An exponentially local spectral flow for possibly non-self-adjoint perturbations of non-interacting quantum spins, inspired by KAM theory

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• 作者：Wojciech De Roeck ; Marius Schütz
• 关键词：Quantum spin systems ; Gapped ground states ; Stationary states of quantum Markov dynamics ; Frustration ; free systems ; Non ; self ; adjoint perturbation theory
• 刊名：Letters in Mathematical Physics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：107
• 期：3
• 页码：505-532
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Theoretical, Mathematical and Computational Physics; Complex Systems; Geometry; Group Theory and Generalizations;
• 出版者：Springer Netherlands
• ISSN：1573-0530
• 卷排序：107

文摘

Since its introduction by Hastings (Phys Rev B 69:104431, 2004), the technique of quasi-adiabatic continuation has become a central tool in the discussion and classification of ground-state phases. It connects the ground states of self-adjoint Hamiltonians in the same phase by a unitary quasi-local transformation. This paper takes a step towards extending this result to non-self-adjoint perturbations, though, for technical reason, we restrict ourselves here to weak perturbations of non-interacting spins. The extension to non-self-adjoint perturbation is important for potential applications to Glauber dynamics (and its quantum analogues). In contrast to the standard quasi-adiabatic transformation, the transformation constructed here is exponentially local. Our scheme is inspired by KAM theory, with frustration-free operators playing the role of integrable Hamiltonians.