Introduces a non-Bloch winding number on a generalized Brillouin zone to predict and control boundary-localized magnon modes in an antiferromagnetic chain where conventional bulk-boundary correspondence fails.
Xiao, Theory of transformation for the diagonalization of quadratic Hamiltonians (2009), arXiv:0908.0787 [math-ph]
6 Pith papers cite this work. Polarity classification is still indexing.
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abstract
A theory of transformation is presented for the diagonalization of a Hamiltonian that is quadratic in creation and annihilation operators or in coordinates and momenta. It is the systemization and theorization of Dirac and Bogoliubov-Valatin transformations, and thus provides us an operational procedure to answer, in a direct manner, the questions as to whether a quadratic Hamiltonian is diagonalizable, whether the diagonalization is unique, and how the transformation can be constructed if the diagonalization exists. The underlying idea is to consider the dynamic matrix. Each quadratic Hamiltonian has a dynamic matrix of its own. The eigenvalue problem of the dynamic matrix determines the diagonalizability of the quadratic Hamiltonian completely. In brief, the theory ascribes the diagonalization of a quadratic Hamiltonian to the eigenvalue problem of its dynamic matrix, which is familiar to all of us. That makes it much easy to use. Applications to various physical systems are discussed, with especial emphasis on the quantum fields, such as Klein-Gordon field, phonon field, etc..
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2026 6representative citing papers
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Skyrmionium lattices with zero topological charge support nontrivial topological magnon states through a weighted magnetic flux concept and a mapping to the Haldane model.
Synthetic antiferromagnetic skyrmion lattices support layer-polarized spin-Hall-like magnon edge modes from opposing layer Hall responses, not Z2 topology, due to absent pseudo-time-reversal symmetry.
Quantum fluctuations generate nonzero scalar spin chirality in collinear or coplanar magnetic orders on a triangular lattice with XXZ and spin-orbit interactions under magnetic field.
Non-secular Redfield dynamics for unequally damped strongly interacting oscillators produces non-Gibbs steady states via bath-induced coherences between nearly-degenerate levels.
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Bath-induced deviations from Gibbs statistics for strongly interacting oscillators
Non-secular Redfield dynamics for unequally damped strongly interacting oscillators produces non-Gibbs steady states via bath-induced coherences between nearly-degenerate levels.