Non-Bloch Band Theory of Non-Hermitian Systems.

By Kazuki Yokomizo, Shuichi Murakami. Physical Review Letters, 2019

780 citations recorded by the source corpus.

In spatially periodic Hermitian systems, such as electronic systems in crystals, the band structure is described by the band theory in terms of the Bloch wave functions, which reproduce energy levels for large systems with open boundaries. In this paper, we establish a generalized Bloch band theory in one-dimensional spatially periodic tight-binding models. We show how to define the Brillouin zone in non-Hermitian systems. From this Brillouin zone, one can calculate continuum bands, which reproduce the band structure in an open chain. As an example, we apply our theory to the non-Hermitian Su-Schrieffer-Heeger model. We also show the bulk-edge correspondence between the winding number and existence of the topological edge states.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/10c5e7c122dd7864929fce192eb54e5c5059b012

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Citations in the corpus

Higher-order non-Hermitian skin effect (2020, methodology): “Although the skin effect invalidates the conventional Bloch band theory, researchers formulated a non-Bloch band theory that works even under arbitrary boundary conditions [46, 68].”
A review on non-Hermitian skin effect (2022, methodology): “This theory takes a complex wave vector k0 ¼ k ilnr (it is in this form for the sake of concise formulism, with r some real values) to replace the initial real wave vector k and defines the GBZ based on k0 so that the nonHermitian dynamics can be characterized as the non-Bloch wave propagation gover”
Exceptional topology of non-Hermitian systems (2019, background): “A recent realization of a NH phase in mechanical metamaterials is presented by Yoshida and Hatsugai, 2019, where exceptional rings are proposed to appear in mechanical metamaterials with friction.”
Entanglement Phase Transition Induced by the Non-Hermitian Skin Effect (2022, background): “The skin effect can be understood by the imaginary gauge transformation (GL (1) gauge transformation; GL (n) is the general linear group of n × n invertible matrices) [93, 118, 134].”
Non-Bloch band theory of non-Hermitian Hamiltonians in the symplectic class (2020, methodology): “To elucidate such a non-Bloch feature of non-Hermitian systems, recent works have developed a non-Bloch band theory that works even under arbitrary boundary conditions [25, 27, 30, 34, 40, 53, 54].”