线性矩阵积切空间的激发谱与秩断层扫描
Excitation spectra and rank tomography of finite MPS tangent spaces
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中文总结 AI 辅助
为研究具有开放边界条件的非均匀量子多体系统激发谱，提出矩阵积态代数簇的切空间方法，引入MPS切空间秩断层扫描，以玻色-哈伯德模型为例说明该方法能重现低激发并捕捉Mott绝缘体到超流体转变的有限尺寸前兆。
中文摘要 AI 辅助
我们为矩阵积态（MPS）的代数簇制定了一种切空间方法，以研究具有开放边界条件的非均匀量子多体系统的激发谱。我们进一步引入了MPS切空间的秩断层扫描，它根据基础MPS簇的粒子扇区秩分布来表征其表现力。以玻色 - 哈伯德模型为基准，我们说明了该方法能重现低激发并捕捉Mott绝缘体到超流体转变的有限尺寸前兆。
英文摘要
We formulate the matrix product state (MPS) tangent-space excitation construction for finite, non-uniform systems with open boundary conditions, using the smooth full-rank stratum of the MPS variety as the variational manifold. The resulting linear tangent ansatz yields a projected-Hamiltonian eigenproblem for approximating excitation spectra. We further introduce a rank tomography that characterizes the particle-sector expressivity of the MPS tangent space. For number-conserving systems, we resolve the Schmidt ranks of reference states by particle number and derive an explicit relation between the resulting rank profile and the dimensions of the tangent-space sectors. This allows sector completeness and parametric deficiency to be determined directly from the reference state, without explicitly constructing a tangent basis, and provides a direct diagnostic of the sectorwise expressivity of the MPS excitation ansatz. We benchmark the finite-system construction on Bose--Hubbard chains against exact diagonalization, finding accurate low-lying excitation branches while identifying sector-dependent limitations of the linear tangent ansatz.
发表机构
- Università di Trento（特伦托大学）
- Max Planck Institute for Mathematics in the Sciences（马克斯·普朗克数学科学研究所）
- INO-CNR Pitaevskii BEC Center（意大利国家研究委员会光学研究所皮塔耶夫斯基玻色-爱因斯坦凝聚中心）
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