Spin excitation of the Heisenberg antiferromagnet with frustration: from the bounce-lattice antiferromagnet through the maple-leaf-lattice antiferromagnet to the exact-dimer system

Abstract

The spin-S Heisenberg antiferromagnet on the two-dimensional lattice is investigated for S=1/2 and S=1. We consider interaction at isolated dimers ($J_{\mathrm{d}}$) and interaction bonds that form the bounce lattice ($J_{\mathrm{b}}$). For $J_{\mathrm{d}}=J_{\mathrm{b}}$, the system is reduced to the maple-leaf-lattice antiferromagnet. We primarily conduct highly parallelized numerical diagonalization to examine the spin excitation gap above the ground state for various $J_{\mathrm{b}}/J_{\mathrm{d}}$ cases. For S=1/2, we report calculations for a 42-site cluster that has not been previously treated. The S=1 case is examined for the first time for clusters up to 24 sites. Regardless of whether S=1/2 or 1, we find that the system has a gapped nature for small $J_{\mathrm{d}}/J_{\mathrm{b}}$ and becomes gapless at $J_{\mathrm{d}}/J_{\mathrm{b}}\sim 1.4$. For S=1, we also find that another gapped region appears between the gapless case at $J_{\mathrm{d}}/J_{\mathrm{b}}\sim 1.4$ and the boundary of the exact-dimer phase.

arXiv comment8 pages, 9 figures, to be published in Zeitschrift fur Naturforschung A

References in corpus (19)

• Numerical-Diagonalization Study of Spin Gap Issue of the Kagome Lattice Heisenberg Antiferromagnet
• Vanishing spin gap in a competing spin-liquid phase in the kagome Heisenberg antiferromagnet
• Reexamination of Finite-Lattice Extrapolation of Haldane Gaps
• Quantum s = 1/2 Antiferromagnets on Archimedean Lattices: The Route from Semiclassical Magnetic Order to Nonmagnetic Quantum States
• The spin-half Heisenberg antiferromagnet on two Archimedian lattices: From the bounce lattice to the maple-leaf lattice and beyond
• Anomalous Behavior of the Magnetization Process of the S = 1/2 Kagome-Lattice Heisenberg Antiferromagnet at One-Third Height of the Saturation
• The spin-1/2 Heisenberg antiferromagnet on a 1/7-depleted triangular lattice: Ground-state properties
• Magnetization Process of the Spin-S Kagome-Lattice Heisenberg Antiferromagnet
• Another Exact Ground State of a 2D Quantum Antiferromagnet
• The Interplay Between Lattice Topology, Frustration, and Spin Quantum Number in Quantum Antiferromagnets on Archimedean Lattices
• Quantum antiferromagnet bluebellite comprising a maple-leaf lattice made of spin-1/2 Cu${}^{2+}$ ions
• Maple Leaf Antiferromagnet in a Magnetic Field
• Candidate quantum disordered intermediate phase in the Heisenberg antiferromagnet on the maple-leaf lattice
• Phase diagram of the $J$-$J_d$ Heisenberg Model on the Maple-Leaf Lattice: Neural networks and density matrix renormalization group
• Noncoplanar orders and quantum disordered states in maple-leaf (anti)ferromagnets
• Two-dimensional short-range spin-spin correlations in the layered spin-3/2 maple leaf lattice antiferromagnet Na2Mn3O7 with crystal stacking disorder
• Effective spin-1 breathing kagome Hamiltonian induced by the exchange hierarchy in the maple leaf mineral bluebellite
• Haldane Gaps of Large-S Heisenberg Antiferromagnetic Chains and Asymptotic Behavior
• Chiral crossroads in $\mathrm{H}{\mathrm{o}}_3\mathrm{Sc}{\mathrm{O}}_6$: a tale of frustration in maple leaf lattice