Simulation of novel cell-like topological structures with quantum walk
Helmholtz-Institut Jena, Fröbelstieg 3, 07743, Jena, Germany
2 GSI Helmholtzzentrum für Schwerionenforschung, 64291, Darmstadt, Germany
3 Theoretisch-Physikalisches Institut, Friedrich-Schiller-University Jena, 07743, Jena, Germany
Accepted: 28 July 2020
Published online: 5 August 2020
We demonstrate how quantum walk can simulate exotic cell-like structures for topological phases and boundary states. These cell-like structures contain the three known boundary states of Dirac cone, Fermi arc and flat bands alongside of all trivial and non-trivial phases of BDI family of topological phases. We also characterize the behavior of boundary states through Bloch spheres. In addition, we investigate the topological phase transitions and critical behavior of the system that take place over boundary states through curvature function. We confirm that critical behavior of the simulated topological phenomena can be described by peak-divergence scenario. We extract the critical exponents and length scale, establish a scaling law and show that band crossing is 1. Furthermore, we find the correlation function through Wannier states and show that it decays as a function of length scale.
© The Author(s) 2020
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.