一维纳米结构中的量子相变：DFT与DMRG方法的比较
Quantum phase transitions in one-dimensional nanostructures: a comparison between DFT and DMRG methodologies
AI总结：
本研究比较了DFT和DMRG方法在费米子一维Hubbard模型描述的均匀、超晶格和受限链中预测量子相变特性的表现，揭示了两者在不同系统结构和相态下的精度差异及适用性。
摘要：
在量子化学领域，准确预测纳米结构的电子结构和性质仍然是一个艰巨的挑战。密度泛函理论（DFT）和密度矩阵重正化群（DMRG）已成为解决各种分子系统中电子关联效应的两种强大计算方法。我们比较了由费米子一维Hubbard模型描述的均匀链、超晶格链和简谐受限链在金属、绝缘体以及金属-绝缘体相变处的基态能量（$e_0$）、密度分布（$n$）和平均纠缠熵（$\ar S$）。对于均匀系统，偏差之间存在明确的层级关系，即$D\%(\ar S)<D\%(e_0)< \ar D\%(n)$，且所有偏差均随链尺寸的增大而减小；对于超晶格和简谐受限链，偏差之间的关系则不那么简单，且强烈依赖于所考虑的超晶格结构和受限强度。对于超晶格，通常增加晶胞中的杂质数量会降低DFT计算的精度。对于受限链，DFT在金属相中表现更好，而最大偏差出现在Mott绝缘体和能带绝缘体相中。本研究对这些方法进行了全面的比较分析，阐明了它们各自的优势、局限性和应用。
英文摘要：
In the realm of quantum chemistry, the accurate prediction of electronic structure and properties of nanostructures remains a formidable challenge. Density Functional Theory (DFT) and Density Matrix Renormalization Group (DMRG) have emerged as two powerful computational methods for addressing electronic correlation effects in diverse molecular systems. We compare ground-state energies ($e_0$), density profiles ($n$) and average entanglement entropies ($\bar S$) in metals, insulators and at the transition from metal to insulator, in homogeneous, superlattices and harmonically confined chains described by the fermionic one-dimensional Hubbard model. While for the homogeneous systems there is a clear hierarchy between the deviations, $D\%(\bar S)<D\%(e_0)< \bar D\%(n)$, and all the deviations decrease with the chain size; for superlattices and harmonical confinement the relation among the deviations is less trivial and strongly dependent on the superlattice structure and the confinement strength considered. For the superlattices, in general increasing the number of impurities in the unit cell represents less precision on the DFT calculations. For the confined chains, DFT performs better for metallic phases, while the highest deviations appear for the Mott and band-insulator phases. This work provides a comprehensive comparative analysis of these methodologies, shedding light on their respective strengths, limitations, and applications.
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