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Deconfined criticalities and dualities between chiral spin liquid, topological superconductor and charge density wave Chern insulator

by Xue-Yang Song, Ya-Hui Zhang

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Submission summary

Authors (as registered SciPost users): Xue-Yang Song
Submission information
Preprint Link: scipost_202309_00008v1  (pdf)
Date accepted: 2023-11-08
Date submitted: 2023-09-09 00:17
Submitted by: Song, Xue-Yang
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • High-Energy Physics - Theory
Approaches: Theoretical, Phenomenological


We propose bi-critical and tri-critical theories between chiral spin liquid (CSL), topological superconductor (SC) and charge density wave (CDW) ordered Chern insulator with Chern number $C=2$ on square, triangular and kagome lattices. The three CDW order parameters form a manifold of $S^2$ or $S^1$ depending on whether there is easy-plane anisotropy. The skyrmion defect of the CDW order carries physical charge $2e$ and its condensation leads to a topological superconductor. The CDW-SC transitions are in the same universality classes as the celebrated deconfined quantum critical points (DQCP) between Neel order and valence bond solid order on square lattice. Both SC and CDW order can be accessed from the CSL phase through a continuous phase transition. At the CSL-SC transition, there is still CDW order fluctuations although CDW is absent in both sides. We propose three different theories for the CSL-SC transition (and CSL to easy-plane CDW transition): a $U(1)$ theory with two bosons, a $U(1)$ theory with two Dirac fermions, and an $SU(2)$ theory with two bosons. Our construction offers a derivation of the duality between these three theories as well as a promising physical realization. The $SU(2)$ theory offers a unified framework for a series of fixed points with explicit $SO(5), O(4)$ or $SO(3)\times O(2)$ symmetry. There is also a transparent duality transformation mapping SC order to easy-plane CDW order. The CSL-SC-CDW tri-critical points are invariant under this duality mapping and have an enlarged $SO(5)$ or $O(4)$ symmetry. The DQCPs between CDW and SC inherit the enlarged symmetry, emergent anomaly, and self-duality from the tri-critical point. Our analysis unifies the well-studied DQCP between symmetry breaking phases into a larger framework where they are proximate to a topologically ordered phase.

List of changes

Changes to the manuscript:
1. Add explanation for CS[g] under eq (30).
2. Cite the article of Shyta et al. PRL 127, 045701 (2021) at the end of Sec VII B.
3. Cite article Shyta et al. PRD 105, 065019 (2022) above eq (79).
4. Elaborate the derivation of eq (70) and added footnote (ref[66]).
5. Change the sign of coupling of A_r to psi in eqs(70),(71).
6. Corrected typos/notations pointed out by referee 1 in requested changes.

Published as SciPost Phys. 15, 215 (2023)

Reports on this Submission

Anonymous Report 1 on 2023-10-20 (Invited Report)


In the resubmitted version of the manuscript the authors have addressed, albeit somewhat terse, all my comments as well as fixed the majority of typos and notation inconsistencies. All in all, I believe that the manuscript is scientifically sound and meets SciPost publication criteria.

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