SciPost logo

SciPost Submission Page

Topological Holography: Towards a Unification of Landau and Beyond-Landau Physics

by Heidar Moradi, Seyed Faroogh Moosavian, Apoorv Tiwari

This is not the latest submitted version.

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Seyed Faroogh Moosavian · Heidar Moradi · Apoorv Tiwari
Submission information
Preprint Link:  (pdf)
Date submitted: 2022-11-24 23:32
Submitted by: Tiwari, Apoorv
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • High-Energy Physics - Theory
  • Mathematical Physics
Approach: Theoretical


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.

Current status:
Has been resubmitted

Reports on this Submission

Anonymous Report 1 on 2023-1-29 (Invited Report)


I recommend a major revision before the second review. This paper contain results that were known and some new results. In principle, it is publishable, but a major revision is needed.


  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

Author:  Apoorv Tiwari  on 2023-04-12  [id 3583]

(in reply to Report 1 on 2023-01-29)
answer to question

We would like to thank the referee for a detailed review and some good suggestions. Many of the comments and questions were very useful to us, while others might have stemmed from misunderstandings of our constructions which we have attempted to clarify.

However, we feel that the statement “This paper contain results that were known and some new results.” is a great understatement and we believe it does not fairly characterise the content of our paper.

In the attached PDF file, we provide a detailed response and clarifications to the points raised by
the referee and a summary of changes to the manuscript.



Login to report or comment