arXiv subjects

Hyeongmuk Lim

Publications and source records attributed to Hyeongmuk Lim.

5 recordsLinked to original sources

arXiv2026

Quaternion-Kahler geometry of time reversal symmetric crystals

Quantum geometry reveals how the shape of Bloch wave functions governs correlated quantum phenomena. Its standard formulation describes isolated complex bands, where Berry curvature is Abelian and ideal geometry is Kahler. However, time reversal symmetric crystals with spin require a different language since Kramers degeneracy pairs Bloch states and turns Berry curvature into a non-Abelian SU(2) field. Here we show that Kramers pair band geometry is quaternionic. A minimal Kramers pair defines a map into quaternion projective space, and its quaternionic quantum geometric tensor unifies the quantum metric with the three SU(2) Berry curvature components. The non-negativity of this tensor imposes local metric-curvature inequalities, whose saturation defines the non-Abelian counterpart of ideal Chern bands. In four dimensions, the ideal limit further yields an algebraic structure related to the four-dimensional quantum Hall effect. Our results promote ideal quantum geometry from the Abelian geometry of Chern bands to the quaternionic, non-Abelian geometry of time reversal symmetric quantum matter.

cond-mat.mes-hall↗

arXiv2026

CoReVAD: A Contextual Reasoning Framework for Training-Free Video Anomaly Detection

Existing Video Anomaly Detection (VAD) methods typically rely on task-specific training, leading to strong domain dependency and high training costs. Moreover, most existing methods output only scalar anomaly scores, providing limited insight into why specific events are considered abnormal. Recent advances in Vision-Language Models (VLMs) have enabled both anomaly detection and human-interpretable reasoning. However, many VLM-based approaches still require additional training steps (e.g., instruction tuning or verbalized learning) or external Large Language Models (LLMs), incurring further training costs and inference overhead. To address these challenges, we propose CoReVAD, a contextual reasoning framework for training-free video anomaly detection that operates with a single frozen VLM. CoReVAD directly generates anomaly scores and temporal descriptions from the VLM. To mitigate noise in generative outputs, we introduce a Local Response Cleaning (LRC) module based on local vision-text alignment. Furthermore, global temporal context and progression are incorporated through softmax-based refinement, Gaussian smoothing, and position weighting. Experiments on UCF-Crime and XD-Violence demonstrate that CoReVAD achieves competitive performance among training-free methods while providing reliable and interpretable explanations. Our official code is available at: https://github.com/Muk-00/CoReVAD

cs.CV↗

arXiv2024

Unconventional topological phase transition of the Hopf insulator

The topological phase transition between two band insulators is mediated by a gapless state whose low-energy band structure normally contains sufficient information for describing the topology change. In this work, we show that there is a class of topological insulators whose topological phase transition cannot be explained by this conventional paradigm. Taking the Hopf insulator as a representative example, we show that the change of the Hopf invariant requires the information of wave functions as well as the gapless band structure simultaneously. More explicitly, the description of the Hopf invariant change requires us to trace not only the trajectory of Weyl points but also the evolution of the preimages for two distinct eigenstates. We show that such an unconventional topological phase transition originates from the fact that the Hopf invariant is well-defined when all the lower dimensional topological invariants are trivial, which in turn allows us to lift the classifying space of occupied state projectors to the corresponding universal 2-covering space of wave functions. Generalizing our theory to inversion-symmetric 10-fold Altland-Zirnbauer symmetry classes, we provide a complete list of symmetry classes, all of which turn out to have delicate band topology related to the Hopf invariant, where similar unconventional topological phase transitions can appear.

cond-mat.mes-hall↗

arXiv2023

Quantum Geometry and Landau Levels of Quadratic Band Crossings

We study the relation between the quantum geometry of wave functions and the Landau level (LL) spectrum of two-band Hamiltonians with a quadratic band crossing point (QBCP) in two-dimensions. By investigating the influence of interband coupling parameters on the wave function geometry of general QBCPs, we demonstrate that the interband coupling parameters can be entirely determined by the projected elliptic image of the wave functions on the Bloch sphere, which can be characterized by three parameters, i.e., the major $d_1$ and minor $d_2$ diameters of the ellipse, and one angular parameter $ϕ$ describing the orientation of the ellipse. These parameters govern the geometric properties of the system such as the Berry phase and modified LL spectra. Explicitly, by comparing the LL spectra of two quadratic band models with and without interband couplings, we show that the product of $d_1$ and $d_2$ determines the constant shift in LL energy while their ratio governs the initial LL energies near a QBCP. Also, by examining the influence of the rotation and time-reversal symmetries on the wave function geometry, we construct a minimal continuum model which exhibits various wave function geometries. We calculate the LL spectra of this model and discuss how interband couplings give LL structure for dispersive bands as well as nearly flat bands.

cond-mat.mes-hall↗

arXiv2023

Real Hopf Insulator

Establishing the fundamental relation between the homotopy invariants and the band topology of Hamiltonians has played a critical role in the recent development of topological phase research. In this work, we establish the homotopy invariant and the related band topology of three-dimensional (3D) real-valued Hamiltonians with two occupied and two unoccupied bands. Such a real Hamiltonian generally appears in $\mathcal{PT}$ symmetric spinless fermion systems where $\mathcal{P}$ and $\mathcal{T}$ indicate the inversion and time-reversal symmetries, respectively. We show that the 3D band topology of the system is characterized by two independent Hopf invariants when the lower-dimensional band topology is trivial. Thus, the corresponding 3D band insulator with nonzero Hopf invariants can be called a real Hopf insulator (RHI). In sharp contrast to all the other topological insulators discovered up to now, the topological invariants of RHI can be defined only when the fixed number of both the occupied and unoccupied states are simultaneously considered. Thus, the RHI belongs to the category of delicate topological insulators proposed recently. We show that finite-size systems with slab geometry support surface states with nonzero Chern numbers in a $\mathcal{PT}$-symmetric manner independent of the Fermi level position, and establish the bulk-boundary correspondence. We also discuss the bulk-boundary correspondence of rotation symmetric RHIs using the returning Thouless pump.

cond-mat.mes-hall↗