Theoretical Study of Quantum-Spin Systems with Competing Interactions

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We have studied the static and dynamic properties of the spin-1/2 Heisenberg magnet on the one-dimensional lattice with first- and second-neighbor interactions. Assuming that the second-neighbor interaction is antiferromagnetic, we have considered the case where the first-neighbor inter-action is antiferromagnetic and the case where it is ferromagnetic. (The former and latter cases are called case AF and case F, respectively.)1. static Properties(1) Ground-state properties: We have calculated exactly the energy, the singlet-triplet energy gap, the spin correlation function, and the magnetization for finite-size systems of up to 20 spins, and have extrapolated these results to estimate the values of the above quantities in the infinite-size limit. In particular, we have found that with increasing magnitude of the second-neighbor interaction the ground state in case AF undergoes a phase transition from the spin-fluid phase with no energy gap to the dimer phase with finite energy gap, whe … More n both interactions are isotropic or have the XY-type anisotropy.(2) Finite-temperature properties: Using the quantum transfer matrix method, we have calculated the temperature dependence of the internal energy and the specific heat and also that of the inverse correlation length and the wave number, by both of which the asymptotic behavior of the spin cor-relation function in the long-distance limit is described. We have found that, both in case AF and case F, there exists a quantum analog of the disorder line which characterizes the interaction and temperature dependence of the asymptotic behavior of the spin correlation function in the long-distance limit.2. Dynamic PropertiesWe have investigated the dynamic properties of case AF, confining ourselves to the case where the interactions have the Ising-type anisotropy. Near the degenerate point in the Ising limit, solitons in the Neel and (2,2)-antiphase states and triplet-dimer excitations in the dimer state have been found as propagating modes. These excitations have also been found to dominate the shape of the central peak in the dynamic spin correlation function, through the comparison with the numerical results obtained by an exact diagonalization method for a finite-size system of 12 spins. Less