Invariance of Topological Indices Under Hilbert Space Truncation
Here, 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 spin1 AffleckKennedyLiebTasaki 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 from 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.
 Authors:

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 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Univ. of California San Diego, La Jolla, CA (United States)
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States); NORDITA, Stockholm (Sweden)
 Publication Date:
 Report Number(s):
 LAUR1724060
Journal ID: ISSN 00319007; PRLTAO; TRN: US1801298
 Grant/Contract Number:
 AC5206NA25396; BES E3B7
 Type:
 Accepted Manuscript
 Journal Name:
 Physical Review Letters
 Additional Journal Information:
 Journal Volume: 120; Journal Issue: 1; Journal ID: ISSN 00319007
 Publisher:
 American Physical Society (APS)
 Research Org:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22); USDOE National Nuclear Security Administration (NNSA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Material Science
 OSTI Identifier:
 1418765
 Alternate Identifier(s):
 OSTI ID: 1415875
Huang, Zhoushen, Zhu, Wei, Arovas, Daniel P., Zhu, Jian Xin, and Balatsky, Alexander V.. Invariance of Topological Indices Under Hilbert Space Truncation. United States: N. p.,
Web. doi:10.1103/PhysRevLett.120.016403.
Huang, Zhoushen, Zhu, Wei, Arovas, Daniel P., Zhu, Jian Xin, & Balatsky, Alexander V.. Invariance of Topological Indices Under Hilbert Space Truncation. United States. doi:10.1103/PhysRevLett.120.016403.
Huang, Zhoushen, Zhu, Wei, Arovas, Daniel P., Zhu, Jian Xin, and Balatsky, Alexander V.. 2018.
"Invariance of Topological Indices Under Hilbert Space Truncation". United States.
doi:10.1103/PhysRevLett.120.016403.
@article{osti_1418765,
title = {Invariance of Topological Indices Under Hilbert Space Truncation},
author = {Huang, Zhoushen and Zhu, Wei and Arovas, Daniel P. and Zhu, Jian Xin and Balatsky, Alexander V.},
abstractNote = {Here, 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, Z2 topological insulators, and spin1 AffleckKennedyLiebTasaki 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 from 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.},
doi = {10.1103/PhysRevLett.120.016403},
journal = {Physical Review Letters},
number = 1,
volume = 120,
place = {United States},
year = {2018},
month = {1}
}