110594 20240319081002.0 doi 10.1007/s00220-021-04284-8 sideral 127164 ART-2022-127164 eng Cedzich C. Quantum Walks: Schur Functions Meet Symmetry Protected Topological Phases 2022 Access copy available to the general public Unrestricted This paper uncovers and exploits a link between a central object in harmonic analysis, the so-called Schur functions, and the very hot topic of symmetry protected topological phases of quantum matter. This connection is found in the setting of quantum walks, i.e. quantum analogs of classical random walks. We prove that topological indices classifying symmetry protected topological phases of quantum walks are encoded by matrix Schur functions built out of the walk. This main result of the paper reduces the calculation of these topological indices to a linear algebra problem: calculating symmetry indices of finite-dimensional unitaries obtained by evaluating such matrix Schur functions at the symmetry protected points ± 1. The Schur representation fully covers the complete set of symmetry indices for 1D quantum walks with a group of symmetries realizing any of the symmetry types of the tenfold way. The main advantage of the Schur approach is its validity in the absence of translation invariance, which allows us to go beyond standard Fourier methods, leading to the complete classification of non-translation invariant phases for typical examples. info:eu-repo/grantAgreement/ES/DGA/E26-17R info:eu-repo/grantAgreement/ES/DGA/E48-20R info:eu-repo/grantAgreement/EC/FP7/337603/EU/Multipartite Quantum Information Theory/QMULT info:eu-repo/grantAgreement/EC/FP7/600645/EU/Simulators and Interfaces with Quantum Systems/SIQS info:eu-repo/grantAgreement/ES/MICINN-AEI-FEDER/MTM2017-89941-P info:eu-repo/semantics/openAccess by http://creativecommons.org/licenses/by/3.0/es/ 2.4 2022 PHYSICS, MATHEMATICAL 11 / 56 = 0.196 2022 Q1 T1 1.413 2022 Statistical and Nonlinear Physics 2022 Q1 Mathematical Physics 2022 Q1 4.3 2022 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Geib T. Grünbaum F.A. Velázquez Campoy, L. F. Universidad de Zaragoza (orcid)0000-0002-3050-9540 Werner A.H. Werner R.F. 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 389 (2022), 31-74 Commun. Math. Phys. Communications in Mathematical Physics 0010-3616 799833 http://zaguan.unizar.es/record/110594/files/texto_completo.pdf Versión publicada 1751544 http://zaguan.unizar.es/record/110594/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:110594 articulos driver 2024-03-18-14:14:19 ARTICLE