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Invariance of Topological Indices Under Hilbert Space Truncation
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Number of Authors: 52018 (English)In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 120, no 1, article id 016403Article in journal (Refereed) Published
Abstract [en]

We show that the topological index of a wave function, computed in the space of twisted boundary phases, is preserved under Hilbert space truncation, provided the truncated state remains normalizable. If truncation affects the boundary condition of the resulting state, the invariant index may acquire a different physical interpretation. If the index is symmetry protected, the truncation should preserve the protecting symmetry. We discuss implications of this invariance using paradigmatic integer and fractional Chern insulators, Z(2) topological insulators, and spin-1 Affleck-Kennedy-Lieb-Tasaki and Heisenberg chains, as well as its relation with the notion of bulk entanglement. As a possible application, we propose a partial quantum tomography scheme trom which the topological index of a generic multicomponent wave function can be extracted by measuring only a small subset of wave function components, equivalent to the measurement of a bulk entanglement topological index.

Place, publisher, year, edition, pages
2018. Vol. 120, no 1, article id 016403
Keywords [en]
Quantum entanglement, Topological phases of matter
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:su:diva-152555DOI: 10.1103/PhysRevLett.120.016403ISI: 000419325000011PubMedID: 29350954OAI: oai:DiVA.org:su-152555DiVA, id: diva2:1183776
Available from: 2018-02-19 Created: 2018-02-19 Last updated: 2018-02-19Bibliographically approved

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Balatsky, Alexander V.
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Nordic Institute for Theoretical Physics (Nordita)
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