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arXiv:0710.3457 · Physical Review B

Disordered ground states in a quantum frustrated spin chain with side chains

Ken'ichi Takano, Kazuo Hida

Published Apr 3, 2008• 10 citations
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Abstract

We study a frustrated mixed spin chain with side chains, where the spin species and the exchange interactions are spatially varied. A nonlinear $\ensuremath{\sigma}$ model method is formulated for this model, and a phase diagram with two disordered spin-gap phases is obtained for typical cases. Among them, we examine the case with a main chain, which consists of an alternating array of spin-1 and spin-$\frac{1}{2}$ sites, and side chains, each of which consists of a single spin-$\frac{1}{2}$ site, in great detail. Based on numerical, perturbational, and variational approaches, we propose a singlet cluster solid picture for each phase, where the ground state is expressed as a tensor product of local singlet states.

DOI
10.1103/physrevb.77.134412

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We study mixed quantum spin chains consisting of two kinds of spins with magnitudes sa{s}_{a}sa​ and sb.{s}_{b}.sb​. The spins are arrayed as ${s}_{a}\ensuremath{-}{s}_{a}\ensuremath{-}{s}_{b}\ensuremath{-}{s}_{b}$ in a unit cell and the exchange couplings are accordingly periodic with period 4. The spin Hamiltonian is mapped onto a nonlinear $\ensuremath{\sigma}$ model based on the general formula for periodic inhomogeneous spin chains. The gapless condition given by the nonlinear $\ensuremath{\sigma}$ model determines boundaries between disordered phases in the space of the exchange parameters. The phase diagram has a rich phase structure characterized by the values of sa{s}_{a}sa​ and sb.{s}_{b}.sb​. We explain all phases in the singlet-cluster-solid picture which is an extension of the valence-bond-solid picture.
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A mixed Heisenberg spin chain with frustrated side chains is investigated by numerical and perturbational calculations.A frustration-induced quantum partially polarized ferrimagnetic phase and a nonmagnetic spin quadrupolar phase are found adjacent to the conventional Lieb-Mattis-type ferrimagnetic phase or the nonmagnetic singlet cluster solid phases.The partially polarized ferrimagnetic phase has an incommensurate spin structure.Similar structures are commonly found in other frustration-induced partially polarized ferrimagnetic phases.Numerical results also suggest a series of almost critical nonmagnetic ground states in a highly frustrated regime if the side chain spins weakly couple to the main chain.
We examine the ground state of a Heisenberg model with arbitrary spin S on a one-dimensional lattice composed of diamond-shaped units. A unit includes two types of antiferromagnetic exchange interaction which frustrate each other. The system undergoes phase changes when the ratio between the exchange parameters varies. In some phases, strong frustration leads to larger local structures or clusters of spins than a dimer. We prove for arbitrary S that there exists a phase with four-spin cluster states, which was previously found numerically for a special value of in the S = 1/2 case. For S = 1/2 we show that there are three ground-state phases, and determine their boundaries.
We investigate the ground-state phase diagram of frustrated mixed-spin (1, 1/2) chains with three-site four-spin interactions employing different approaches, such as cluster mean field theory, cluster variational method, and spin-wave theory. The interplay of next-nearest-neighbor and three-site interactions leads to a plethora of magnetic and nonmagnetic phases in the ground-state phase diagram. We show that aside from the ferromagnetic and Neel orders, the ground state possesses a magnetic phase in which magnon excitations are dispersionless. The emergence of flat-band magnons is a consequence of the inhomogeneity of our frustrated mixed-spin chains and does not occur in similar uniform spin chains. We also demonstrate that the presence of three-site interaction gives rise to various nonmagnetic phases, such as antiferroquadrupole order and quantum spin-liquid phase.