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

Published Jan 1, 2013• 2 citations

OpenAlex

Abstract

Related papers

Kiyomi Okamoto

arXiv:1310.3394Asia Pacific Physics Conference (APPC)Mar 19, 20140 citations

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

Kiyomi Okamoto

arXiv:cond-mat/0201014Progress of Theoretical Physics SupplementJan 1, 200212 citations

Inversion Phenomena of the Anisotropies of the Hamiltonian and the Wave-Function in the Distorted Diamond Type Spin Chain

Kiyomi Okamoto, Yutaka Ichikawa

Jan 1, 20019 citations

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

Akiyuki Tokuno, Kiyomi Okamoto

arXiv:cond-mat/0504360Journal of the Physical Society of JapanJan 1, 20058 citations

Ground-State Phase Diagram of an Anisotropic S = 1/2 Ladder with Different Leg Interactions

Takashi Tonegawa, Toshiya Hikihara, Kiyomi Okamoto +2 more

arXiv:1808.01090Journal of the Physical Society of JapanSep 12, 20188 citations

Ground-state phase diagram of an anisotropic S=l/2 ladder with alternating rung interactions

Takashi Tonegawa, Kiyomi Okamoto, Toshiya Hikihara +1 more

arXiv:1510.04928Journal of Physics Conference SeriesFeb 5, 20162 citations

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

Published Jan 1, 2013• 2 citations

OpenAlex

Abstract

Related papers

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

Kiyomi Okamoto

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.

arXiv:1310.3394Asia Pacific Physics Conference (APPC)Mar 19, 20140 citations

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

Kiyomi Okamoto

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 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.

arXiv:cond-mat/0201014Progress of Theoretical Physics SupplementJan 1, 200212 citations

Inversion Phenomena of the Anisotropies of the Hamiltonian and the Wave-Function in the Distorted Diamond Type Spin Chain

Kiyomi Okamoto, Yutaka Ichikawa

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 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:

Jan 1, 20019 citations

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

Akiyuki Tokuno, Kiyomi Okamoto

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.

arXiv:cond-mat/0504360Journal of the Physical Society of JapanJan 1, 20058 citations

Ground-State Phase Diagram of an Anisotropic S = 1/2 Ladder with Different Leg Interactions

Takashi Tonegawa, Toshiya Hikihara, Kiyomi Okamoto +2 more

We explore the ground-state phase diagram of the $S=1/2$ two-leg ladder with different leg interactions. The $xy$ and $z$ components of the leg interactions between nearest-neighbor spins in the $a$ ( $b$ ) leg are respectively denoted by $J_{{\rm l},a}$ and $Δ_{\rm l} J_{{\rm l},a}$ ( $J_{{\rm l},b}$ and $Δ_{\rm l} J_{{\rm l},b}$ ). On the other hand, the $xy$ and $z$ components of the uniform rung interactions are respectively denoted by $Γ_{\rm r} J_{\rm r}$ and $J_{\rm r}$ . In the above, $Δ_{\rm l}$ and $Γ_{\rm r}$ are the $XXZ$ -type anisotropy parameters for the leg and rung interactions, respectively. This system has a frustration when $J_{{\rm l},a} J_{{\rm l},b}<0$ irrespective of the sign of $J_{\rm r}$ . The phase diagram on the $Δ_{\rm l}$ ( $|Δ_{\rm l}| \leq 1.0$ ) versus $J_{{\rm l},b}$ ( $-2.0\leq J_{{\rm l},b}\leq 3.0$ ) plane in the case where $J_{{\rm l},a}=0.2$ , $J_{\rm r}=-1.0$ , and $Γ_{\rm r} = 0.5$ is determined numerically. We employ the physical consideration, and the level spectroscopy and phenomenological renormalization-group analyses of the numerical date obtained by the exact diagonalization method. The resultant phase diagram contains the ferromagnetic, Haldane, N{é}el, nematic Tomonaga-Luttinger liquid (TLL), partial ferrimagnetic, and $XY1$ phases. Interestingly enough, the nematic TLL phase appears in the strong-rung unfrustrated region as well as in the strong-rung frustrated one. We perform the first-order perturbational calculations from the strong rung coupling limit to elucidate the characteristic features of the phase diagram. Furthermore, we make the density-matrix renormalization-group calculations for some physical quantities such as the energy gaps, the local magnetization, and the spin correlation functions to supplement the reliability of the phase diagram.We explore the ground-state phase diagram of the $S=1/2$ two-leg ladder with different leg interactions. The $xy$ and $z$ components of the leg interactions between nearest-neighbor spins in the $a$ ($b$) leg are respectively denoted by $J_{{\rm l},a}$ and $Δ_{\rm l} J_{{\rm l},a}$ ($J_{{\rm l},b}$ and $Δ_{\rm l} J_{{\rm l},b}$). On the other hand, the $xy$ and $z$ components of the uniform rung interactions are respectively denoted by $Γ_{\rm r} J_{\rm r}$ and $J_{\rm r}$. In the above, $Δ_{\rm l}$ and $Γ_{\rm r}$ are the $XXZ$-type anisotropy parameters for the leg and rung interactions, respectively. This system has a frustration when $J_{{\rm l},a} J_{{\rm l},b}<0$ irrespective of the sign of $J_{\rm r}$. The phase diagram on the $Δ_{\rm l}$ ($|Δ_{\rm l}| \leq 1.0$) versus $J_{{\rm l},b}$ ($-2.0\leq J_{{\rm l},b}\leq 3.0$) plane in the case where $J_{{\rm l},a}=0.2$, $J_{\rm r}=-1.0$, and $Γ_{\rm r} = 0.5$ is determined numerically. We employ the physical consideration, and the level spectroscopy and phenomenological renormalization-group analyses of the numerical date obtained by the exact diagonalization method. The resultant phase diagram contains the ferromagnetic, Haldane, N{é}el, nematic Tomonaga-Luttinger liquid (TLL), partial ferrimagnetic, and $XY1$ phases. Interestingly enough, the nematic TLL phase appears in the strong-rung unfrustrated region as well as in the strong-rung frustrated one. We perform the first-order perturbational calculations from the strong rung coupling limit to elucidate the characteristic features of the phase diagram. Furthermore, we make the density-matrix renormalization-group calculations for some physical quantities such as the energy gaps, the local magnetization, and the spin correlation functions to supplement the reliability of the phase diagram.

