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Physical Review B

Frustration-induced quantum phases in mixed spin chain with frustrated side chains

和男 飛田

Published Aug 1, 2008• 0 citations
OpenAlex

Abstract

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.

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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.
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.
The ground-state properties of the S=1/2 frustrated Heisenberg spin chain with interactions up to fourth nearest neighbors are investigated by the exact-diagonalization method and density matrix renormalization group method. Our numerical calculations clarify that the ferrimagnetic state is realized in the ground state in spite of the fact that a multi-sublattice structure in the shape of the system is absent. We find that there are two types of ferrimagnetic phases: one is the well-known ferrimagnetic phase of the Lieb-Mattis type and the other is the nontrivial ferrimagnetic phase that is different from that of the Lieb-Mattis type. Our results suggest that a multi-sublattice structure of the shape is not necessarily required for the occurrence of ferrimagnetism.
The ground state phase diagram of the spin-1/2 Heisenberg frustrated ΔΔΔ-chain with a ferromagnetic main chain is investigated. In addition to the ferromagnetic phase, various nonmagnetic ground states are found. If the ferromagnetic coupling between apical spins and the main chain is strong, this model is approximated by a spin-1 bilinear-biquadratic chain and the spin quadrupolar phase with spin-2 gapless excitation is realized in addition to the Haldane and ferromagnetic phases. In the regime where the coupling between the apical spins and the main chain is weak, the numerical results which suggest the possibility of a series of phase transitions among different nonmagnetic phases are obtained. Physical pictures of these phases are discussed based on the numerical results.
The ground state phase diagram of the spin-1/2 Heisenberg frustrated ∆-chain with a ferromagnetic main chain is investigated.In addition to the ferromagnetic phase, various nonmagnetic ground states are found.If the ferromagnetic coupling between apical spins and the main chain is strong, this model is approximated by a spin-1 bilinear-biquadratic chain and the spin quadrupolar phase with spin-2 gapless excitation is realized in addition to the Haldane and ferromagnetic phases.In the regime where the coupling between the apical spins and the main chain is weak, the numerical results which suggest the possibility of a series of phase transitions among different nonmagnetic phases are obtained.Physical pictures of these phases are discussed based on the numerical results.
Using exact numerical diagonalization and the conformal field theory approach, we study the effect of magnetic frustrations due to diagonal exchange bonds in a system of two coupled mixed-spin (1,12)(1,\frac{1}{2})(1,21​) Heisenberg chains. It is established that relatively moderate frustrations are able to destroy the ferrimagnetic state and to stabilize the critical spin-liquid phase typical for half-integer-spin antiferromagnetic Heisenberg chains. Both phases are separated by a narrow but finite region occupied by a critical partially polarized ferromagnetic phase.
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-12\frac{1}{2}21​ sites, and side chains, each of which consists of a single spin-12\frac{1}{2}21​ 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.