Crystallographic interacting topological phases and equivariant cohomology: to assume or not to assume
Abstract For symmorphic crystalline interacting gapped systems we derive a classification under adiabatic evolution. This classification is complete for non-degenerate ground states. For the degenerate case we discuss some invariants given by equivariant characteristic classes. We do not assume an e...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-07-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP07(2021)139 |
| _version_ | 1818658014087872512 |
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| author | Daniel Sheinbaum Omar Antolín Camarena |
| author_facet | Daniel Sheinbaum Omar Antolín Camarena |
| author_sort | Daniel Sheinbaum |
| collection | DOAJ |
| description | Abstract For symmorphic crystalline interacting gapped systems we derive a classification under adiabatic evolution. This classification is complete for non-degenerate ground states. For the degenerate case we discuss some invariants given by equivariant characteristic classes. We do not assume an emergent relativistic field theory nor that phases form a topological spectrum. We also do not restrict to systems with short-range entanglement, stability against stacking with trivial systems nor assume the existence of quasi-particles as is done in SPT and SET classifications respectively. Using a slightly generalized Bloch decomposition and Grassmanians made out of ground state spaces, we show that the P-equivariant cohomology of a d-dimensional torus gives rise to different interacting phases, where P denotes the point group of the crystalline structure. We compare our results to bosonic symmorphic crystallographic SPT phases and to non-interacting fermionic crystallographic phases in class A. Finally we discuss the relation of our assumptions to those made for crystallographic SPT and SET phases. |
| first_indexed | 2024-12-17T03:50:38Z |
| format | Article |
| id | doaj.art-f26092a0273a47ad88b73e7cbf5ff3b6 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-17T03:50:38Z |
| publishDate | 2021-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-f26092a0273a47ad88b73e7cbf5ff3b62022-12-21T22:04:46ZengSpringerOpenJournal of High Energy Physics1029-84792021-07-012021712310.1007/JHEP07(2021)139Crystallographic interacting topological phases and equivariant cohomology: to assume or not to assumeDaniel Sheinbaum0Omar Antolín Camarena1Facultad de Química, Universidad Nacional Autónoma de MéxicoInstituto de Matematicas, Universidad Nacional Autónoma de MéxicoAbstract For symmorphic crystalline interacting gapped systems we derive a classification under adiabatic evolution. This classification is complete for non-degenerate ground states. For the degenerate case we discuss some invariants given by equivariant characteristic classes. We do not assume an emergent relativistic field theory nor that phases form a topological spectrum. We also do not restrict to systems with short-range entanglement, stability against stacking with trivial systems nor assume the existence of quasi-particles as is done in SPT and SET classifications respectively. Using a slightly generalized Bloch decomposition and Grassmanians made out of ground state spaces, we show that the P-equivariant cohomology of a d-dimensional torus gives rise to different interacting phases, where P denotes the point group of the crystalline structure. We compare our results to bosonic symmorphic crystallographic SPT phases and to non-interacting fermionic crystallographic phases in class A. Finally we discuss the relation of our assumptions to those made for crystallographic SPT and SET phases.https://doi.org/10.1007/JHEP07(2021)139Discrete SymmetriesTopological States of MatterTopological Field Theories |
| spellingShingle | Daniel Sheinbaum Omar Antolín Camarena Crystallographic interacting topological phases and equivariant cohomology: to assume or not to assume Journal of High Energy Physics Discrete Symmetries Topological States of Matter Topological Field Theories |
| title | Crystallographic interacting topological phases and equivariant cohomology: to assume or not to assume |
| title_full | Crystallographic interacting topological phases and equivariant cohomology: to assume or not to assume |
| title_fullStr | Crystallographic interacting topological phases and equivariant cohomology: to assume or not to assume |
| title_full_unstemmed | Crystallographic interacting topological phases and equivariant cohomology: to assume or not to assume |
| title_short | Crystallographic interacting topological phases and equivariant cohomology: to assume or not to assume |
| title_sort | crystallographic interacting topological phases and equivariant cohomology to assume or not to assume |
| topic | Discrete Symmetries Topological States of Matter Topological Field Theories |
| url | https://doi.org/10.1007/JHEP07(2021)139 |
| work_keys_str_mv | AT danielsheinbaum crystallographicinteractingtopologicalphasesandequivariantcohomologytoassumeornottoassume AT omarantolincamarena crystallographicinteractingtopologicalphasesandequivariantcohomologytoassumeornottoassume |