Topological phase diagram of the disordered 2XY model in presence of generalized Dzyaloshinskii-Moriya Interaction.

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ID: 28356
2019
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Ranked #31 of 53 articles by views in journal of physics condensed matter : an institute of physics journal

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Abstract
Topological index of a system determines its edge physics. However, in situations such as strong disorder where due to level repulsion the spectral gap closes, the topological indices are not well-defined. In this paper, we show that the localization length of zero modes determined by the transfer matrix method reveals much more information than the topological index. The localization length can provide not only information about the topological index of the Hamiltonian itself, but it can also provide information about the topological indices
 of the "relative" Hamiltonians. As a case study, we study a generalized XY model (2XY model) further augmented by a generalized Dziyaloshinskii-Moriya-like (DM) interaction parameterized by $\phi$ that after fermionization breaks the time-reversal invariance. The {\em parent} Hamiltonian at $\phi=0$ which belongs to BDI class is indexed by integer winding number while the $\phi\ne 0$ {\em daughter} Hamiltonian which belongs to class D is specified by a $Z_2$ index $\nu=\pm 1$. We show that the localization length in addition to determining the $Z_2$ can count the number of Majorana zero modes left over at the boundary of the daughter Hamiltonian -- which are not protected by winding number anymore. Therefore the localization length outperforms the standard topological indices in two respects: (i) it is much faster and more accurate to calculate and (ii) it can count the winding number of the parent Hamiltonian by looking into the edges of the daughter Hamiltonian.
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habibi2019topologicaljournal Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Habibi, Alireza;Ghadimi, Rasoul;Jafari, Seyed Akbar;
Journal journal of physics condensed matter : an institute of physics journal
Year 2019
DOI
10.1088/1361-648X/ab401c
URL
Keywords Keywords not found

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