AI 中文总结
本研究对一维横场伊辛模型开展完整数值研究，采用精确对角化与DMRG方法，解决收敛伪影后提取相变中心电荷，验证其与二维伊辛模型的一致性，兼具物理成果与方法学示例价值。
AI 中文摘要
我们对一维横场伊辛模型（TFIM）开展了自包含的数值研究，追踪其基态纠缠结构，覆盖从小系统尺寸（L=8、14、20）的精确对角化，到最大L=100的密度矩阵重整化群（DMRG）计算。所有7种系统尺寸均采用单一、一致的方法——相同的场网格、相同的收敛判据（每个键维度chi=100和chi=200的独立运行），并明确展示了精确对角化与DMRG必须完全一致而非仅近似一致的情形。研究过程中，我们记录并解决了一种键维度收敛伪影，该伪影曾在早期较不系统的数据集中产生虚假不连续性，可作为从业者的警示示例。利用解决后的数据集，我们通过两种互补途径提取相变的中心电荷：链中间熵的领先对数有限尺寸标度，以及同时应用于所有系统尺寸所有键的完整Calabrese-Cardy公式，在系统排除短程晶格修正后得到c_eff为0.51-0.52，与精确二维伊辛值c=1/2一致。我们回顾了支撑该一致性的量子-经典（Suzuki-Trotter）对应关系，并讨论Widom-Kadanoff标度假设如何从经典问题过渡到量子问题。本手稿既是一项物理研究成果，也是严谨有限尺寸数值计算的方法学示例。
英文摘要
We present a self-contained numerical study of the one-dimensional transverse-field Ising model (TFIM), tracing its ground-state entanglement structure from exact diagonalization at small system size (L=8,14,20) through density-matrix renormalization group (DMRG) calculations up to L=100. A single, consistent methodology - identical field grid, identical convergence diagnostic (independent runs at bond dimensions chi=100 and chi=200 at every point) - is used across all seven system sizes, and we show explicitly where exact diagonalization and DMRG must agree exactly rather than merely approximately. Along the way we document and resolve a bond-dimension convergence artifact that produced a spurious discontinuity in an earlier, less systematic dataset, as a worked cautionary example for practitioners. Using the resolved dataset we extract the central charge of the transition via two complementary routes - the leading logarithmic finite-size scaling of the mid-chain entropy, and the full Calabrese-Cardy formula applied to every bond of every system size simultaneously - obtaining c_eff to 0.51-0.52 as short-distance lattice corrections are systematically excluded, consistent with the exact two-dimensional Ising value c=1/2. We review the quantum-classical (Suzuki-Trotter) correspondence that underlies this agreement and discuss how the Widom-Kadanoff scaling hypothesis transplants from the classical to the quantum problem. The manuscript is intended as both a physics result and a worked methodological example of careful finite-size numerics.
Comments9 pages, 5 figures
