Anyon condensation: coherent states, symmetry enriched topological phases, Goldstone theorem, and dynamical rearrangement of symmetry
Abstract Although the mathematics of anyon condensation in topological phases has been studied intensively in recent years, a proof of its physical existence is tantamount to constructing an effective Hamiltonian theory. In this paper, we concretely establish the physical foundation of anyon condens...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2022-03-01
|
| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP03(2022)026 |
| _version_ | 1830352345587777536 |
|---|---|
| author | Yuting Hu Zichang Huang Ling-Yan Hung Yidun Wan |
| author_facet | Yuting Hu Zichang Huang Ling-Yan Hung Yidun Wan |
| author_sort | Yuting Hu |
| collection | DOAJ |
| description | Abstract Although the mathematics of anyon condensation in topological phases has been studied intensively in recent years, a proof of its physical existence is tantamount to constructing an effective Hamiltonian theory. In this paper, we concretely establish the physical foundation of anyon condensation by building the effective Hamiltonian and the Hilbert space, in which we explicitly construct the vacuum of the condensed phase as the coherent states that are the eigenstates of the creation operators creating the condensate anyons. Along with this construction, which is analogous to Laughlin’s construction of wavefunctions of fractional quantum hall states, we generalize the Goldstone theorem in the usual spontaneous symmetry breaking paradigm to the case of anyon condensation. We then prove that the condensed phase is a symmetry enriched (protected) topological phase by directly constructing the corresponding symmetry transformations, which can be considered as a generalization of the Bogoliubov transformation. |
| first_indexed | 2024-12-20T00:55:14Z |
| format | Article |
| id | doaj.art-2176b34668bd4479b18562e55d11f72d |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-20T00:55:14Z |
| publishDate | 2022-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-2176b34668bd4479b18562e55d11f72d2022-12-21T19:59:08ZengSpringerOpenJournal of High Energy Physics1029-84792022-03-012022314510.1007/JHEP03(2022)026Anyon condensation: coherent states, symmetry enriched topological phases, Goldstone theorem, and dynamical rearrangement of symmetryYuting Hu0Zichang Huang1Ling-Yan Hung2Yidun Wan3State Key Laboratory of Surface Physics, Department of Physics, Center for Field Theory and Particle Physics and Institute for Nanoelectronic devices and Quantum computing, Fudan UniversityState Key Laboratory of Surface Physics, Department of Physics, Center for Field Theory and Particle Physics and Institute for Nanoelectronic devices and Quantum computing, Fudan UniversityState Key Laboratory of Surface Physics, Department of Physics, Center for Field Theory and Particle Physics and Institute for Nanoelectronic devices and Quantum computing, Fudan UniversityState Key Laboratory of Surface Physics, Department of Physics, Center for Field Theory and Particle Physics and Institute for Nanoelectronic devices and Quantum computing, Fudan UniversityAbstract Although the mathematics of anyon condensation in topological phases has been studied intensively in recent years, a proof of its physical existence is tantamount to constructing an effective Hamiltonian theory. In this paper, we concretely establish the physical foundation of anyon condensation by building the effective Hamiltonian and the Hilbert space, in which we explicitly construct the vacuum of the condensed phase as the coherent states that are the eigenstates of the creation operators creating the condensate anyons. Along with this construction, which is analogous to Laughlin’s construction of wavefunctions of fractional quantum hall states, we generalize the Goldstone theorem in the usual spontaneous symmetry breaking paradigm to the case of anyon condensation. We then prove that the condensed phase is a symmetry enriched (protected) topological phase by directly constructing the corresponding symmetry transformations, which can be considered as a generalization of the Bogoliubov transformation.https://doi.org/10.1007/JHEP03(2022)026Topological States of MatterAnyonsSpontaneous Symmetry BreakingTopological Field Theories |
| spellingShingle | Yuting Hu Zichang Huang Ling-Yan Hung Yidun Wan Anyon condensation: coherent states, symmetry enriched topological phases, Goldstone theorem, and dynamical rearrangement of symmetry Journal of High Energy Physics Topological States of Matter Anyons Spontaneous Symmetry Breaking Topological Field Theories |
| title | Anyon condensation: coherent states, symmetry enriched topological phases, Goldstone theorem, and dynamical rearrangement of symmetry |
| title_full | Anyon condensation: coherent states, symmetry enriched topological phases, Goldstone theorem, and dynamical rearrangement of symmetry |
| title_fullStr | Anyon condensation: coherent states, symmetry enriched topological phases, Goldstone theorem, and dynamical rearrangement of symmetry |
| title_full_unstemmed | Anyon condensation: coherent states, symmetry enriched topological phases, Goldstone theorem, and dynamical rearrangement of symmetry |
| title_short | Anyon condensation: coherent states, symmetry enriched topological phases, Goldstone theorem, and dynamical rearrangement of symmetry |
| title_sort | anyon condensation coherent states symmetry enriched topological phases goldstone theorem and dynamical rearrangement of symmetry |
| topic | Topological States of Matter Anyons Spontaneous Symmetry Breaking Topological Field Theories |
| url | https://doi.org/10.1007/JHEP03(2022)026 |
| work_keys_str_mv | AT yutinghu anyoncondensationcoherentstatessymmetryenrichedtopologicalphasesgoldstonetheoremanddynamicalrearrangementofsymmetry AT zichanghuang anyoncondensationcoherentstatessymmetryenrichedtopologicalphasesgoldstonetheoremanddynamicalrearrangementofsymmetry AT lingyanhung anyoncondensationcoherentstatessymmetryenrichedtopologicalphasesgoldstonetheoremanddynamicalrearrangementofsymmetry AT yidunwan anyoncondensationcoherentstatessymmetryenrichedtopologicalphasesgoldstonetheoremanddynamicalrearrangementofsymmetry |