Topological holography: Towards a unification of Landau and beyond-Landau physics

Author:

Moradi Heidar12,Moosavian Seyed Faroogh3,Tiwari Apoorv4

Affiliation:

1. University of Cambridge

2. University of Kent

3. McGill University

4. Royal Institute of Technology (KTH)

Abstract

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+1d1+1d quantum spin chains with finite Abelian group symmetry, using topologically-ordered systems in 2+1d2+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.

Funder

Alfred P. Sloan Foundation

Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada

Engineering and Physical Sciences Research Council

Vetenskapsrådet

Publisher

Stichting SciPost

Subject

Statistical and Nonlinear Physics,Atomic and Molecular Physics, and Optics,Nuclear and High Energy Physics,Condensed Matter Physics

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