Simplex solid states of SU(N) quantum antiferromagnets

Abstract

I define a set of wavefunctions for SU(N) lattice antiferromagnets, analogous to the valence bond solid states of Affleck, Kennedy, Lieb, and Tasaki (AKLT), in which the singlets are extended over N-site simplices. As with the valence bond solids, the new simplex solid (SS) states are extinguished by certain local projection operators, allowing us to construct Hamiltonians with local interactions which render the SS states exact ground states. Using a coherent state representation, we show that the quantum correlations in each SS state are calculable as the finite temperature correlations of an associated classical model, with N-spin interactions, on the same lattice. In three and higher dimensions, the SS states can spontaneously break SU(N) and exhibit N-sublattice long-ranged order, as a function of a discrete parameter which fixes the local representation of SU(N). I analyze this transition using a classical mean field approach. For N>2 the ordered state is selected via an "order by disorder" mechanism. As in the AKLT case, the bulk representations fractionalize at an edge, and the ground state entropy is proportional to the volume of the boundary.

14 pages, 8 figures, minor typos corrected

References in corpus (6)

• Quantum dimer model on the kagome lattice: solvable dimer liquid and Ising gauge theory
• Fractionalization, topological order, and cuprate superconductivity
• Valence bond solids for SU(n) spin chains: exact models, spinon confinement, and the Haldane gap
• Exact spontaneous plaquette ground states for high-spin ladder models
• Resonating singlet valence plaquettes
• Generalized Valence Bond State and Solvable Models for Spin-1/2 Systems with Orbital degeneracy

Cited by in corpus (54)

• Quantum Spin Liquid States
• Gapless spin-liquid ground state in the $S=1/2$ kagome antiferromagnet
• Entanglement of Exact Excited States of AKLT Models: Exact Results, Many-Body Scars and the Violation of Strong ETH
• Tensor renormalization of quantum many-body systems using projected entangled simplex states
• Class of exactly solvable SO(n) symmetric spin chains with matrix product ground states
• Topological liquids and valence cluster states in two-dimensional SU(N) magnets
• Resonating plaquette phases in large spin cold atom systems
• Dimerized Solids and Resonating Plaquette Order in SU(N)-Dirac Fermions
• Simplex solids in SU(N) Heisenberg models on the kagome and checkerboard lattices
• Simplex valence-bond crystal in the spin-1 kagome Heisenberg antiferromagnet
• Optimized contraction scheme for tensor-network states
• Trimerized ground state of the spin-1 Heisenberg antiferromagnet on the kagome lattice
• Entropy dependence of correlations in one-dimensional SU(N) antiferromagnets
• Quantum spin models for the SU(n)_1 Wess-Zumino-Witten model
• Gapless spin liquid in the kagome Heisenberg antiferromagnet with Dzyaloshinskii-Moriya interactions
• Competing states in the SU(3) Heisenberg model on the honeycomb lattice: Plaquette valence-bond crystal versus dimerized color-ordered state
• Valence bond solid states with symplectic symmetry
• Topologically distinct classes of valence bond solid states with their parent Hamiltonians
• Supersymmetric Valence Bond Solid States
• Exact diagonalization of Heisenberg $SU(N)$ chains in the fully symmetric and antisymmetric representations
• SU(3) Fermions on the Honeycomb Lattice at 1/3-Filling
• Order and Disorder in AKLT Antiferromagnets in Three Dimensions
• 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
• Tetramerization in a SU(4)-Heisenberg model on the honeycomb lattice
• Continuous quantum phase transition between two topologically distinct valence bond solid states associated with the same spin value
• Entanglement and SU(n) symmetry in one-dimensional valence bond solid states
• Spontaneous Parity Violation in a Quantum Spin Chain
• Heisenberg antiferromagnet on the Husimi lattice
• Phase diagram of the chiral SU(3) antiferromagnet on the kagome lattice
• A gapped SU(3) spin liquid with Z_3 topological order
• Mott insulators of ultracold fermionic alkaline earth atoms in three dimensions
• Spin 3/2 dimer model
• Spontaneous trimerization in two-dimensional Antiferromagnets
• Hidden Bethe states in a partially integrable model
• Hidden Order and Dynamics in Supersymmetric Valence Bond Solid States -- Super-Matrix Product State Formalism
• Possible SU(3) Chiral Spin Liquid on the Kagome Lattice
• SU($N$) altermagnetism: Lattice models, magnon modes, and flavor-split bands
• Critical exponents of nonlinear sigma model on Grassmann manifold $U(N)/U(m)U(N-m)$ by $1/N$ expansion
• 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
• Entanglement blossom in a simplex matryoshka
• Classes of topological qubits from low-dimensional quantum spin systems
• Transition from band insulator to Mott insulator and formation of local moment in half-filled ionic SU($N$) Hubbard model
• Lowest-energy states in parity-transformation eigenspaces of SO(N) spin chain
• Competition between three-sublattice order and superfluidity in the quantum 3-state Potts model of ultracold bosons and fermions on a square optical lattice
• Topological Many-Body States in Quantum Antiferromagnets via Fuzzy Super-Geometry
• Momentum classification of SU($n$) spin chains using extended Young Tableaux
• Unnecessary quantum criticality in $SU(3)$ kagome magnets
• Self-consistent spin-wave analysis of the 1/3 magnetization plateau in the kagome antiferromagnet
• Ground-state phase diagram of the SU($4$) Heisenberg model on a plaquette lattice
• Ground State Phase Diagram of $\text{SU}(3)$ $t$-$J$ Chain
• A brief note on the G${}_2$ Affleck-Kennedy-Lieb-Tasaki chain
• SU(4) Kondo Lattice in Semiconductor Moiré Materials
• The algebraic spin liquid in the SU(6) Heisenberg model on the kagome lattice