized bond-dependent Ising-type interaction, induced jointly by chalcogen-mediated SOC and the tetrahedral crystal-field geometry. A microscopic spin model for these bond-dependent interactions is derived via strong-coupling perturbation theory, and the strengths of the individual exchange terms are extracted by partitioning the magnetic anisotropy energy calculated using density functional theory across various collinear magnetic orders. We reveal that the Kitaev-like interaction dominates the magnetic anisotropy in FeTe, whereas in FeSe, it strongly competes with a single-ion anisotropy of opposite sign. The resulting noncollinear local anisotropy axes generate intrinsic single-site spin frustration, providing a microscopic mechanism for magnetic disorder that transcends isotropic exchange models. Our results establish edge-sharing tetrahedral magnets as a new platform for bond-dependent interactions and extend the scope of Kitaev physics beyond octahedral coordination.

physics.comp-ph↗

arXiv2026

Szeg\"o limit theorem and Heisenberg Laplacian

The aim of this paper is to obtain a version of the classical Szeg\"o limit theorem, where instead of the operator of second derivative on a circle we consider the Heisenberg-H\"ormander Laplacian in $L^2(\Bbb R^3)$. Besides, we derive a sharp inequality for convex functions that we call Szeg\"o-type inequality.

math.SP↗

arXiv2026

Time dependent Schr\"odinger equation for harmonic oscillator in the Aharonov-Bohm magnetic field

We construct an approximation of the kernel of the solution of the time dependent Schr\"odinger equation whose Hamiltonian is a 2D harmonic oscillator in Aharonov-Bohm magnetic field. The main tools used here were established in the paper of A. Laptev and I.M. Sigal, where the authors considered a class of Fourier Integral Operators with global complex phases approximating the fundamental solutions (propagators) for time-dependent Schr\"odinger equations. For the example considered in this paper we are able to find the main term in the approximation of the kernel that equals a version of the Mehler formula.

math.AP↗

arXiv2026

Phase-slip residual-order spin state in FeSe

In unconventional superconductors, the microscopic form of magnetic correlations is crucial for identifying the origin of spin fluctuations and the associated pairing interaction. FeSe superconducts without chemical doping and shows no static long-range magnetic order, yet inelastic neutron scattering reveals a strong stripe response, finite linewidths, and reproducible Neel-side spectral weight. Here we propose a phase-slip residual-order spin state (ROSS). Stripe, Neel, pair-checkerboard, and staggered trimer antiferromagnetic states can be unified as symmetric phase-slip derivatives of a stripe background, while more general asymmetric phase slips form lower-energy configurations and reconstruct the spin structure factor S(q) within a finite coherence length. The ROSS therefore reconciles the absence of static magnetic order with strong spin excitations, provides a microscopic picture for the origin of spin fluctuations in FeSe, and establishes a magnetic basis for understanding pairing in unconventional superconducting systems with similar magnetic fingerprints.

cond-mat.supr-con↗

arXiv2025

Generalized Persistent Laplacians and their Spectral Properties

Laplacian operators are classical objects that are fundamental in both pure and applied mathematics and are becoming increasingly prominent in modern computational and data science fields such as applied and computational topology and application areas such as machine learning and network science. In this paper, we introduce a unifying operator-theoretic framework of generalized Laplacians as invariants that encompasses and extends all existing constructions, from discrete combinatorial settings to de Rham complexes of smooth manifolds. Within this framework, we introduce and study a generalized notion of persistent Laplacians. While the classical persistent Laplacian fails to satisfy the desirable properties of monotonicity and stability -- both crucial for robustness and interpretability -- our framework allows us to isolate and analyze these properties systematically. We demonstrate that their component maps, the up- and down-persistent Laplacians, satisfy these properties individually. Moreover, we prove that the spectra of these separate components fully determine the spectra of the full Laplacians, making them not only preferable but sufficient for analysis. We study these questions comprehensively, in both the finite and infinite dimensional settings. Our work expands and strengthens the theoretical foundation of generalized Laplacian-based methods in pure, applied, and computational mathematics.

math.AT↗

arXiv2023

Evidence of Kitaev interaction in the monolayer 1T-CrTe$_2$

The two-dimensional 1T-CrTe$_2$ has been an attractive room-temperature van der Waals magnet which has a potential application in spintronic devices. Although it was recognized as a ferromagnetism in the past, the monolayer 1T-CrTe$_2$ was recently found to exhibit zigzag antiferromagnetism with the easy axis oriented at $70^\circ$ to the perpendicular direction of the plane. Therefore, the origin of the intricate anisotropic magnetic behavior therein is well worthy of thorough exploration. Here, by applying density functional theory with spin spiral method, we demonstrate that the Kitaev interaction, together with the single-ion anisotropy and other off-diagonal exchanges, is amenable to explain the magnetic orientation in the metallic 1T-CrTe$_2$. Moreover, the Ruderman-Kittle-Kasuya-Yosida interaction can also be extracted from the dispersion calculations, which explains the metallic behavior of 1T-CrTe$_2$. Our results demonstrate that 1T-CrTe$_2$ is potentially a rare metallic Kitaev material.

cond-mat.str-el↗