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Unnecessary quantum criticality in $SU(3)$ kagome magnets

Yunchao Zhang, Xue-Yang Song, T. Senthil

Abstract

Algebraic/Dirac spin liquids (DSLs) are a class of critical quantum ground states that do not have a quasi-particle description. DSLs and related spin liquid phases often arise in strongly frustrated quantum spin systems, in which strong correlations and quantum fluctuations among constituent spins persist down to zero temperature. In this work, we analyze Mott insulating phases of $SU(3)$ fermions on a kagome lattice which may realize a DSL phase, described at low energies by $(2 + 1)d$ quantum electrodynamics (QED$_3$) with $N_f=6$ Dirac fermions. By analyzing the action of physical symmetries on the operators of the QED$_3$ theory, we conclude that the low energy DSL is a quantum critical point that can be accessed by tuning a single microscopic parameter. Aided by the emergent symmetry and anomalies of the low energy effective theory, we conjecture and present supporting arguments that the $SU(3)$ Kagome magnet DSL is an unnecessary quantum critical point, lying completely within a single phase.

Unnecessary quantum criticality in $SU(3)$ kagome magnets

Abstract

Algebraic/Dirac spin liquids (DSLs) are a class of critical quantum ground states that do not have a quasi-particle description. DSLs and related spin liquid phases often arise in strongly frustrated quantum spin systems, in which strong correlations and quantum fluctuations among constituent spins persist down to zero temperature. In this work, we analyze Mott insulating phases of fermions on a kagome lattice which may realize a DSL phase, described at low energies by quantum electrodynamics (QED) with Dirac fermions. By analyzing the action of physical symmetries on the operators of the QED theory, we conclude that the low energy DSL is a quantum critical point that can be accessed by tuning a single microscopic parameter. Aided by the emergent symmetry and anomalies of the low energy effective theory, we conjecture and present supporting arguments that the Kagome magnet DSL is an unnecessary quantum critical point, lying completely within a single phase.

Paper Structure

This paper contains 22 sections, 71 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Candidate DSL on on the kagome lattice
  3. Low energy field theory
  4. Monopole operators
  5. Symmetries of the DSL
  6. Symmetries of the microscopic system: the group $G_{UV}$
  7. Symmetries of QED$_3$: the group $G_{IR}$
  8. Embedding $G_{UV}$ into $G_{IR}$
  9. 't Hooft anomalies of $N_f=6$ QED$_3$
  10. $(SU(6)\times U(1)_{top})/\mathbb{Z}_6$
  11. $(SU(3)\times SU(3))/\mathbb{Z}_3$
  12. Unnecessary Criticality
  13. Discussion and Outlook
  14. Acknowledgments
  15. Mean field state and continuum limit
  16. ...and 7 more sections

Figures (3)

  • Figure 1: (a) Dispersion of the tight binding spinon Hamiltonian, Eq. \ref{['eq:hopping']}, with $t=1$. The Brioullin zone path is shown in (b). We observe an upper flat band and lower bands which intersect at Dirac points at $\boldsymbol{K}$ and $\boldsymbol{K}'$.
  • Figure 2: A schematic illustration of the ground state in the $U\rightarrow \infty$ limit, known as a simplex VBS state, with each collection of $SU(3)$ spins forming a trimer singlet that covers the entire kagome lattice. The ground state preserves $C_3$ and lattice translation symmetries, with $C_6$ (and consequently, lattice inversion) spontaneously broken.
  • Figure 3: Conventions for the kagome lattice symmetries. The choice of unit cell is outlined in red, and the lattice space group generators are $C_6$, $\mathcal{R}_y$, and translations along the primitive lattice vectors $\boldsymbol{R}_{1,2}$.