Gross-Neveu Heisenberg criticality: Dynamical generation of quantum spin Hall masses

Liu, Yuhai; Wang, Zhenjiu; Sato, Toshihiro; Guo, Wenan; Assaad, Fakher F.

doi:10.1103/physrevb.104.035107

Cited by 12 publications

(5 citation statements)

References 54 publications

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“…Very recently, the similar enlarged emergent symmetry has been stressed in the Dirac system with competing orders [23,64,76,77]. As pointed above, the critical properties of the transition from a semimetal to a gapped broken phase can be captured by GNY model [78][79][80][81], therefore it is believed that the GNY model is accessible to the emergent symmetry with an appropriate way [82,83]. Indeed, on the basis of GNY model, it is stressed that the emergent symmetry is responsible for various deconfined transitions in Dirac systems [50,62,64,84].…”

Section: Introductionmentioning

confidence: 79%

Critical structure and emergent symmetry of Dirac fermion systems

Zhou

2022

Preprint

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Emergent symmetry in Dirac system means that the system acquires an enlargement of two basic symmetries at some special critical point. The continuous quantum criticality between the two symmetry broken phases can be described within the framework of Gross-Neveu-Yukawa (GNY) model. Using the first-order expansion in 4 − dimensions, we study the critical structure and emergent symmetry of the chiral GNY model with N f flavors of four-component Dirac fermions coupled strongly to an O(N ) scalar field under a small O(N )-symmetry breaking perturbation. After determining the stable fixed point, we calculate the inverse correlation length exponent and the anomalous dimensions (bosonic and fermionic) for general N and N f . Further, we discuss the emergent-symmetry and the emergent supersymmetric critical point for N ≥ 4 on the basis of O(N )-GNY model. It turns out that the chiral emergent-O(N ) universality class is physically meaningful if and only if N < 2N f + 4. On this premise, the small O(N )-symmetry breaking perturbation is always irrelevant in the chiral emergent-O(N ) universality class. Our studies show that the emergent symmetry in Dirac systems has an upper boundary O(2N f + 3), depending on the flavor numbers N f . As a result, the emergent-O(4) and O(5) symmetries are possible to be found in the systems with fermion flavor N f = 1, and the emergent-O(4), O(5), O(6) and O(7) symmetries are expected to be found in the systems with fermion flavor N f = 2. Our result also suggests some rich transitions with emergent-Z2 × O(2) × O(3) symmetry and so on. Interestingly, in the emergent-O(4) universality class, there is a supersymmetric critical point which is expected to be found in the systems with fermion flavor N f = 1.

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Section: Introductionmentioning

confidence: 79%

Critical structure and emergent symmetry of Dirac fermion systems

Zhou

2022

Preprint

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“…Conversely, topological skyrmion defects of the AFM order parame- [QSHI to s-wave superconductor (SSC)] were established in Refs. [7,8]. The DQCP quantum critical region is shown above T = 5.35|λ − λc2| zν (red dashed lines, z = 1, ν = 0.58, prefactor obtained using Tc(λ = 0.04) ≈ 1/6.5) and to the right of the crossover temperature scale 30.7|λ − λc1| zν associated with the DSM-QSHI QCP (black dashed lines, z = 1, ν = 1/1.14 [7], prefactor from ∆sp(λ = 0.026) ≈ 0.41).…”

mentioning

confidence: 99%

“…The T = 0 line was previously established in Refs. [7,8]. The interaction is irrelevant for λ < λ c1 = 0.0187 (2), where the ground state is a Dirac semimetal (DSM).…”

mentioning

confidence: 99%

“…For λ > λ c2 , the spin symmetry is restored and the QSH order gives way to the SSC with a spontaneously broken U(1) symmetry. The DSM-QSHI transition exhibits fermionic Gross-Neveu-Heisenberg criticality [7,8], whereas the QSHI-SSC transition appears to be described by the theory of DQCPs. Similar to AFM-VBS transitions in other fermionic models [16][17][18], the QSHI-SSC transition can be understood within a bosonic (single-fermion excitations being gapped) DQCP picture: the QSHI is destroyed by the proliferation of charge-2e skyrmion defects in its order parameter whose condensation produces the SSC [9].…”

mentioning

confidence: 99%

“…Phase diagram of Hamiltonian(1). Two quantum critical points at λc1 = 0.0187(2) [Dirac semimetal (DSM) to quantum spin Hall insulator (QSHI)] and λc2 = 0.0332(2) [QSHI to s-wave superconductor (SSC)] were established in Refs [7,8]…”

mentioning

confidence: 99%

See 2 more Smart Citations

Thermodynamic and Dynamical Signatures of a Quantum Spin-Hall Insulator to Superconductor Transition

Hohenadler,

Liu,

Sato

et al. 2021

Preprint

Self Cite

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Critical structure and emergent symmetry of Dirac fermion systems

Zhou

2022

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

Emergent symmetry in Dirac system means that the system acquires an enlargement of two basic symmetries at some special critical point. The continuous quantum criticality between the two symmetry broken phases can be described within the framework of Gross-Neveu-Yukawa (GNY) model. Using the first-order $\epsilon$ expansion in $4-\epsilon$ dimensions, we study the critical structure and emergent symmetry of the $O(N)$-GNY model with $N_f$ flavors of four-component Dirac fermions coupled strongly to an $O(N)$ scalar field under a small $O(N)$-symmetry breaking perturbation. After determining the stable fixed point, we calculate the inverse correlation length exponent and the anomalous dimensions (bosonic and fermionic) for general $N$ and $N_f$. Further, we discuss the emergent-symmetry and the emergent supersymmetric critical point for $N\geq4$ on the basis of $O(N)$-GNY model. It turns out that the $O(N)$-GNY universality class is physically meaningful if and only if $N<2N_f+4$. On this premise, the small $O(N)$-symmetry breaking perturbation is always irrelevant in the $O(N)$-GNY universality class. Our studies show that the emergent symmetry in Dirac systems has an upper limit $O(2N_f+3)$, depending on the flavor numbers $N_f$. As a result, the emergent-$O(4)$ and $O(5)$ symmetries are possible to be found in Dirac systems with fermion flavor $N_f=1$, and the emergent-$O(4)$, $O(5)$, $O(6)$ and $O(7)$ symmetries are expected to be found in the systems with fermion flavor $N_f=2$. Our result suggests some richer transitions with emergent-$Z_2\times O(2)\times O(3)$ symmetry, and so on. Interestingly, in the $O(4)$-GNY universality class, we find that there is a new supersymmetric critical point which is expected to be found in Dirac systems with fermion flavor $N_f=1$.

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Gross-Neveu Heisenberg criticality: Dynamical generation of quantum spin Hall masses

Cited by 12 publications

References 54 publications

Critical structure and emergent symmetry of Dirac fermion systems

Critical structure and emergent symmetry of Dirac fermion systems

Thermodynamic and Dynamical Signatures of a Quantum Spin-Hall Insulator to Superconductor Transition

Critical structure and emergent symmetry of Dirac fermion systems

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