约束系统中可激发零模的高效搜索
Efficient search for excitable zero-modes in constrained systems
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中文总结 AI 辅助
本研究提出基于局域无约束哈密顿量本征分解的高效方案，在修饰里德伯链模型中找到可激发零模等的解析表达式，相关流形张成随系统指数增长，还能推导非零动量零模及特定能量的精确伤疤。
中文摘要 AI 辅助
动力学约束系统（如代表阻塞区域里里德伯原子阵列的系统）因能谱中存在非本征态而受到大量关注，这些非本征态表现为量子多体伤疤以及包含具有不同纠缠标度的可解析本征态的异常大的零模（ZM）子空间。其中一些是可激发零模（EZM），即开放边界条件下可被提升至非零能量的零模。本研究提出一种基于局域无约束哈密顿量本征分解的高效方案，用于寻找约束系统中平移不变EZM的解析表达式。在修饰里德伯链模型中，该方案直接生成完全处于周期边界条件零能量本征空间的连续矩阵乘积态流形，其张成随系统指数增长，且系统尺寸为奇数时覆盖整个零动量零能量本征空间。此外，该流形与局域本征基相关的物理结构还可用于推导非零动量ZM的解析表达式，以及E=±√3处多项式数量的精确伤疤。
英文摘要
Kinetically constrained systems, such as those representing Rydberg atom arrays in the blockade regime, have gathered considerable attention due to the presence of atypical eigenstates in their spectrum. The latter manifests itself through the presence of quantum many-body scars as well as unusually large zero-mode (ZM) subspaces which contain analytically tractable eigenstates with various entanglement scalings. In particular, some of the latter are excitable zero-modes (EZMs), meaning that they can be promoted to a non-zero energy for open boundary conditions. In this work, I present an efficient protocol for finding analytical expressions for translation-invariant EZMs in constrained systems, based on the eigendecomposition of the local unconstrained Hamiltonian. I demonstrate the power of this method on a decorated Rydberg chain. In that model, my protocol directly produces a continuous matrix-product-state manifold located entirely in the zero-energy eigenspace for periodic boundary conditions. The span of that manifold grows exponentially with the system, and for odd system sizes it covers the entire zero-momentum eigenspace with zero energy. I then show how the physical structure of the manifold, which is tied to the local eigenbasis, also allows one to derive analytical expressions for ZMs at non-zero momentum and for a polynomial number of exact scars at $E=\pm\sqrt{3}$.
发表机构
- Institute of Science and Technology Austria (ISTA)（奥地利科学与技术研究所）
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