arXiv:1808.01090Journal of the Physical Society of JapanSep 12, 20188 citations

Ground-state phase diagram of an anisotropic S=l/2 ladder with alternating rung interactions

Takashi Tonegawa, Kiyomi Okamoto, Toshiya Hikihara +1 more

Employing mainly numerical methods, we explore the ground-state phase diagram of an anisotropic S = 1/2 ladder, in which leg interactions are uniform and isotropic, while rung interactions are alternating and have a common Ising-t.ype anisotropy. We determine the phase diagram in the case where J leg = 0.2 (antiferromagnetic), J rung = —1.0 (ferromagnetic) and | J ' rung | ≤ 1.0, the first one being the magnitude of the leg interaction and the second and third ones those of the rung interactions, which are alternating. It is emphasized that the system has a frustration when J ' rung is positive. We find that., in the frustrated region, the Haldane state appears as the ground state even when the Ising character of rung interactions is strong. This appearance of the Haldane phase is contrary to the ordinary situation, and it is called the inversion phenomenon concerning the interaction anisotropy. We also find that an incommensurate state becomes the ground state in a portion of the Haldane phase region.Employing mainly numerical methods, we explore the ground-state phase diagram of an anisotropic S = 1/2 ladder, in which leg interactions are uniform and isotropic, while rung interactions are alternating and have a common Ising-t.ype anisotropy. We determine the phase diagram in the case where J leg = 0.2 (antiferromagnetic), J rung = —1.0 (ferromagnetic) and | J ' rung | ≤ 1.0, the first one being the magnitude of the leg interaction and the second and third ones those of the rung interactions, which are alternating. It is emphasized that the system has a frustration when J ' rung is positive. We find that., in the frustrated region, the Haldane state appears as the ground state even when the Ising character of rung interactions is strong. This appearance of the Haldane phase is contrary to the ordinary situation, and it is called the inversion phenomenon concerning the interaction anisotropy. We also find that an incommensurate state becomes the ground state in a portion of the Haldane phase region.

arXiv:1510.04928Journal of Physics Conference SeriesFeb 5, 20162 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 explore the ground-state phase diagram of the

S=1/2

two-leg ladder with different leg interactions. The

xy

and

z

components of the leg interactions between nearest-neighbor spins in the

a

(

b

) leg are respectively denoted by

J_{{\rm l},a}

and

Δ_{\rm l} J_{{\rm l},a}

(

J_{{\rm l},b}

and

Δ_{\rm l} J_{{\rm l},b}

). On the other hand, the

xy

and

z

components of the uniform rung interactions are respectively denoted by

Γ_{\rm r} J_{\rm r}

and

J_{\rm r}

. In the above,

Δ_{\rm l}

and

Γ_{\rm r}

are the

XXZ

-type anisotropy parameters for the leg and rung interactions, respectively. This system has a frustration when

J_{{\rm l},a} J_{{\rm l},b}<0

irrespective of the sign of

J_{\rm r}

. The phase diagram on the

Δ_{\rm l}

(

|Δ_{\rm l}| \leq 1.0

) versus

J_{{\rm l},b}

(

-2.0\leq J_{{\rm l},b}\leq 3.0

) plane in the case where

J_{{\rm l},a}=0.2

J_{\rm r}=-1.0

, and

Γ_{\rm r} = 0.5

is determined numerically. We employ the physical consideration, and the level spectroscopy and phenomenological renormalization-group analyses of the numerical date obtained by the exact diagonalization method. The resultant phase diagram contains the ferromagnetic, Haldane, N{é}el, nematic Tomonaga-Luttinger liquid (TLL), partial ferrimagnetic, and

XY1

phases. Interestingly enough, the nematic TLL phase appears in the strong-rung unfrustrated region as well as in the strong-rung frustrated one. We perform the first-order perturbational calculations from the strong rung coupling limit to elucidate the characteristic features of the phase diagram. Furthermore, we make the density-matrix renormalization-group calculations for some physical quantities such as the energy gaps, the local magnetization, and the spin correlation functions to supplement the reliability of the phase diagram.