四分之一磁通的Harper-Hofstadter模型的精确解析谱、本征态及量子几何
Exact quantum geometry from sublattice symmetry: Closed-form solution of the quarter-flux Harper-Hofstadter model
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中文总结 AI 辅助
本文针对实验实现的四分之一磁通Harper-Hofstadter四带模型，利用子晶格对称性解析推导其谱、本征态及量子几何张量，证实其最低能带为近理想陈带，为相关拓扑研究提供关键理论结果。
中文摘要 AI 辅助
量子几何已成为原子与凝聚态物理学中的指导性原理，塑造了布洛赫带的拓扑响应及其所承载关联相的稳定性。然而，超出两带模型范畴后，谱与量子几何的闭式表达式极为罕见。本文针对一种近期已通过超冷原子、光子及超导电路实验实现的典型四带模型——四分之一磁通下的Harper-Hofstadter模型（描述均匀磁场作用下二维正方晶格上的带电粒子），给出了这类闭式表达式。我们首先证明该模型具有子晶格对称性，这使其布洛赫哈密顿量呈现反分块对角形式，从而可解析推导谱与本征态。在此基础上，我们还得到了该模型所有能带的完整量子几何张量（QGT）的闭式表达式，包括贝里曲率与量子度量。为此，我们先推导了子晶格对称系统的QGT的通用表达式，其由各子晶格区域的贡献构成。最后，我们解析计算了分数量子霍尔绝缘体稳定性判据，并量化得出四分之一磁通Harper-Hofstadter模型的最低能带为近理想陈带。
英文摘要
Quantum geometry has emerged as a guiding principle across atomic and condensed-matter physics, shaping the topological responses of Bloch bands and the stability of the correlated phases they host. Sublattice symmetry, though common among bipartite lattice models, has not yet been exploited to obtain closed-form quantum geometry in multiband systems. For this purpose, we derive a general expression for the QGT of sublattice-symmetric systems in terms of contributions from the individual sublattice sectors, and show that this symmetry renders the Bloch Hamiltonian of a paradigmatic four-band model, the quarter-flux Harper-Hofstadter model, anti-block-diagonal, analytically yielding the spectrum, eigenstates, and full quantum geometric tensor (QGT), including the Berry curvature and quantum metric, for all four bands. The model, describing charged particles on a two-dimensional square lattice subjected to a uniform magnetic field, has recently been realized experimentally with ultracold atoms, photons, and superconducting circuits. Finally, we evaluate fractional-Chern-insulator stability criteria analytically and quantify the lowest band of the quarter-flux Harper-Hofstadter model to be a nearly ideal Chern band. Our approach opens a route for studying also the quantum geometry of other sublattice-symmetric multiband systems.
发表机构
- Technische Universität Berlin（柏林工业大学）
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