arXiv:cond-mat/0201014 · Progress of Theoretical Physics Supplement

Anisotropies of the Hamiltonian and the Wave Function: Inversion Phenomena in Quantum Spin Chains

Kiyomi Okamoto

Published Jan 1, 2002• 12 citations

Abstract

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.

DOI: 10.1143/ptps.145.208

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arXiv:cond-mat/0201014 · Progress of Theoretical Physics Supplement

Anisotropies of the Hamiltonian and the Wave Function: Inversion Phenomena in Quantum Spin Chains

Kiyomi Okamoto

Published Jan 1, 2002• 12 citations

arXiv HTML PDF

Abstract

DOI: 10.1143/ptps.145.208

Related papers

Inversion Phenomena of the Anisotropies of the Hamiltonian and the Wave Function in Quantum Spin Chains

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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.

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

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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.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.

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arXiv:cond-mat/0105119Physical review. B, Condensed matterJun 19, 200152 citations

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.

We calculate the quantum phase diagram of an XXZ chain with nearest-neighbor (NN)

{J}_{1}

and next-NN exchange

{J}_{2}

with anisotropies ${\ensuremath{\Delta}}_{1}$ and ${\ensuremath{\Delta}}_{2},$ respectively. In particular we consider the case ${\ensuremath{\Delta}}_{1}=\ensuremath{-}{\ensuremath{\Delta}}_{2},$ to interpolate between the XX chain $({\ensuremath{\Delta}}_{i}=0)$ and the isotropic model with ferromagnetic phase

{J}_{2}.

For ${\ensuremath{\Delta}}_{1}<\ensuremath{-}1,$ a ferromagnetic phase and two antiferromagnetic phases exist. For $|{\ensuremath{\Delta}}_{i}|<1,$ the boundary between the dimer and spin fluid phases is determined by the method of crossing of excitation spectra. For large

{J}_{2}{/J}_{1},

this method seems to indicate the existence of a second spin fluid critical phase. However, an analysis of the spin stiffness and magnetic susceptibility for ${\ensuremath{\Delta}}_{1}={\ensuremath{\Delta}}_{2}=1$ suggests that a small gap is present.