隐藏自由费米子模型的精确解
Exact solutions of hidden free fermion models
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所凝聚态物理北京实验室）
- MTA-ELTE “Momentum” Integrable Quantum Dynamics Research Group, ELTE Eötvös Loránd University（布达佩斯罗兰大学MTA-ELTE“动量”可积量子动力学研究组）
- School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文通过扭曲多态Perk–Schultz R矩阵的Lax算子实现，统一解释了隐藏自由费米子模型的代数来源，并精确求解了非齐次与齐次FFD链，揭示了耦合依赖的谱组织和涌现的有限尺寸能隙。
AI中文摘要：
隐藏自由费米子（HFF）哈密顿量尽管缺乏显式的二次型表示，却展现出自由费米子谱，但其代数来源和周期边界行为仍是悬而未决的问题。在此，我们证明一大类HFF模型源于扭曲多态Perk–Schultz R矩阵的不同Lax算子实现。其反射退化生成一个封闭的有限层级相互对易的转移矩阵，这些矩阵的函数关系决定了完整的多体谱。作为一个决定性示例，我们求解了非齐次“伪装自由费米子”（FFD）链，该链根据其耦合表现出HFF、嵌套HFF或相互作用谱。具有单环绕和周期边界条件的齐次FFD链展现出涌现的三次方有限尺寸能隙，同时保持精确的z=3/2体行为。该构造可推广到更高态和面型实现，为相互作用量子系统中耦合依赖的谱组织和多尺度行为提供了一个统一的代数框架。
英文摘要：
Hidden-free-fermion (HFF) Hamiltonians exhibit free-fermion spectra despite lacking an explicit quadratic representation, yet their algebraic provenance and periodic-boundary behavior remain open questions. Here we establish that a broad class of HFF models arises from distinct Lax operator realizations of a twisted multistate Perk--Schultz \(R\) matrix. Its reflected degeneration generates a closed finite hierarchy of mutually commuting transfer matrices, whose functional relations determine the complete many-body spectrum. As a decisive example, we solve the inhomogeneous free-fermions-in-disguise (FFD) chain, which exhibits HFF, nested HFF, or interacting spectra, depending on its coupling. The homogeneous FFD chain with both one-wrap and periodic boundary conditions exhibits an emergent cubic finite-size gap while retaining the exact \(z=3/2\) bulk behavior. The construction extends to higher-state and face-type realizations, providing a common algebraic framework for coupling-dependent spectral organization and multiscale behavior in interacting quantum systems.
