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Topological holography: Towards a unification of Landau and beyond-Landau physics
Physics and Astronomy, Division of Natural Sciences, University of Kent, Canterbury CT2 7NZ, United Kingdom; Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, United Kingdom, Wilberforce Road; The Cavendish Laboratory, Department of Physics, 19 J J Thomson Avenue, Cambridge CB3 0HE, United Kingdom, 19 J J Thomson Avenue.
Department of Physics, McGill University, Ernest Rutherford Physics Building, 3600 Rue University, Montréal, QC H3A 2T8, Canada, 3600 Rue University, Ernest Rutherford Physics Building.
KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.ORCID iD: 0000-0003-4742-775X
2023 (English)In: SciPost Physics Core, E-ISSN 2666-9366, Vol. 6, no 4, article id 066Article in journal (Refereed) Published
Abstract [en]

We outline a holographic1 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 Gsymmetric 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.

Place, publisher, year, edition, pages
Stichting SciPost , 2023. Vol. 6, no 4, article id 066
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URN: urn:nbn:se:kth:diva-339479DOI: 10.21468/SciPostPhysCore.6.4.066ISI: 001122868700002Scopus ID: 2-s2.0-85175161664OAI: oai:DiVA.org:kth-339479DiVA, id: diva2:1811426
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QC 20231113

Available from: 2023-11-13 Created: 2023-11-13 Last updated: 2024-01-03Bibliographically approved

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Tiwari, Apoorv

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