Theoretical Study of S = 1/2 Frustrate Magnets by Large-scale Simulation of Numerical Diagonalizations

Abstract

We study several cases of the Heisenberg antiferromagnet by large-scale simulation of numerical- diagonalizations based on the Lanczos algorithm. This review paper presents recently obtained results for three cases: the S = 1/2 orthogonal-dimer system, the S = 1/2 kagome-lattice antiferromagnet, and the integer-spin one-dimensional antiferromagnet showing the Haldane gap. Concerning the S = 1/2 orthogonal-dimer system, our numerical-diagonalization results suggest the existence of an unknown boundary that is different from the edge of the exact-dimer phase and the edge of the Néel-ordered phase. The studies for the latter two cases treat extraordinarily large dimensions of the Hamiltonian matrices for the target systems. Calculations for the cases require use of almost all the resources in a modern powerful supercomputer.