Excited State of Dimer in Quantum Antiferromagnetic Spin System

Takehiko Oguchi

Hiroki Nakano, Tôru Sakai

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 d ) and interaction bonds that form the bounce lattice ( J b ). For J d = J 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 b / J 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 d / J b and becomes gapless at J d / J b ∼ 1.4. For S = 1, we also find that another gapped region appears between the gapless case at J d / J b ∼ 1.4 and the boundary of the exact-dimer phase.

Johannes Richter, Nedko B. Ivanov, J. Schulenburg

We examine the ground state and the excitations of an one-dimensional Heisenberg spin 1/2 antiferromagnet with alternating dimers and four-spin plaquettes (dimer-plaquette chain). The properties of the system depend on the competing dimer and plaquette bonds. Several exact, exact-numerical and perturbational results are presented. We find that the system is gapped for all parameter values. For the latter one we find an effective S=1 Haldane like behaviour in the limit of dominating dimer bonds. The model considered is related to the recently found 1/5-depleted square-lattice Heisenberg system $CaV_4O_9$.

W.J. Caspers, Wim Magnus

Valeri N. Kotov, Oleg P. Sushkov, Zheng Weihong +1 more

We consider quantum spin systems with dimerization, which at strong coupling have singlet ground states. To account for strong correlations, the $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ elementary excitations are described as a dilute Bose gas with infinite on-site repulsion. This approach is applied to the two-layer Heisenberg antiferromagnet at $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ with general couplings. Our analytic results for the triplet gap, the excitation spectrum, and the location of the quantum critical point are in excellent agreement with numerical results obtained by dimer series expansions.

Wolfram Brenig