arXiv subjects

Jinling Zhou

Publications and source records attributed to Jinling Zhou.

6 recordsLinked to original sources

arXiv2026

Field-induced asymmetric band flattening and ideal quantum geometry in rhombohedral graphene

Rhombohedral graphene exhibits an exceptionally diverse array of correlated phases that depend sensitively on the displacement field. Compiling reported phases into a unified phase diagram reveals a pronounced field-dependent electron-hole asymmetry: correlated states on the hole-doped side emerge at small displacement fields, whereas the fractional quantum anomalous Hall effect (FQAHE) is observed exclusively on the electron-doped side under large displacement fields. This stark asymmetry highlights the need to understand how flat bands evolve with displacement fields. Here, we directly visualize the field-induced electron-hole asymmetric band flattening in rhombohedral pentalayer graphene (R5G) using nanospot angle-resolved photoemission spectroscopy with electrostatic gating. Beyond gap opening and spectral weight redistribution indicative of layer polarization, the gating field drives a strongly asymmetric modification of the flat bands: the flat valence band (FVB) evolves into an M-shaped dispersion at high field, whereas the flat conduction band (FCB) progressively flattens with increasing field. Comparison with calculations identifies critical parameters governing the band curvature of R5G, from which the resulting finite Berry curvature and near-ideal quantum geometry support the emergence of topological phases under electron doping at large fields. These results establish a direct link between the asymmetric phase diagram, band structure evolution, and quantum geometry, providing a microscopic framework for understanding correlated and topological phases in rhombohedral graphene.

cond-mat.mes-hall↗

arXiv2026

Sparse Copositive Polynomial Optimization

This paper studies the copositive optimization problem whose objective is a sparse polynomial, with linear constraints over the nonnegative orthant. We propose sparse Moment-SOS relaxations to solve it. Necessary and sufficient conditions are shown for these relaxations to be tight. In particular, we prove they are tight under the cop-SOS convexity assumption. Compared to the traditional dense ones, the sparse Moment-SOS relaxations are more computationally efficient. Numerical experiments are given to show the efficiency.

math.OC↗

arXiv2025

A Tight SDP Relaxation for the Cubic-Quartic Regularization Problem

This paper studies how to compute global minimizers of the cubic-quartic regularization (CQR) problem \[ \min_{s \in \mathbb{R}^n} \quad f_0+g^Ts+\frac{1}{2}s^THs+\frac{\beta}{6}\| s \|^3+ \frac{\sigma}{4} \| s\|^4, \] where $f_0$ is a constant, $g$ is an $n$-dimensional vector, $H$ is an $n$-by-$n$ symmetric matrix, and $\| s \|$ denotes the Euclidean norm of $s$. The parameter $\sigma$ is nonnegative while $\beta$ can have any sign. The CQR problem arises as a critical subproblem for getting efficient regularization methods for solving unconstrained nonlinear optimization. Its properties are recently well studied by Cartis and Zhu {\it [cubic-quartic regularization models for solving polynomial subproblems in third-order tensor methods, Math. Program, 2025]}. We propose a structured semidefinite programming (SDP) relaxation method for solving the CQR problem globally. The SDP relaxation has only three symmetric positive semidefinite matrix variables of sizes $(n+1)$-by-$(n+1)$, $3$-by-$3$ and $2$-by-$2$ respectively. We show that our SDP relaxation is tight if and only if $\| s^* \| ( \beta + 3 \sigma \| s^* \|) \ge 0$ holds for a global minimizer $s^*$. When $s^* \ne 0$, this aligns with the sufficient global optimality condition $\beta + 3 \sigma \| s^* \| \ge 0$ given by Cartis and Zhu. In particular, if either $\beta \ge 0$ or $H$ has a nonpositive eigenvalue, then the SDP relaxation is shown to be tight. Second, we show that all nonzero global minimizers have the same Euclidean norm for the tight case. Third, we give an algorithm to detect tightness and to obtain the set of all global minimizers. Numerical experiments demonstrate that our SDP relaxation method is both effective and computationally efficient. This paper gives a polynomial time algorithm for solving the CQR problem globally, under the sufficient global optimality condition.

math.OC↗

arXiv2025

Ultrahigh room-temperature hole conductivity in a perovskite cuprate with vanishing electron-correlation

Electron-correlated two-dimensional (2D) cuprates have been extensively studied since the discovery of high-Tc superconductivity, in contrast, the three-dimensional (3D) counterpart perovskite cuprates remain largely unexplored due to their chemical instability and synthesis challenges. Herein, we develop an efficient two-step approach that combines symmetry-selective growth and topotactic oxidization to synthesize high-quality perovskite LaCuO3 films, and furthermore reveal its exotic electronic states. The compressively strained LaCuO3 films exhibit an unexpected ultrahigh p-type conductivity of ~1.5*10^5 S/cm with a hole mobility of ~30 cm2 V-1 s-1 at room-temperature. X-ray absorption spectra and first-principles calculations unveil a ligand-hole state of p-d hybridization with degenerate eg orbitals and light effective mass, indicating nearly-vanishing electron-correlation. These features contrast sharply with 2D cuprates and offer physical insights into the design of high-performance electronic devices.

cond-mat.str-el↗

arXiv2025

Robust Completion for Rank-1 Tensors with Noises

This paper studies the rank-1 tensor completion problem for cubic tensors when there are noises for observed tensor entries. First, we propose a robust biquadratic optimization model for obtaining rank-1 completing tensors. When the observed tensor is sufficiently close to be rank-1, we show that this biquadratic optimization produces an accurate rank-$1$ tensor completion. Second, we give an efficient convex relaxation for solving the biquadratic optimization. When the optimizer matrix is separable, we show how to get optimizers for the biquadratic optimization and how to compute the rank-$1$ completing tensor. When that matrix is not separable, we apply its spectral decomposition to obtain an approximate rank-1 completing tensor. The software SDPNAL+ is applied to solve the resulting large size semidefinite programs. Numerical experiments are given to explore the efficiency of this biquadratic optimization model and the proposed convex relaxation.

math.OC↗

arXiv2024

The Rank-1 Completion Problem for Cubic Tensors

This paper studies the rank-$1$ tensor completion problem for cubic tensors. First of all, we show that this problem is equivalent to a special rank-$1$ matrix recovery problem. When the tensor is strongly rank-$1$ completable, we show that the problem is equivalent to a rank-$1$ matrix completion problem and it can be solved by an iterative formula. For other cases, we propose both nuclear norm relaxation and moment relaxation methods for solving the resulting rank-$1$ matrix recovery problem. The nuclear norm relaxation sometimes returns a rank-$1$ tensor completion, while sometimes it does not. When it fails, we apply the moment hierarchy of semidefinite programming relaxations to solve the rank-$1$ matrix recovery problem. The moment hierarchy can always get a rank-$1$ tensor completion, or detect its nonexistence. Numerical experiments are shown to demonstrate the efficiency of these proposed methods.

math.OC↗