Haldane Phases and Ferrimagnetic Phases with Spontaneous Translational Symmetry Breakdown in Distorted Mixed Diamond Chains with Spins 1 and 1/2

Abstract

The ground states of two types of distorted mixed diamond chains with spins 1 and 1/2 are investigated using exact diagonalization, DMRG, and mapping onto low-energy effective models. In the undistorted case, the ground state consists of an array of independent spin-1 clusters separated by singlet dimers. The lattice distortion induces an effective interaction between cluster spins. When this effective interaction is antiferromagnetic, several Haldane phases appear with or without spontaneous translational symmetry breakdown (STSB). The transition between the Haldane phase without STSB and that with ðn þ 1Þ-fold STSB (n ¼ 1, 2, and 3) belongs to the same universality class as the ðn þ 1Þ-clock model. In contrast, when the effective interaction is ferromagnetic, the quantized and partial ferrimagnetic phases appear with or without STSB. An effective low-energy theory for the partial ferrimagnetic phase is presented.

Ground State Phases of Distorted S = 1 Diamond Chains

“…The origin of these PF phases can be understood by the same argument as that for the mixed diamond chain with (S, τ ) = (1, 1/2). 9) In contrast to the case of type A distortion, PF phases are also present for λ < λ c (H, F 1/6 ). The physical mechanism to stabilize the latter PF phases remains unresolved.…”

“…As in Ref. 9, we carried out the size extrapolation of the order parameter assuming the 2-dimensional (n + 1)clock model universality class. The results are shown in the phase diagrams of Figs.…”

“…In the case of the type B distortion, the effective interaction between the spins of two cluster-n's separated by a dimer is ferromagnetic for small δ B as discussed in Ref. 9. Therefore, we expect the ferrimagnetic ground state with spontaneous magnetization quantized as m = 1/(3(n + 1)) per site for small δ B in the range λ c (n, n + 1) < λ < λ c (n − 1, n).…”

“…The nature of the HDCn phase is essentially the same as that of the mixed diamond chain with (S, τ ) = (1, 1/2). Hence, we have determined the phase diagram in the same way as in Ref 9…”

Collapse of Ferrimagnetism in Two-Dimensional Heisenberg Antiferromagnet due to Frustration

“…[3][4][5][6][7][8][9] The ferrimagnetic ground state of this type is a nontrivial quantum state whose behavior is difficult to explain well only within the classical picture. Ferrimagnetism of this type was first predicted in ref.…”