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arXiv:cond-mat/0504360 · Journal of the Physical Society of Japan

Inversion Phenomenon and Phase Diagram of theS=1/2 Distorted Diamond Chain with theXXZInteraction Anisotropy

Akiyuki Tokuno, Kiyomi Okamoto

Published Jan 1, 2005• 8 citations
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Abstract

We discuss the anisotropies of the Hamiltonian and the wave-function in an $S=1/2$ distorted diamond chain. The ground-state phase diagram of this model is investigated using the degenerate perturbation theory up to the first order and the level spectroscopy analysis of the numerical diagonalization data. In some regions of the obtained phase diagram, the anisotropy of the Hamiltonian and that of the wave-function are inverted, which we call inversion phenomenon; the Néel phase appears for the XY-like anisotropy and the spin-fluid phase appears for the Ising-like anisotropy. Three key words are important for this nature, which are frustration, the trimer nature, and the $XXZ$ anisotropy.

DOI
10.1143/jpsjs.74s.157

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We discuss the anisotropies of the Hamiltonian and the wave-function in an S=1/2S=1/2S=1/2 distorted diamond chain. The ground-state phase diagram of this model is investigated using the degenerate perturbation theory up to the first order and the level spectroscopy analysis of the numerical diagonalization data. In some regions of the obtained phase diagram, the anisotropy of the Hamiltonian and that of the wave-function are inverted, which we call inversion phenomenon; the Néel phase appears for the XY-like anisotropy and the spin-fluid phase appears for the Ising-like anisotropy. Three key words are important for this nature, which are frustration, the trimer nature, and the XXZXXZXXZ anisotropy.
We investigate the ground-sate phase diagram of the XXZ version of the S = 1/2 distorted diamond chain by use of the degenerate perturbation theory near the truncation point. In case of the XY-like interaction anisotropy, the phase diagram consists of the Néel phase and the spin-fluid phase. For the Ising-like interaction anisotropy case, it consists of three phases: the ferrimagnetic phase, the Néel phase and the spin-fluid phase. The magnetization in the ferrimagnetic phase is 1/3 of the saturation magnetization. The remarkable nature of the phase diagram is the existence of the Néel phase, although the interaction anisotropy is XY-like. And also, the spin-fluid phase appears in spite of the Ising-like interaction anisotropy. We call these regions “inversion regions”. *Corresponding author:
We investigate the inversion phenomenon between the XXZ anisotropies of the Hamiltonian and the wave function in quantum spin chains, focusing mainly on the S = 1/2 trimerized XXZ model with the next-nearest-neighbor interactions. We have obtained the ground-state phase diagram by use of the degenerate perturbation theory and the level spectroscopy analysis of the numerical data calculated by the Lanczös method. In some parameter regions, the spin-fluid phase is realized for the Ising-like anisotropy, and the Néel phase for the XY-like anisotropy, against the ordinary situation.
We investigate the inversion phenomena between the XXZ anisotropies of the Hamiltonian and the wave function in quantum spin chains. We focus on the S=1/2 geometrically frustrated 3-leg ladder system with the XXZ interaction anisotropy. By use of the degenerate perturbation theory from the strong rung coupling limit, we have obtained the ground-state phase diagram. In some parameter regions, the Tomonaga-Luttinger spin liquid state is realized in spite of the Ising-like anisotropy, and the Neel state in spite of the XY-like anisotropy.
We investigate the inversion phenomena between the XXZ anisotropies of the Hamiltonian and the wave function in quantum spin chains. We focus on the S = 1/2 geometrically frustrated 3-leg ladder system with the XXZ interaction anisotropy. By use of the degenerate perturbation theory from the strong rung coupling limit, we have obtained the ground-state phase diagram. In some parameter regions, the Tomonaga-Luttinger spin liquid state is realized in spite of the Ising-like anisotropy, and the Neel state in spite of the XY-like anisotropy.
We explore, at T = 0, the magnetic properties of the S = 1/2 antiferromagnetic distorted diamond chain described by the Hamiltonian = ∑ j = 1 N /3 { J 1 ( S 3 j −1 · S 3 j + S 3 j · S 3 j +1 )+ J 2 S 3 j +1 · S 3 j +2 + J 3 ( S 3 j −2 · S 3 j + S 3 j · S 3 j +2 )}− H ∑ l = 1 N S l z with J 1 , J 2 , J 3 ≥ 0, which models well A 3 Cu 3 (PO 4 ) 4 with A = Ca, Sr, Bi 4 Cu 3 V 2 O 14 and azurite Cu 3 (OH) 2 (CO 3 ) 2 . We employ the physical consideration, degenerate perturbation theory, level spectroscopy analysis of the numerical diagonalization data obtained by the Lanczos method and also the density matrix renormalization group (DMRG) method. We investigate the mechanisms of the magnetization plateaux at M = M s /3 and (2/3) M s , and also show the precise phase diagrams of the ( J 2 / J 1 , J 3 / J 1 ) plane concerned with these magnetization plateaux, where M = ∑ l = 1 N S l z and M s is the saturation magnetization. We also calculate the magnetization curves and the magnetization phase diagrams by means of the DMRG method.
Ground-State Phase Diagram of (1/2,1/2,1)(1/2,1/2,1)(1/2,1/2,1) Mixed Diamond Chains with Single-Site Anisotropy
The ground-state phases of mixed diamond chains with (S,τ(1),τ(2))=(1/2,1/2,1)S, τ^{(1)}, τ^{(2)})=(1/2,1/2,1)S,τ(1),τ(2))=(1/2,1/2,1), where SSS is the magnitude of vertex spins, and τ(1)τ^{(1)}τ(1) and τ(2)τ^{(2)}τ(2) are those of apical spins, are investigated with the single-site anisotropy DDD on the τ(2)τ^{(2)}τ(2)-site. The two apical spins in each unit cell are coupled by an exchange coupling λλλ. The vertex spins are coupled with the top and bottom apical spins by exchange couplings 1+δ1+δ1+δ and 1−δ1-δ1−δ, respectively. The ground-state phase diagram is determined using the numerical exact diagonalization and DMRG method in addition to the analytical approximations in various limiting cases. The phase diagram consists of a Néel ordered phase, a nonmagnetic Tomonaga-Luttinger liquid phase, and quantized and partial ferrimagnetic phases. A region with anisotropy inversion is found where the Ising-like Néel phase is realized for the easy-plane anisotropy D>0D >0D>0 and the XY-like Tomonaga-Luttinger liquid phase is realized for the easy-axis anisotropy D<0D <0D<0 on the S=1S=1S=1 sites.