ORCID Profile
0000-0001-8234-0081
Current Organisations
Nagoya University
,
RIKEN
Does something not look right? The information on this page has been harvested from data sources that may not be up to date. We continue to work with information providers to improve coverage and quality. To report an issue, use the Feedback Form.
Publisher: IOP Publishing
Date: 16-05-2018
Publisher: Springer Science and Business Media LLC
Date: 09-07-2015
Publisher: World Scientific Pub Co Pte Ltd
Date: 03-2016
DOI: 10.1142/S0129055X16500045
Abstract: We study topological insulators, regarded as physical systems giving rise to topological invariants determined by symmetries both linear and anti-linear. Our perspective is that of non-commutative index theory of operator algebras. In particular, we formulate the index problems using Kasparov theory, both complex and real. We show that the periodic table of topological insulators and superconductors can be realized as a real or complex index pairing of a Kasparov module capturing internal symmetries of the Hamiltonian with a spectral triple encoding the geometry of the s le’s (possibly non-commutative) Brillouin zone.
Publisher: World Scientific Pub Co Pte Lt
Date: 16-03-2020
DOI: 10.1142/S0129055X20500282
Abstract: For parity-conserving fermionic chains, we review how to associate [Formula: see text]-indices to ground states in finite systems with quadratic and higher-order interactions as well as to quasifree ground states on the infinite CAR algebra. It is shown that the [Formula: see text]-valued spectral flow provides a topological obstruction for two systems to have the same [Formula: see text]-index. A rudimentary definition of a [Formula: see text]-phase label for a class of parity-invariant and pure ground states of the one-dimensional infinite CAR algebra is also provided. Ground states with differing phase labels cannot be connected without a closing of the spectral gap of the infinite GNS Hamiltonian.
Publisher: Springer International Publishing
Date: 2018
Publisher: Cambridge University Press (CUP)
Date: 21-07-2016
Publisher: Springer Science and Business Media LLC
Date: 28-06-2018
Publisher: Springer Science and Business Media LLC
Date: 06-02-2019
Publisher: American Chemical Society (ACS)
Date: 30-12-2021
Publisher: World Scientific Pub Co Pte Ltd
Date: 03-09-2020
DOI: 10.1142/S1793525320500557
Abstract: In this paper, we give a comprehensive treatment of a “Clifford module flow” along paths in the skew-adjoint Fredholm operators on a real Hilbert space that takes values in [Formula: see text] via the Clifford index of Atiyah–Bott–Shapiro. We develop its properties for both bounded and unbounded skew-adjoint operators including an axiomatic characterization. Our constructions and approach are motivated by the principle that [Formula: see text] That is, we show how the [Formula: see text]-valued spectral flow relates to a [Formula: see text]-valued index by proving a Robbin–Salamon type result. The Kasparov product is also used to establish a [Formula: see text] result at the level of bivariant [Formula: see text]-theory. We explain how our results incorporate previous applications of [Formula: see text]-valued spectral flow in the study of topological phases of matter.
Publisher: World Scientific Pub Co Pte Lt
Date: 08-2020
DOI: 10.1142/S0129167X20500743
Abstract: We use the Cayley transform to provide an explicit isomorphism at the level of cycles from van Daele [Formula: see text]-theory to [Formula: see text]-theory for graded [Formula: see text]-algebras with a real structure. Isomorphisms between [Formula: see text]-theory and complex or real [Formula: see text]-theory for ungraded [Formula: see text]-algebras are a special case of this map. In all cases, our map is compatible with the computational techniques required in physical and geometrical applications, in particular, index pairings and Kasparov products. We provide applications to real [Formula: see text]-theory and topological phases of matter.
Publisher: Springer Science and Business Media LLC
Date: 03-01-2017
Publisher: IOP Publishing
Date: 02-03-2022
Abstract: We consider quasifree ground states of Araki’s self-dual canonical anti-commutation relation algebra from the viewpoint of index theory and symmetry protected topological (SPT) phases. We first review how Clifford module indices characterise a topological obstruction to connect pairs of symmetric gapped ground states. This construction is then generalised to give invariants in K O * ( A r ) with A a C * , r -algebra of allowed deformations. When A = C *( X ), the Roe algebra of a coarse space X , and we restrict to gapped ground states that are locally equivalent with respect X , a K -homology class is also constructed. The coarse assembly map relates these two classes and clarifies the relevance of K -homology to free-fermionic SPT phases.
Publisher: SIGMA (Symmetry, Integrability and Geometry: Methods and Application)
Date: 28-07-2023
Abstract: Building from work by Cedzich et al. and Suzuki et al., we consider topological and index-theoretic properties of chiral unitaries, which are an abstraction of the time evolution of a chiral-symmetric self-adjoint operator. Split-step quantum walks provide a rich class of ex les. We use the index of a pair of projections and the Cayley transform to define topological indices for chiral unitaries on both Hilbert spaces and Hilbert $C^*$-modules. In the case of the discrete time evolution of a Hamiltonian-like operator, we relate the index for chiral unitaries to the index of the Hamiltonian. We also prove a double-sided winding number formula for anisotropic split-step quantum walks on Hilbert $C^*$-modules, extending a result by Matsuzawa.
Publisher: Cambridge University Press (CUP)
Date: 2021
DOI: 10.1017/FMS.2021.19
Abstract: We introduce an index for symmetry-protected topological (SPT) phases of infinite fermionic chains with an on-site symmetry given by a finite group G . This index takes values in $\\mathbb {Z}_2 \\times H^1(G,\\mathbb {Z}_2) \\times H^2(G, U(1)_{\\mathfrak {p}})$ with a generalised Wall group law under stacking. We show that this index is an invariant of the classification of SPT phases. When the ground state is translation invariant and has reduced density matrices with uniformly bounded rank on finite intervals, we derive a fermionic matrix product representative of this state with on-site symmetry.
Publisher: Springer Science and Business Media LLC
Date: 08-2021
Start Date: 2016
End Date: 2018
Funder: Japan Society for the Promotion of Science
View Funded ActivityStart Date: 2019
End Date: 2023
Funder: Japan Society for the Promotion of Science
View Funded ActivityStart Date: 2016
End Date: 2018
Funder: Japan Society for the Promotion of Science
View Funded Activity