Topological Multipartite Entanglement in a Fermi Liquid
We show that the topology of the Fermi sea of a D-dimensional Fermi gas is reflected in the multipartite entanglement characterizing D+1 regions that meet at a point. For odd D we introduce the multipartite mutual information and show that it exhibits a log^{D}L divergence as a function of system si...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2022-08-01
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| Series: | Physical Review X |
| Online Access: | http://doi.org/10.1103/PhysRevX.12.031022 |
| _version_ | 1818175259765899264 |
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| author | Pok Man Tam Martin Claassen Charles L. Kane |
| author_facet | Pok Man Tam Martin Claassen Charles L. Kane |
| author_sort | Pok Man Tam |
| collection | DOAJ |
| description | We show that the topology of the Fermi sea of a D-dimensional Fermi gas is reflected in the multipartite entanglement characterizing D+1 regions that meet at a point. For odd D we introduce the multipartite mutual information and show that it exhibits a log^{D}L divergence as a function of system size L with a universal coefficient that is proportional to the Euler characteristic χ_{F} of the Fermi sea. This provides a generalization, for a Fermi gas, of the well-known result for D=1 that expresses the logL divergence of the bipartite entanglement entropy in terms of the central charge c characterizing a conformal field theory. For even D we introduce a charge-weighted entanglement entropy that is manifestly odd under a particle-hole transformation. We show that the corresponding charge-weighted mutual information exhibits a similar log^{D}L divergence proportional to χ_{F}. Our analysis relates the universal behavior of the multipartite mutual information in the absence of interactions to the D+1 order equal-time density correlation function, which we show exhibits a universal behavior in the long wavelength limit proportional to χ_{F}. Our analytic results are based on the replica method. In addition, we perform a numerical study of the charge-weighted mutual information for D=2 that confirms several aspects of the analytic theory. Finally, we consider the effect of interactions perturbatively within the replica theory. We show that for D=3 the log^{3}L divergence of the topological mutual information is not perturbed by weak short-ranged interactions, though for D=2 the charge-weighted mutual information is perturbed. Thus, for D=3 the multipartite mutual information provides a robust classification that distinguishes distinct topological Fermi liquid phases. |
| first_indexed | 2024-12-11T19:57:27Z |
| format | Article |
| id | doaj.art-162d73def2b84a2c8d710f5063726690 |
| institution | Directory Open Access Journal |
| issn | 2160-3308 |
| language | English |
| last_indexed | 2024-12-11T19:57:27Z |
| publishDate | 2022-08-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review X |
| spelling | doaj.art-162d73def2b84a2c8d710f50637266902022-12-22T00:52:36ZengAmerican Physical SocietyPhysical Review X2160-33082022-08-0112303102210.1103/PhysRevX.12.031022Topological Multipartite Entanglement in a Fermi LiquidPok Man TamMartin ClaassenCharles L. KaneWe show that the topology of the Fermi sea of a D-dimensional Fermi gas is reflected in the multipartite entanglement characterizing D+1 regions that meet at a point. For odd D we introduce the multipartite mutual information and show that it exhibits a log^{D}L divergence as a function of system size L with a universal coefficient that is proportional to the Euler characteristic χ_{F} of the Fermi sea. This provides a generalization, for a Fermi gas, of the well-known result for D=1 that expresses the logL divergence of the bipartite entanglement entropy in terms of the central charge c characterizing a conformal field theory. For even D we introduce a charge-weighted entanglement entropy that is manifestly odd under a particle-hole transformation. We show that the corresponding charge-weighted mutual information exhibits a similar log^{D}L divergence proportional to χ_{F}. Our analysis relates the universal behavior of the multipartite mutual information in the absence of interactions to the D+1 order equal-time density correlation function, which we show exhibits a universal behavior in the long wavelength limit proportional to χ_{F}. Our analytic results are based on the replica method. In addition, we perform a numerical study of the charge-weighted mutual information for D=2 that confirms several aspects of the analytic theory. Finally, we consider the effect of interactions perturbatively within the replica theory. We show that for D=3 the log^{3}L divergence of the topological mutual information is not perturbed by weak short-ranged interactions, though for D=2 the charge-weighted mutual information is perturbed. Thus, for D=3 the multipartite mutual information provides a robust classification that distinguishes distinct topological Fermi liquid phases.http://doi.org/10.1103/PhysRevX.12.031022 |
| spellingShingle | Pok Man Tam Martin Claassen Charles L. Kane Topological Multipartite Entanglement in a Fermi Liquid Physical Review X |
| title | Topological Multipartite Entanglement in a Fermi Liquid |
| title_full | Topological Multipartite Entanglement in a Fermi Liquid |
| title_fullStr | Topological Multipartite Entanglement in a Fermi Liquid |
| title_full_unstemmed | Topological Multipartite Entanglement in a Fermi Liquid |
| title_short | Topological Multipartite Entanglement in a Fermi Liquid |
| title_sort | topological multipartite entanglement in a fermi liquid |
| url | http://doi.org/10.1103/PhysRevX.12.031022 |
| work_keys_str_mv | AT pokmantam topologicalmultipartiteentanglementinafermiliquid AT martinclaassen topologicalmultipartiteentanglementinafermiliquid AT charleslkane topologicalmultipartiteentanglementinafermiliquid |