arXiv subjects

Zezhi Wang

Publications and source records attributed to Zezhi Wang.

5 recordsLinked to original sources

arXiv2026

Sparsity-Constraint Optimization via Splicing Iteration

Sparsity-constrained optimization underlies many problems in signal processing, statistics, and machine learning. State-of-the-art hard-thresholding (HT) algorithms rely on an appropriately selected continuous step-size parameter to ensure convergence. In this paper, we propose a naturally convergent iterative algorithm, SCOPE (Sparsity-Constrained Optimization via sPlicing itEration). The algorithm is capable of optimizing nonlinear differentiable objective functions that are strongly convex and smooth on low-dimensional subspaces. SCOPE replaces the gradient step with a splicing operation guided directly by the objective value, thereby eliminating the need to tune any continuous hyperparameter. Theoretically, it achieves a linear convergence rate and recovers the true support set when the sparsity level is correctly specified. We also establish parallel theoretical results without relying on restricted-isometry-property-type conditions. We apply SCOPE's versatility and power to solve sparse quadratic optimization, learn sparse classifiers, and recover sparse Markov networks for binary variables. With our C++ implementation of SCOPE, numerical experiments on these tasks show that it achieves superior support recovery performance, confirming both its algorithmic efficiency and theoretical guarantees.

stat.ML↗

arXiv2026

Observation of sequential quantum oscillations induced by mini-Landau bands in a three-dimensional Dirac semiconductor

Quantum oscillations, the oscillatory behavior of electrical and thermodynamic properties, are typically observed in metals and vanish in the quantum limit under strong magnetic fields1. Phenomena such as the fractional quantum Hall effect2, the Hofstadter butterfly3,4, and recent observations of quantum oscillations in exotic insulators are notable exceptions5-12. The narrow-gap Dirac semiconductor ZrTe5, a less exotic material without strong correlations or artificially engineered superlattices, nevertheless exhibits resistance oscillations in the quantum limit13 but can be interpreted within a simple Zeeman-effect-based picture14,15, which remains conventional quantum oscillations without exotic properties. Here, we report the observation of unexpected mini-oscillations superimposed on Zeeman-effect-induced main oscillations in the quantum limit. The subtracted mini-oscillations are periodic in 1/B with the highest frequency equal to 2.1% of the first Brillouin zone and have extremely heavy effective mass ~ 2me, which is unexpected in ZrTe5 given its ultralow carrier density. Additionally, the mini-oscillations exhibit sequential features that are synchronized with the main oscillations, suggesting an internal structure of the Landau bands. However, they appear incompatible with the Hofstadter butterfly due to the highly anisotropic/three-dimensional crystal structure. These sequential mini-oscillations correlate with the commensurability resonance effect with subunity fractions observed in angular magnetoresistance, relating to the formation of mini-Landau bands. Our results present solid experimental evidence of exotic quantum oscillations in the quantum limit beyond currently available mechanisms, and establish ZrTe5, a prototypical Dirac semiconductor, as a simple platform parallel to correlated insulators for exploring exotic oscillations.

cond-mat.mes-hall↗

arXiv2025

Defects Engineering of ZrTe5 for Stabilizing Ideal Topological States

ZrTe5 is a highly tunable, high-mobility topological material that hosts a rich variety of quantum phenomena, making it a promising platform for next-generation quantum technologies. Despite intensive research efforts, experimental studies have reported inconsistent and sometimes conflicting results for its electronic and topological states, largely due to variations in sample quality. Here, through systematic frst-principles investigations of all intrinsic point defects, we identify a practical route to achieving stable and ideal topological characteristics in ZrTe5. We show that the competition between two dominant charged defects, donor-like Zr interstitials and acceptor-like Te vacancies, governs the Fermi-level position. Furthermore, variations in defect density determine the topological phases of the samples. We theoretically propose and experimentally confrm that increasing the Te/Zr ratio during crystal growth effectively suppresses intrinsic defects and stabilizes ZrTe5 in a nearly ideal weak topological insulator state. These fndings provide clear guidance for defect control and sample optimization, paving the way toward robust and reproducible realization of topological quantum states in ZrTe5 for future quantum applications.

cond-mat.mtrl-sci↗

arXiv2024

skscope: Fast Sparsity-Constrained Optimization in Python

Applying iterative solvers on sparsity-constrained optimization (SCO) requires tedious mathematical deduction and careful programming/debugging that hinders these solvers' broad impact. In the paper, the library skscope is introduced to overcome such an obstacle. With skscope, users can solve the SCO by just programming the objective function. The convenience of skscope is demonstrated through two examples in the paper, where sparse linear regression and trend filtering are addressed with just four lines of code. More importantly, skscope's efficient implementation allows state-of-the-art solvers to quickly attain the sparse solution regardless of the high dimensionality of parameter space. Numerical experiments reveal the available solvers in skscope can achieve up to 80x speedup on the competing relaxation solutions obtained via the benchmarked convex solver. skscope is published on the Python Package Index (PyPI) and Conda, and its source code is available at: https://github.com/abess-team/skscope.

stat.ML↗

arXiv2024

Rashba-splitting-induced topological flat band detected by anomalous resistance oscillations beyond the quantum limit in ZrTe$_5$

Topological flat band, on which the kinetic energy of topological electrons is quenched, represents a platform for investigating the topological properties of correlated systems. Recent experimental studies on flattened electronic bands have mainly concentrated on 2-dimensional materials created by van der Waals heterostructure-based engineering. Here, we report the observation of a topological flat band formed by polar-distortion-assisted Rashba splitting in a 3-dimensional Dirac material ZrTe$_5$. The polar distortion and resulting Rashba splitting on the band are directly detected by torque magnetometry and the anomalous Hall effect, respectively. The local symmetry breaking further flattens the band, on which we observe resistance oscillations beyond the quantum limit. These oscillations follow the temperature dependence of the Lifshitz-Kosevich formula but are evenly distributed in B instead of 1/B in high magnetic fields. Furthermore, the cyclotron mass anomalously gets enhanced about 10$^2$ times at field ~20 T. These anomalous properties of oscillations originate from a topological flat band with quenched kinetic energy. The topological flat band, realized by polar-distortion-assisted Rashba splitting in the 3-dimensional Dirac system ZrTe$_5$, signifies an intrinsic platform without invoking moiré or order-stacking engineering, and also opens the door for studying topologically correlated phenomena beyond the dimensionality of two.

cond-mat.mes-hall↗