Heisenberg antiferromagnet on the Husimi lattice

Abstract

We perform a systematic study of the antiferromagnetic Heisenberg model on the Husimi lattice using numerical tensor-network methods based on Projected Entangled Simplex States (PESS). The nature of the ground state varies strongly with the spin quantum number, $S$. For $S=1/2$, it is an algebraic (gapless) quantum spin liquid. For $S=1$, it is a gapped, non-magnetic state with spontaneous breaking of triangle symmetry (a trimerized simplex-solid state). For $S=2$, it is a simplex-solid state with a spin gap and no symmetry-breaking; both integer-spin simplex-solid states are characterized by specific degeneracies in the entanglement spectrum. For $S=3/2$, and indeed for all spin values $S\ge 5/2$, the ground states have $120$-degree antiferromagnetic order. In a finite magnetic field, we find that, irrespective of the value of $S$, there is always a plateau in the magnetization at $m=1/3$.

18 pages, 25 figures;minor changes, refs updated

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Cited by in corpus (11)

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• Finite correlation length scaling with infinite projected entangled-pair states
• Optimized contraction scheme for tensor-network states
• Gapless spin liquid in the kagome Heisenberg antiferromagnet with Dzyaloshinskii-Moriya interactions
• A universal tensor network algorithm for any infinite lattice
• Husimi lattice solutions and the coherent-anomaly-method analysis for hard-square lattice gases
• Efficient calculation of three-dimensional tensor networks
• Reduction of the sign problem near $T=0$ in quantum Monte Carlo simulations
• The Hubbard model on the Bethe lattice via variational uniform tree states: metal-insulator transition and a Fermi liquid
• Self-consistent spin-wave analysis of the 1/3 magnetization plateau in the kagome antiferromagnet
• Binary lattice-gases of particles with soft exclusion: Exact phase diagrams for tree-like lattices