Topological holography: Towards a unification of Landau and beyond-Landau physics
We outline a holographic framework that attempts to unify Landau and beyond-Landau paradigms of quantum phases and phase transitions. Leveraging a modern understanding of symmetries as topological defects/operators, the framework uses a topological order to organize the space of quantum systems with...
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| Format: | Article |
| Language: | English |
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SciPost
2023-10-01
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| Series: | SciPost Physics Core |
| Online Access: | https://scipost.org/SciPostPhysCore.6.4.066 |
| _version_ | 1827792984804950016 |
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| author | Heidar Moradi, Seyed Faroogh Moosavian, Apoorv Tiwari |
| author_facet | Heidar Moradi, Seyed Faroogh Moosavian, Apoorv Tiwari |
| author_sort | Heidar Moradi, Seyed Faroogh Moosavian, Apoorv Tiwari |
| collection | DOAJ |
| description | We outline a holographic framework that attempts to unify Landau and beyond-Landau paradigms of quantum phases and phase transitions. Leveraging a modern understanding of symmetries as topological defects/operators, the framework uses a topological order to organize the space of quantum systems with a global symmetry in one lower dimension. The global symmetry naturally serves as an input for the topological order. In particular, we holographically construct a String Operator Algebra (SOA) which is the building block of symmetric quantum systems with a given symmetry G in one lower dimension. This exposes a vast web of dualities which act on the space of G-symmetric quantum systems. The SOA facilitates the classification of gapped phases as well as their corresponding order parameters and fundamental excitations, while dualities help to navigate and predict various corners of phase diagrams and analytically compute universality classes of phase transitions. A novelty of the approach is that it treats conventional Landau and unconventional topological phase transitions on an equal footing, thereby providing a holographic unification of these seemingly-disparate domains of understanding. We uncover a new feature of gapped phases and their multi-critical points, which we dub fusion structure, that encodes information about which phases and transitions can be dual to each other. Furthermore, we discover that self-dual systems typically posses emergent non-invertible, i.e., beyond group-like symmetries. We apply these ideas to $1+1d$ quantum spin chains with finite Abelian group symmetry, using topologically-ordered systems in $2+1d$. We predict the phase diagrams of various concrete spin models, and analytically compute the full conformal spectra of non-trivial quantum phase transitions, which we then verify numerically. |
| first_indexed | 2024-03-11T18:11:01Z |
| format | Article |
| id | doaj.art-3f691a9272f94e14b43d873fec2ddc20 |
| institution | Directory Open Access Journal |
| issn | 2666-9366 |
| language | English |
| last_indexed | 2024-03-11T18:11:01Z |
| publishDate | 2023-10-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics Core |
| spelling | doaj.art-3f691a9272f94e14b43d873fec2ddc202023-10-16T12:39:26ZengSciPostSciPost Physics Core2666-93662023-10-016406610.21468/SciPostPhysCore.6.4.066Topological holography: Towards a unification of Landau and beyond-Landau physicsHeidar Moradi, Seyed Faroogh Moosavian, Apoorv TiwariWe outline a holographic framework that attempts to unify Landau and beyond-Landau paradigms of quantum phases and phase transitions. Leveraging a modern understanding of symmetries as topological defects/operators, the framework uses a topological order to organize the space of quantum systems with a global symmetry in one lower dimension. The global symmetry naturally serves as an input for the topological order. In particular, we holographically construct a String Operator Algebra (SOA) which is the building block of symmetric quantum systems with a given symmetry G in one lower dimension. This exposes a vast web of dualities which act on the space of G-symmetric quantum systems. The SOA facilitates the classification of gapped phases as well as their corresponding order parameters and fundamental excitations, while dualities help to navigate and predict various corners of phase diagrams and analytically compute universality classes of phase transitions. A novelty of the approach is that it treats conventional Landau and unconventional topological phase transitions on an equal footing, thereby providing a holographic unification of these seemingly-disparate domains of understanding. We uncover a new feature of gapped phases and their multi-critical points, which we dub fusion structure, that encodes information about which phases and transitions can be dual to each other. Furthermore, we discover that self-dual systems typically posses emergent non-invertible, i.e., beyond group-like symmetries. We apply these ideas to $1+1d$ quantum spin chains with finite Abelian group symmetry, using topologically-ordered systems in $2+1d$. We predict the phase diagrams of various concrete spin models, and analytically compute the full conformal spectra of non-trivial quantum phase transitions, which we then verify numerically.https://scipost.org/SciPostPhysCore.6.4.066 |
| spellingShingle | Heidar Moradi, Seyed Faroogh Moosavian, Apoorv Tiwari Topological holography: Towards a unification of Landau and beyond-Landau physics SciPost Physics Core |
| title | Topological holography: Towards a unification of Landau and beyond-Landau physics |
| title_full | Topological holography: Towards a unification of Landau and beyond-Landau physics |
| title_fullStr | Topological holography: Towards a unification of Landau and beyond-Landau physics |
| title_full_unstemmed | Topological holography: Towards a unification of Landau and beyond-Landau physics |
| title_short | Topological holography: Towards a unification of Landau and beyond-Landau physics |
| title_sort | topological holography towards a unification of landau and beyond landau physics |
| url | https://scipost.org/SciPostPhysCore.6.4.066 |
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