Simplex solids in SU(N) Heisenberg models on the kagome and checkerboard lattices

Abstract

We present a numerical study of the SU(N) Heisenberg model with the fundamental representation at each site for the kagome lattice (for N=3) and the checkerboard lattice (for N=4), which are the line graphs of the honeycomb and square lattices and thus belong to the class of bisimplex lattices. Using infinite projected entangled-pair states (iPEPS) and exact diagonalizations, we show that in both cases the ground state is a simplex solid state with a two-fold ground state degeneracy, in which the N spins belonging to a simplex (i.e. a complete graph) form a singlet. Theses states can be seen as generalizations of valence bond solid states known to be stabilized in certain SU(2) spin models.

5 pages, 5 figures, and 1 page of supplemental material

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Cited by in corpus (32)

• Spin-orbital quantum liquid on the honeycomb lattice
• Exact Diagonalization of Heisenberg SU(N) models
• Simplex valence-bond crystal in the spin-1 kagome Heisenberg antiferromagnet
• Entropy dependence of correlations in one-dimensional SU(N) antiferromagnets
• Solving correlation clustering with QAOA and a Rydberg qudit system: a full-stack approach
• Quantum spin models for the SU(n)_1 Wess-Zumino-Witten model
• Variational Monte-Carlo investigation of SU($N$) Heisenberg chains
• Structure of Spin Correlations in High Temperature SU($N$) Quantum Magnets
• Variational optimization of tensor-network states with the honeycomb-lattice corner transfer matrix
• Many-body Physics of Ultracold Alkaline-Earth atoms with SU($N$)-symmetric interactions
• Exact diagonalization of $\mathrm{SU}(N)$ Heisenberg and AKLT chains using the full $\mathrm{SU}(N)$ symmetry
• Thermodynamics of 3D Kitaev quantum spin liquids via tensor networks
• Numerical study of magnetization plateaux in the spin-1/2 Heisenberg antiferromagnet on the checkerboard lattice
• Phase diagram of the chiral SU(3) antiferromagnet on the kagome lattice
• Density Matrix Renormalization Group Study of Nematicity in Two Dimensions: Application to a Spin-$1$ Bilinear-Biquadratic Model on the Square Lattice
• Critical line of the triangular Ising antiferromagnet in a field from a $C_3$-symmetric corner transfer matrix algorithm
• Corner transfer matrix renormalization group approach in the zoo of Archimedean lattices
• Quantum trimer models and topological SU(3) spin liquids on the kagome lattice
• Nearly degenerate ground states of a checkerboard antiferromagnet and their bosonic interpretation
• Coherent control over the high-dimensional space of the nuclear spin of alkaline-earth atoms
• Relation between the noise correlations and the spin structure factor for Mott-insulating states in SU$(N)$ Hubbard models
• Stabilization of the chiral phase of the SU($6m$) Heisenberg model on the honeycomb lattice with $m$ particles per site for $m$ larger than 1
• Single-layer tensor network approach for three-dimensional quantum systems
• Transition from band insulator to Mott insulator and formation of local moment in half-filled ionic SU($N$) Hubbard model
• State selective cooling of $\mathrm{SU}(N)$ Fermi-gases
• Valence-Bond Solid phases in the spin-$1/2$ Kekule-Heisenberg model
• Anisotropy-driven magnetic phase transitions in SU(4)-symmetric Fermi gas in three-dimensional optical lattices
• Ground-state phase diagram of the SU($4$) Heisenberg model on a plaquette lattice
• Unnecessary quantum criticality in $SU(3)$ kagome magnets
• Simplex Crystal Ground State and Magnetization Plateaus in the Spin-$1/2$ Heisenberg Model on the Ruby Lattice
• Fragility of the nematic spin liquid induced by diagonal couplings in the square-lattice SU(3) model
• The algebraic spin liquid in the SU(6) Heisenberg model on the kagome lattice