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arXiv:2206.08939 · SciPost Physics

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

Xue-Yang Song, Ya-Hui Zhang

Published Nov 29, 2023• 15 citations
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Abstract

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 C = 2 on square, triangular and Kagome lattices. The three CDW order parameters form a manifold of S^2 S 2 or S^1 S 1 depending on whether there is easy-plane anisotropy. The skyrmion defect of the CDW order carries physical charge 2e 2 e 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) U ( 1 ) theory with two bosons, a U(1) U ( 1 ) theory with two Dirac fermions, and an SU(2) S U ( 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) S U ( 2 ) theory offers a unified framework for a series of fixed points with explicit SO(5), O(4) S O ( 5 ) , O ( 4 ) or SO(3)× O(2) S O ( 3 ) × 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) S O ( 5

DOI
10.21468/scipostphys.15.5.215

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We show that several distinct broken-symmetry phases in a spin-12\frac{1}{2}21​ antiferromagnet on a square lattice with easy-plane anisotropy, including valence bond solid, chiral spin liquid, and the XY-ordered state, can all be accessed by perturbing a multicritical point with two massless Dirac fermions coupled to a level-one Chern-Simons gauge field. This allows for a unified description of these phases, as well as the phase transitions between them. In a specific phase transition, our analysis provides a lattice realization of one of the recently proposed fermion-boson dualities, thus lending support to it. We also briefly discuss the relation between our paper and the long-sought deconfined criticality in such systems.
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