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Chern-Simons fermionization approach to two-dimensional quantum magnets: Implications for antiferromagnetic magnons and unconventional quantum phase transitions

Rui Wang, Baigeng Wang, and Tigran A. Sedrakyan
Phys. Rev. B 98, 064402 – Published 2 August 2018
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  • INTRODUCTION
  • MODEL
  • MAGNONS IN PLANAR NÉEL ANTIFERROMAGNETS
  • NAMBU-GOLDSTONE MODE IN A CHERN-SIMONS…
  • COMPARISON: MAGNONS OF THE NÉEL STATE…
  • UNCONVENTIONAL PHASE TRANSITIONS
  • CONCLUSIONS
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    We develop an approach to describe antiferromagnetic magnons on a bipartite lattice supporting the Néel state using fractionalized degrees of freedom typically inherent to quantum spin liquids. In particular, we consider a long-range magnetically ordered state of interacting two-dimensional quantum spin-1/2 XY models using the Chern-Simons (CS) fermion representation of interacting spins. The interaction leads to Cooper instability and pairing of CS fermions, and to CS superconductivity which spontaneously violates the continuous U(1) symmetry generating a linearly dispersing gapless Nambu-Goldstone mode due to phase fluctuations. We evaluate this mode and show that it is in high-precision agreement with magnons of the corresponding Néel antiferromagnet irrespective to the lattice symmetry. Using the fermion formulation of the system with frustration, we show that the competing interactions emerge in the form of long-range interaction vertices mediated by the CS gauge field, which are responsible for restoring the continuous symmetry at sufficiently strong frustration. We identify these new interaction vertices and discuss their implications for unconventional phase transitions. We also apply the proposed theory to a model of anyons that can be tuned continuously from fermions to bosons, and discuss the results.

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    • Received 9 September 2017
    • Revised 14 July 2018

    DOI:https://doi.org/10.1103/PhysRevB.98.064402

    ©2018 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    AnyonsBosonsElectronic structureFermionsFractionalizationMagnetic orderMagnetic phase transitionsMagnonsOrder parametersQuantum phase transitionsSpin wavesSuperconducting gapSuperconducting order parameterSuperconducting phase transitionTopological materialsXY model
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    Rui Wang1,2, Baigeng Wang1,2,*, and Tigran A. Sedrakyan3,†

    • 1National Laboratory of Solid State Microstructures and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
    • 2Department of Physics, Nanjing University, Nanjing 210093, China
    • 3Department of Physics, University of Massachusetts Amherst, Amherst, Massachusetts 01003, USA

    • *bgwang@nju.edu.cn
    • †tsedrakyan@physics.umass.edu

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    Issue

    Vol. 98, Iss. 6 — 1 August 2018

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    • Figure 1
      Figure 1

      (a) The checkerboard π-flux pattern on the square lattice. The red arrows represent a π/4 (−π/4) phase when the trajectory goes along the (reversed) direction of the arrows. (b) The low-energy spectrum of the CS fermions on square lattice. The orange lines denote the boundaries of the first Brillouin zone. The CS gauge field induces an intravalley interaction (blue arrows) that favors pairing condensation at the Γ point.

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    • Figure 2
      Figure 2

      The evaluated linearity coefficients, I2/I1, of the Nambu-Goldstone modes of CS superconductors on square (a) and honeycomb (b) lattices. The red dashed line at 0.5 denotes the linearity coefficient of the spin-wave dispersion corresponding to the Néel AFM. The vertical width of the gray shaded region shows the error bar due to higher order O(k3) corrections in the self-consistent solution.

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    • Figure 3
      Figure 3

      The unit cell of the honeycomb lattice with J and J′ interactions. NN and NNN vectors ej and μj are shown, while ε is the lattice constant of triangular sublattices.

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    • Figure 4
      Figure 4

      The schematic plot illustrating the unconventional transition in the J−J′ XY model on a honeycomb lattice based on CS fermionization. For small J′, the vortex in the CS superconductor corresponds to the spin vortex in the spin XY model, and the phase fluctuation corresponds to the magnons of the magnetic ordered states. With increasing J′, the nonlocal interactions Hint(2),Hint(3) gradually drive the CS superconductor through the quantum critical point into a CSL state. The Cooper pairs of CS fermions are broken, releasing CS fermions attached to CS flux which leads to the semions in CSL.

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