Split Step Explorer swMATH ID: 24413 Software Authors: C. Cedzich, F. A. Grünbaum, C. Stahl, L. Velázquez, A. H. Werner, R. F. Werner Description: Split-Step-Explorer. Accompanying the paper: Bulk-edge correspondence of one-dimensional quantum walks. We outline a theory of symmetry protected topological phases of one-dimensional quantum walks. We assume spectral gaps around the symmetry-distinguished points +1 and -1, in which only discrete eigenvalues are allowed. The phase classification by integer or binary indices extends the classification known for translation invariant systems in terms of their band structure. However, our theory requires no translation invariance whatsoever, and the indices we define in this general setting are invariant under arbitrary symmetric local perturbations, even those that cannot be continuously contracted to the identity. More precisely we define two indices for every walk, characterizing the behavior far to the right and far to the left, respectively. Their sum is a lower bound on the number of eigenstates at +1 and -1. For a translation invariant system the indices add up to zero, so one of them already characterizes the phase. By joining two bulk phases with different indices we get a walk in which the right and left indices no longer cancel, so the theory predicts bound states at +1 or -1. This is a rigorous statement of bulk-edge correspondence. The results also apply to the Hamiltonian case with a single gap at zero. Homepage: https://qig.itp.uni-hannover.de/bulkedge/sse Related Software: Mathematica Cited in: 21 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Bulk-edge correspondence of one-dimensional quantum walks. Zbl 1342.82064Cedzich, C.; Grünbaum, F. A.; Stahl, C.; Velázquez, L.; Werner, A. H.; Werner, R. F. 2016 all top 5 Cited by 33 Authors 7 Cedzich, Christopher 6 Werner, Albert H. 5 Geib, T. 5 Suzuki, Akito 5 Werner, Reinhard F. 4 Maeda, Masaya 4 Segawa, Etsuo 3 Grünbaum, Francisco Alberto 3 Velázquez, Luis 2 Richard, Serge 2 Sasaki, Hironobu 2 Suzuki, Kanako 2 Tiedra de Aldecoa, Rafael 1 Asahara, Keisuke 1 Bogolyubov, Nikolaĭ Mikhaĭlovich 1 de Oliveira, Marcos Cesar 1 Endo, Takako 1 Fillman, Jake 1 Funakawa, Daiju 1 Jan, Munsif 1 Jia, Suotang 1 Khan, Niaz Ali 1 Konno, Norio 1 Matsue, Kaname 1 Mei, Feng 1 Meng, Ya 1 Moqadam, Jalil Khatibi 1 Obuse, Hideaki 1 Ogurisu, Osamu 1 Sajid, Muhammad 1 Seki, Motoki 1 Shah, Muzamil 1 Tanaka, Yohei all top 5 Cited in 12 Serials 4 Letters in Mathematical Physics 3 Quantum Information Processing 2 Communications in Mathematical Physics 2 Journal of Mathematical Sciences (New York) 2 Annales Henri Poincaré 2 Journal of Physics A: Mathematical and Theoretical 1 Physics Letters. A 1 Reviews in Mathematical Physics 1 Journal of the Mathematical Society of Japan 1 Physica D 1 Discrete and Continuous Dynamical Systems 1 Quantum Studies: Mathematics and Foundations all top 5 Cited in 13 Fields 14 Quantum theory (81-XX) 12 Statistical mechanics, structure of matter (82-XX) 7 Operator theory (47-XX) 6 Partial differential equations (35-XX) 4 Probability theory and stochastic processes (60-XX) 2 Functional analysis (46-XX) 2 Optics, electromagnetic theory (78-XX) 1 Combinatorics (05-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Functions of a complex variable (30-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Numerical analysis (65-XX) 1 Computer science (68-XX) Citations by Year