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Article: Topological invariants for interacting topological insulators. II. Breakdown of single-particle Green's function formalism

TitleTopological invariants for interacting topological insulators. II. Breakdown of single-particle Green's function formalism
Authors
Issue Date2016
PublisherAmerican Physical Society. The Journal's web site is located at http://journals.aps.org/prb/
Citation
Physical Review B: covering condensed matter and materials physics, 2016, v. 93 n. 19, article no. 195164 How to Cite?
Abstract© 2016 American Physical Society. Topological phase transitions in free fermion systems can be characterized by the closing of single-particle gap and the change in topological invariants. However, in the presence of electronic interactions, topological phase transitions can be more complicated. In paper I of this series [Phys. Rev. B 93, 195163 (2016)10.1103/PhysRevB.93.195163], we have proposed an efficient scheme to evaluate the topological invariants based on the single-particle Green's function formalism. Here, in paper II, we demonstrate several interaction-driven topological phase transitions (TPTs) in two-dimensional (2D) interacting topological insulators (TIs) via large-scale quantum Monte Carlo (QMC) simulations, based on the scheme of evaluating topological invariants presented in paper I. Across these transitions, the defining symmetries of the TIs have been neither explicitly nor spontaneously broken. In the first two models, the topological invariants calculated from the Green's function formalism succeed in characterizing the topologically distinct phases and identifying interaction-driven TPTs. However, in the other two models, we find that the single-particle gap does not close and the topological invariants constructed from the single-particle Green's function acquire no change across the TPTs. Unexpected breakdown of the Green's function formalism in constructing the topological invariants is thus discovered. We thence classify the topological phase transitions in interacting TIs into two categories in practical computation: Those that have noninteracting correspondence can be characterized successfully by the topological invariants constructed from the Green's functions, while for the others that do not have noninteracting correspondence, the Green's function formalism experiences a breakdown, but more interesting and exciting phenomena, such as emergent collective critical modes at the transition, arise. Discussion on the success and breakdown of topological invariants constructed from the Green's function formalism in the context of symmetry protected topological (SPT) states is presented.
Persistent Identifierhttp://hdl.handle.net/10722/268478
ISSN
2023 Impact Factor: 3.2
2023 SCImago Journal Rankings: 1.345
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorHe, Yuan Yao-
dc.contributor.authorWu, Han Qing-
dc.contributor.authorMeng, Zi Yang-
dc.contributor.authorLu, Zhong Yi-
dc.date.accessioned2019-03-25T07:59:47Z-
dc.date.available2019-03-25T07:59:47Z-
dc.date.issued2016-
dc.identifier.citationPhysical Review B: covering condensed matter and materials physics, 2016, v. 93 n. 19, article no. 195164-
dc.identifier.issn2469-9950-
dc.identifier.urihttp://hdl.handle.net/10722/268478-
dc.description.abstract© 2016 American Physical Society. Topological phase transitions in free fermion systems can be characterized by the closing of single-particle gap and the change in topological invariants. However, in the presence of electronic interactions, topological phase transitions can be more complicated. In paper I of this series [Phys. Rev. B 93, 195163 (2016)10.1103/PhysRevB.93.195163], we have proposed an efficient scheme to evaluate the topological invariants based on the single-particle Green's function formalism. Here, in paper II, we demonstrate several interaction-driven topological phase transitions (TPTs) in two-dimensional (2D) interacting topological insulators (TIs) via large-scale quantum Monte Carlo (QMC) simulations, based on the scheme of evaluating topological invariants presented in paper I. Across these transitions, the defining symmetries of the TIs have been neither explicitly nor spontaneously broken. In the first two models, the topological invariants calculated from the Green's function formalism succeed in characterizing the topologically distinct phases and identifying interaction-driven TPTs. However, in the other two models, we find that the single-particle gap does not close and the topological invariants constructed from the single-particle Green's function acquire no change across the TPTs. Unexpected breakdown of the Green's function formalism in constructing the topological invariants is thus discovered. We thence classify the topological phase transitions in interacting TIs into two categories in practical computation: Those that have noninteracting correspondence can be characterized successfully by the topological invariants constructed from the Green's functions, while for the others that do not have noninteracting correspondence, the Green's function formalism experiences a breakdown, but more interesting and exciting phenomena, such as emergent collective critical modes at the transition, arise. Discussion on the success and breakdown of topological invariants constructed from the Green's function formalism in the context of symmetry protected topological (SPT) states is presented.-
dc.languageeng-
dc.publisherAmerican Physical Society. The Journal's web site is located at http://journals.aps.org/prb/-
dc.relation.ispartofPhysical Review B: covering condensed matter and materials physics-
dc.titleTopological invariants for interacting topological insulators. II. Breakdown of single-particle Green's function formalism-
dc.typeArticle-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1103/PhysRevB.93.195164-
dc.identifier.scopuseid_2-s2.0-84971501404-
dc.identifier.volume93-
dc.identifier.issue19-
dc.identifier.spagearticle no. 195164-
dc.identifier.epagearticle no. 195164-
dc.identifier.eissn2469-9969-
dc.identifier.isiWOS:000376920400005-
dc.identifier.issnl2469-9950-

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