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Article: The characterization of topological properties in quantum Monte Carlo simulations of the Kane-Mele-Hubbard model
Title | The characterization of topological properties in quantum Monte Carlo simulations of the Kane-Mele-Hubbard model |
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Authors | |
Keywords | Topological insulator Topological invariants Strongly correlated electrons Quantum Monte Carlo simulation |
Issue Date | 2014 |
Citation | Modern Physics Letters B, 2014, v. 28, n. 1, article no. 1430001 How to Cite? |
Abstract | Topological insulators present a bulk gap, but allow for dissipationless spin transport along the edges. These exotic states are characterized by the Z2 topological invariant and are protected by time-reversal symmetry. The Kane-Mele model is one model to realize this topological class in two dimensions, also called the quantum spin Hall state. In this brief review article, we provide a pedagogical introduction to the influence of correlation effects in the quantum spin Hall states, with special focus on the half-filled Kane-Mele-Hubbard model, solved by means of unbiased determinant quantum Monte Carlo (QMC) simulations. We explain the idea of identifying the topological insulator via π-flux insertion, the Z2 invariant and the associated behavior of the zero-frequency Green's function, as well as the spin Chern number in parameter-driven topological phase transitions. The examples considered are two descendants of the Kane-Mele-Hubbard model, the generalized and dimerized Kane-Mele-Hubbard model. From the Z2 index, spin Chern numbers and the Green's function behavior, one can observe that correlation effects induce shifts of the topological phase boundaries. Although the implementation of these topological quantities has been successfully employed in QMC simulations to describe the topological phase transition, we also point out their limitations as well as suggest possible future directions in using numerical methods to characterize topological properties of strongly correlated condensed matter systems. © World Scientific Publishing Company. |
Persistent Identifier | http://hdl.handle.net/10722/268555 |
ISSN | 2021 Impact Factor: 1.948 2020 SCImago Journal Rankings: 0.293 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Meng, Zi Yang | - |
dc.contributor.author | Hung, Hsiang Hsuan | - |
dc.contributor.author | Lang, Thomas C. | - |
dc.date.accessioned | 2019-03-25T08:00:03Z | - |
dc.date.available | 2019-03-25T08:00:03Z | - |
dc.date.issued | 2014 | - |
dc.identifier.citation | Modern Physics Letters B, 2014, v. 28, n. 1, article no. 1430001 | - |
dc.identifier.issn | 0217-9849 | - |
dc.identifier.uri | http://hdl.handle.net/10722/268555 | - |
dc.description.abstract | Topological insulators present a bulk gap, but allow for dissipationless spin transport along the edges. These exotic states are characterized by the Z2 topological invariant and are protected by time-reversal symmetry. The Kane-Mele model is one model to realize this topological class in two dimensions, also called the quantum spin Hall state. In this brief review article, we provide a pedagogical introduction to the influence of correlation effects in the quantum spin Hall states, with special focus on the half-filled Kane-Mele-Hubbard model, solved by means of unbiased determinant quantum Monte Carlo (QMC) simulations. We explain the idea of identifying the topological insulator via π-flux insertion, the Z2 invariant and the associated behavior of the zero-frequency Green's function, as well as the spin Chern number in parameter-driven topological phase transitions. The examples considered are two descendants of the Kane-Mele-Hubbard model, the generalized and dimerized Kane-Mele-Hubbard model. From the Z2 index, spin Chern numbers and the Green's function behavior, one can observe that correlation effects induce shifts of the topological phase boundaries. Although the implementation of these topological quantities has been successfully employed in QMC simulations to describe the topological phase transition, we also point out their limitations as well as suggest possible future directions in using numerical methods to characterize topological properties of strongly correlated condensed matter systems. © World Scientific Publishing Company. | - |
dc.language | eng | - |
dc.relation.ispartof | Modern Physics Letters B | - |
dc.subject | Topological insulator | - |
dc.subject | Topological invariants | - |
dc.subject | Strongly correlated electrons | - |
dc.subject | Quantum Monte Carlo simulation | - |
dc.title | The characterization of topological properties in quantum Monte Carlo simulations of the Kane-Mele-Hubbard model | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1142/S0217984914300014 | - |
dc.identifier.scopus | eid_2-s2.0-84891371741 | - |
dc.identifier.volume | 28 | - |
dc.identifier.issue | 1 | - |
dc.identifier.spage | article no. 1430001 | - |
dc.identifier.epage | article no. 1430001 | - |
dc.identifier.isi | WOS:000330643900001 | - |
dc.identifier.issnl | 0217-9849 | - |