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Emergent Symmetry and Tricritical Points near the deconfined Quantum Critical Point

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arxiv 1708.03050 v1 pith:CGR4A5ER submitted 2017-08-10 cond-mat.str-el

Chao-Ming Jian , Alex Rasmussen , Yi-Zhuang You , Cenke Xu This is my paper · ORCID
classification cond-mat.str-el
keywords symmetrydqcppointeasy-planenoncompacttricriticalbreakingemergent
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abstract

Recent proposal of the duality between the $N=2$ noncompact QED$_3$ and the easy-plane noncompact CP$^1$ (NCCP$^1$) model suggests that the deconfined quantum critical point (dQCP) between the easy-plane antiferromagnet and the VBS order on the square lattice may have an emergent O(4) symmetry, due to the self-duality of the $N=2$ noncompact QED$_3$. Recent numerical progresses suggest that this easy-plane dQCP does exist and it has an emergent O(4) symmetry. But for the O(4) symmetry to really emerge at the dQCP, certain O(4) symmetry breaking perturbations need to be irrelevant at the putative O(4) fixed point. It is more convenient to study these symmetry breaking perturbations in the $N=2$ noncompact QED$_3$. We demonstrate that a natural large-$N$ generalization and a controlled $1/N$ expansion supports the stability of the O(4) fixed point against the symmetry breaking perturbations. We also develop the theory for two tricritical points close to the easy-plane dQCP. One tricritical point is between the dQCP and a {\it self-dual} $Z_2$ topological order; the other is the tricritical point that connects the continuous dQCP and a first order N\'{e}el-VBS transition, motivated by recent numerical results.

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Cited by 4 Pith papers

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  1. Self-dual $S_3$ gauge theory in 2+1d: lattice model and topological phase transitions

    cond-mat.str-el 2026-08 conditional novelty 8.0 of 10

    A new sign-problem-free lattice Hamiltonian realizes the S3 quantum double with electric-magnetic duality as translation, yielding a tetracritical Ising boundary and three predicted topological transitions.

  2. Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies

    hep-th 2026-07 accept novelty 7.0 of 10

    An order-five Sp(4,Z) duality acts projectively on 3d U(1)^2 theories, and its hierarchy operations generate candidate bilayer quantum Hall states at 3/8+3/8 and 5/12+5/12.

  3. Odd Toric Code in a tilted field: Higgs-confinement multicriticality, spontaneous self-duality symmetry breaking, and valence bond solids

    cond-mat.str-el 2025-07 conditional novelty 7.0 of 10

    Numerics on the odd toric code reveal a continuous multicritical point on the self-dual line where confinement, Higgs condensation, VBS order, and self-duality breaking coincide. Hints of additional VBS phases at inte...

  4. Conformal Operator Flows of the Deconfined Quantum Criticality from $\mathrm{SO}(5)$ to $\mathrm{O}(4)$

    cond-mat.str-el 2025-07 conditional novelty 7.0 of 10

    A relevant scalar operator S persists from SO(5) to O(4) deconfined quantum criticality on the fuzzy sphere, indicating the O(4) transition is pseudo-critical rather than a genuine fixed point.

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