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.

arXiv comment5 pages, 5 figures, and 1 page of supplemental material

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• 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
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• SU(6) Heisenberg model on the honeycomb lattice: competition between plaquette and chiral order
• A universal tensor network algorithm for any infinite lattice
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• Global symmetries in tensor network states: symmetric tensors versus minimal bond dimension
• Infinite Projected Entangled-Pair State algorithm for ruby and triangle-honeycomb lattices
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• SU(3) Fermions on the Honeycomb Lattice at 1/3-Filling
• Spin--lattice coupling and the emergence of the trimerized phase in the $S=1$ Kagome antiferromagnet Na${}_2$Ti${}_3$Cl${}_8$
• Variational Monte-Carlo investigation of SU($N$) Heisenberg chains
• Linear Flavor-Wave Theory for Fully Antisymmetric $\mathrm{SU}(N)$ Irreducible Representations
• Structure of Spin Correlations in High Temperature SU($N$) Quantum Magnets
• Tetramerization in a SU(4)-Heisenberg model on the honeycomb lattice
• Kagome model for a ${\mathbb{Z}}_2$ quantum spin liquid
• Variational optimization of tensor-network states with the honeycomb-lattice corner transfer matrix
• Nematic Spin Liquid Phase in a Frustrated Spin-1 System on the Square Lattice
• Abelian and non-abelian symmetries in infinite projected entangled pair states
• Exact diagonalization of $\mathrm{SU}(N)$ Heisenberg and AKLT chains using the full $\mathrm{SU}(N)$ symmetry
• Many-body Physics of Ultracold Alkaline-Earth atoms with SU($N$)-symmetric interactions
• Thermodynamics of 3D Kitaev quantum spin liquids via tensor networks
• Phase diagram of the chiral SU(3) antiferromagnet on the kagome lattice
• Numerical study of magnetization plateaux in the spin-1/2 Heisenberg antiferromagnet on the checkerboard lattice
• A gapped SU(3) spin liquid with Z_3 topological order
• Spin-$\frac{1}{2}$ kagome Heisenberg antiferromagnet with strong breathing anisotropy
• Mott insulators of ultracold fermionic alkaline earth atoms in three dimensions
• Fine-Grained Tensor Network Methods
• Density Matrix Renormalization Group Study of Nematicity in Two Dimensions: Application to a Spin-$1$ Bilinear-Biquadratic Model on the Square Lattice
• Corner transfer matrix renormalization group approach in the zoo of Archimedean lattices
• Critical line of the triangular Ising antiferromagnet in a field from a $C_3$-symmetric corner transfer matrix algorithm
• Thermal bosons in 3d optical lattices via tensor networks
• Quantum trimer models and topological SU(3) spin liquids on the kagome lattice
• Coherent control over the high-dimensional space of the nuclear spin of alkaline-earth atoms
• Nearly degenerate ground states of a checkerboard antiferromagnet and their bosonic interpretation
• Relation between the noise correlations and the spin structure factor for Mott-insulating states in SU$(N)$ Hubbard models
• Single-layer tensor network approach for three-dimensional quantum systems
• 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
• State selective cooling of $\mathrm{SU}(N)$ Fermi-gases
• Transition from band insulator to Mott insulator and formation of local moment in half-filled ionic SU($N$) Hubbard model
• Order by disorder in a four flavor Mott-insulator on the fcc lattice
• Anisotropy-driven magnetic phase transitions in SU(4)-symmetric Fermi gas in three-dimensional optical lattices
• Competition between three-sublattice order and superfluidity in the quantum 3-state Potts model of ultracold bosons and fermions on a square optical lattice
• Valence-Bond Solid phases in the spin-$1/2$ Kekule-Heisenberg model
• Unnecessary quantum criticality in $SU(3)$ kagome magnets
• Ground-state phase diagram of the SU($4$) Heisenberg model on a plaquette 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
• Simplex Crystal Ground State and Magnetization Plateaus in the Spin-$1/2$ Heisenberg Model on the Ruby Lattice