2015/12/31 by Wojciech De Roeck, Marius Schütz
Mathematics · Physics and Astronomy · #Continuation #Dynamical billiards #Exponential growth #Glauber #Integrable system #Perturbation (astronomy) #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum many-body systems #Transformation (genetics) #Unitary state #Unitary transformation #cond-mat.stat-mech #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1007/s11005-016-0913-z
25 pages, minor corrections, matches published version
openalex created_date 2016/06/24 · openalex publication_date 2016/11/19 · arxiv created 2016/12/11 · arxiv updated 2016/12/13 · openalex updated_date 2026/08/05
Since its introduction by Hastings in [10], 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.