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Yang Ge

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Artificial Intelligence cond-mat.quant-gas cond-mat.str-el Cryptography and Security math.CO quant-ph

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preprint2026arXiv

XekRung Technical Report

We present XekRung, a frontier large language model for cybersecurity, designed to provide comprehensive security capabilities. To achieve this, we develop diverse data synthesis pipelines tailored to the cybersecurity domain, enabling the scalable construction of high-quality training data and providing a strong foundation for cybersecurity knowledge and understanding. Building on this foundation, we establish a complete training pipeline spanning continued pre-training (CPT), supervised fine-tuning (SFT), and reinforcement learning (RL) to further extend the model's capabilities. We further introduce a multi-dimensional evaluation system to guide the iterative improvement of both domain-specific and general-purpose abilities. Extensive experiments demonstrate that XekRung achieves state-of-the-art performance on cybersecurity-specific benchmarks among models of the same scale, while maintaining strong performance on general benchmarks.

preprint2022arXiv

Emergent Spinon Dispersion and Symmetry Breaking in Two-Channel Kondo Lattices

Two-channel Kondo lattice serves as a model for a growing family of heavy-fermion compounds. We employ the dynamical large-N technique and go beyond the independent bath approximation to study this model both numerically and analytically using renormalization group ideas. We show that the Kondo effect induces dynamic magnetic correlations that lead to an emergent spinon dispersion. Furthermore, we develop a quantitative framework that interpolates between infinite dimension where the channel-symmetry broken results of mean-field theory are confirmed, and one-dimension where the channel symmetry is restored and a critical fractionalized mode is found.

preprint2021arXiv

Universal Landau-Zener regimes in dynamical topological phase transitions

In finite systems driven unitarily across topological phase transitions, the Chern number and the Bott index have been found to exhibit different behaviors depending on the boundary conditions and on the commensurability of the lattice. For periodic boundary conditions, the Chern number does not change for finite commensurate lattices (or in the thermodynamic limit). On the other hand, the Chern number can change for incommensurate lattices with periodic boundary conditions and the Bott index can change for lattices with open boundary conditions. Here we show that the scalings of the fields at which those two indices change exhibit Landau-Zener and near-adiabatic regimes depending on the speed at which the strength of the drive is ramped up and on the system size. Those regimes are preceded by a regime in which the topological indices do not change. The latter is the only regime that, for nonvanishing ramp speeds, survives in the thermodynamic limit. We then show that the dc Hall response can be used to detect topological phase transitions independently of the behavior of the topological indices.

preprint2010arXiv

Perfect state transfer, graph products and equitable partitions

We describe new constructions of graphs which exhibit perfect state transfer on continuous-time quantum walks. Our constructions are based on variants of the double cones [BCMS09,ANOPRT10,ANOPRT09] and the Cartesian graph products (which includes the n-cube) [CDDEKL05]. Some of our results include: (1) If $G$ is a graph with perfect state transfer at time $t_{G}$, where $t_{G}\Spec(G) \subseteq \ZZπ$, and $H$ is a circulant with odd eigenvalues, their weak product $G \times H$ has perfect state transfer. Also, if $H$ is a regular graph with perfect state transfer at time $t_{H}$ and $G$ is a graph where $t_{H}|V_{H}|\Spec(G) \subseteq 2\ZZπ$, their lexicographic product $G[H]$ has perfect state transfer. (2) The double cone $\overline{K}_{2} + G$ on any connected graph $G$, has perfect state transfer if the weights of the cone edges are proportional to the Perron eigenvector of $G$. This generalizes results for double cone on regular graphs studied in [BCMS09,ANOPRT10,ANOPRT09]. (3) For an infinite family $\GG$ of regular graphs, there is a circulant connection so the graph $K_{1}+\GG\circ\GG+K_{1}$ has perfect state transfer. In contrast, no perfect state transfer exists if a complete bipartite connection is used (even in the presence of weights) [ANOPRT09]. We also describe a generalization of the path collapsing argument [CCDFGS03,CDDEKL05], which reduces questions about perfect state transfer to simpler (weighted) multigraphs, for graphs with equitable distance partitions.