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Cited by 259Topological Materials and PhenomenaElectronic and Structural Properties of OxidesAdvanced Chemical Physics Studies

Macroscopic polarization as a geometric quantum phase: Many-body formulation

Ortiz, Gerardo, Martin, Richard M.·1994·Physical Review B
DOI 10.1103/physrevb.49.14202
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Abstract

During past decades, concepts about the electrostatics of infinite systems have been a challenge for theoretical physicists. In particular, the question of whether the absolute macroscopic polarization or the difference between the polarizations of two states of an insulating crystal is a well-defined bulk property has remained a controversial one. Recently, King-Smith and Vanderbilt, and Resta have provided an approach in terms of the geometric Berrys phase of electronic orbitals in an independent-particle approximation. Here we extend the derivation of Niu and Thouless for quantized charge transport to the case where the quantum adiabatic evolution is noncyclic, and we show how this polarization difference can be written in terms of a Berrys phase for a system with many-body interactions. We also discuss the origin and magnitude of the ``quantum uncertainty'' that appears when a path-independent gauge is used to compute those geometric quantum phases. This geometric viewpoint not only helps us understand the issues raised above but provides a mathematical method to compute polarizations in a many-body framework.

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Crossref · 10.1103/physrevb.49.14202

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  • Other combinations of time-reversal and crystal symmetries could lead to new topological materials beyond those in the exhaustive classification of topological insulators stable to disorder.

    “Other such combinations of time-reversal and crystal symmetries could lead to new topological materials beyond those in the exhaustive classification of topological insulators stable to disorder. 22,37”

    From Antiferromagnetic topological insulators (2010) · cites this paper as [22]

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Authors
Ortiz, G., & Martin, R. M.
Affiliations
University of Illinois Urbana-Champaign (US)
ORCID
Martin, Richard M.
Venue
Physical Review B
Publisher
American Physical Society (APS)
Published
1994-05-15
Volume
49
Issue
20
Pages
14202-14210
ISSN
  • 0163-1829 (ISSN-L)
  • 1095-3795
DOI
10.1103/physrevb.49.14202
OpenAlex
W2013832056
Cited by
259
References
17
Citations by year
2026: 10 · 2025: 6 · 2024: 5 · 2023: 8 · 2022: 4 · 2021: 10 · 2020: 59 · 2019: 9 · 2018: 26 · 2017: 5 · 2016: 3 · 2015: 3 · 2014: 6 · 2013: 7 · 2012: 2
FWCI
2.45
Type
journal article
Language
en
Open access
closed
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical review. B, Condensed matter (publishedVersion)
  • PubMed (publishedVersion)
Funders
National Science Foundation
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
  • Physical Sciences › Materials Science › Materials Chemistry › Electronic and Structural Properties of Oxides
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Advanced Chemical Physics Studies
Keywords
macroscopic polarization, Berry phase, many-body interactions, insulating crystals, quantum uncertainty, gauge choice, polarization difference

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