发表机构
Dartmouth College; SUNY Polytechnic Institute（达特茅斯学院; 纽约州立大学理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
通过二次玻色哈密顿量，揭示动力学稳定性边界与长程关联的关系，利用玻色SSH模型证明拓扑相变与动力学稳定性无关。
AI 中文摘要
对由二次玻色哈密顿量（QBHs）描述的系统中临界性的新理解将长程关联的出现与参数空间中动力学稳定性（而非热力学稳定性）的边界联系起来。这种分离之所以发生，是因为海森堡运动方程的解由一个辅助的赝厄米动力学系统决定。动力学稳定区域的边界点可以是异常点（通常与长程关联相关）或Krein碰撞（其中关联可以是长程或短程的）。我们通过具体例子和一般性论证，研究了这种可能性图景与能带拓扑和边界物理的相互作用。这些例子来自一个双参数、热力学不稳定的QBHs族，该族通过破坏粒子数守恒同时保留手征赝对称性，从玻色Su-Schrieffer-Heeger模型获得。动力学稳定区域被划分为不同区域，每个区域由Berry相的辛模拟整数标记。拓扑相变是一条Krein碰撞线，与零能带隙闭合重合，并导致拓扑强制边界零模的局域长度在消失前发散。在不稳定区域，我们证明尽管粒子数对称性被破坏，模型的手征赝对称性在其关联动力学矩阵上诱导了足够的结构，以支持拓扑分类和体-边界对应，且独立于动力学稳定性。这强烈表明，从基本指标理论中提取的玻色拓扑物理对动力学稳定性以及非相互作用临界性不敏感。
英文摘要
A new understanding of criticality in systems described by quadratic bosonic Hamiltonians (QBHs) ties the emergence of long-range correlations to boundaries of dynamical, not thermodynamical, stability in parameter space. This separation occurs because the solution of the Heisenberg equations of motion is determined by an auxiliary pseudo-Hermitian dynamical system. The boundary points of a region of dynamical stability can be either exceptional points, generically associated with long-range correlations, or Krein collisions, where correlations can be either long- or short-range. We investigate the interplay of this landscape of possibilities with band topology and boundary physics, by relying on both specific examples and general arguments. The examples stem from a two-parameter, thermodynamically unstable family of QBHs obtained from the bosonic Su-Schrieffer-Heeger model by breaking particle conservation while preserving a chiral pseudo-symmetry. As a function of an interpolation parameter, distinct regions emerge within a fixed dynamical-stability phase, which prove to be topologically trivial and nontrivial, respectively. The topological phase transition is a line of Krein collisions, which coincides with the closing of a band gap at zero and causes the localization length of the topologically mandated boundary zero modes to diverge before disappearing. We show that the chiral pseudo-symmetry induces, despite the broken particle-number symmetry, enough structure on its associated dynamical matrices to support a topological classification and a bulk-boundary correspondence, independently of dynamical stability. This strongly suggests that, for non-interacting bosons, topological physics extracted from basic index theory is insensitive to dynamical stability and, a posteriori, criticality.
Comments13 pages, 5 figures
Journal refJ. Appl. Phys. 140, 124401 (2026)
