发表机构
Center for Quantum Technology Research, and Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements (MOE), School of Physics, Beijing Institute of Technology; Center for the Cross-disciplinary Research of Space Science and Quantum-technologies (CROSS-Q), College of Physics, Nanjing University of Aeronautics and Astronautics（北京理工大学物理学院量子技术研究中心及先进光电子量子架构与测量教育部重点实验室; 南京航空航天大学物理学院空间科学与量子技术交叉研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对开放边界玻色Kitaev链，本文采用非对称平面波假设结合玻色Bogoliubov变换，解析求解其非厄米关联矩阵并构造准粒子算符，所得对角哈密顿量与原模型等价，方法可推广至多类玻色配对系统。
AI 中文摘要
开放边界条件下的玻色Kitaev链因在驱动耗散系统中的实现及其引人注目的非厄米边界物理而受到近期关注。该模型已知可通过位置-动量表象中的局域压缩变换求解。本文中，我们提出一种完全依赖标准玻色Bogoliubov变换的替代纯代数解法。对于N格点链，我们提出一种具有不等左、右运动动量的非对称平面波假设，以解析求解相关的2N×2N非厄米“关联矩阵”。左本征值问题产生N个不同的本征值，每个本征值均为二重简并。通过利用玻色对易关系仔细解析这些简并，我们构造出N个物理Bogoliubov准粒子算符。该构造揭示出非唯一性，在特殊情况下恰好反映了原方法中局域压缩变换的自由度。哈密顿量的对角形式被明确得到，且被证明等价于原哈密顿量。所提出的非对称平面波假设与简并解析技术并不局限于当前模型，可推广至其他玻色配对系统，包括具有非均匀配对或跳跃项的系统。
英文摘要
The bosonic Kitaev chain under open boundary conditions has attracted recent attention due to its realization in driven-dissipative systems and its intriguing non-Hermitian boundary physics. The model is known to be solvable via local squeezing transformations in the position-momentum representation. In this paper, we present an alternative, purely algebraic solution that relies entirely on the standard bosonic Bogoliubov transformation. For an $N$-site chain, we propose an asymmetric plane-wave ansatz with unequal left- and right-moving momenta to analytically solve the associated $2N\times 2N$ non-Hermitian ``associated matrix". The left eigenvalue problem yields $N$ distinct eigenvalues, each of which is twofold degenerate. By carefully resolving these degeneracies using the bosonic commutation relations, we construct the $N$ physical Bogoliubov quasiparticle operators. The construction reveals non-uniquenesses that in special cases exactly mirror the freedom in the local squeezing transformations of the original approach. The diagonal form of the Hamiltonian is obtained explicitly and is shown to be equivalent to the original Hamiltonian. The proposed asymmetric plane-wave ansatz and degeneracy-resolution technique are not limited to the present model and can be generalized to other bosonic pairing systems, including those with inhomogeneous pairing or hopping terms.
Comments13 pages, 1 figure
Journal refJ. Phys. A: Math. Theor. 59 395201 (2026)
