Spin Ladder with Anisotropic Ferromagnetic Legs in a Transverse Magnetic Field

G. I. Japaridze, A. Langari, S. Mahdavifar

Published Jan 1, 2007• 13 citations

Abstract

Abstract. We study the ground state phase diagram of a two-leg spin ladder with anisotropic ferromagnetic leg couplings under the influence of a symmetry breaking transverse magnetic field by the exact diagonalization technique. In the case of antiferromagnetic coupling between legs we identified two phase transitions in the plane of magnetic field vs interchain coupling strength. The first one corresponds to the transition from the gapped rung-singlet phase to the gapped stripe-ferromagnetic phase. The second one represents the transition from the gapped stripe-ferromagnetic phase into the fully polarized ferromagnetic phase. PACS numbers: 75.10.Jm Quantized spin models, 75.10.Pq Spin chain modelsSpin Ladder with Anisotropic Ferromagnetic Legs in a Transverse Magnetic Field 2 1.

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Spin Ladder with Anisotropic Ferromagnetic Legs in a Transverse Magnetic Field

G. I. Japaridze, A. Langari, S. Mahdavifar

Published Jan 1, 2007• 13 citations

OpenAlex

Abstract

Related papers

Spin ladder with anisotropic ferromagnetic legs in a transverse magnetic field

G I Japaridze, A Langari, S Mahdavifar

We have studied the ground-state phase diagram of a two-leg spin ladder with anisotropic ferromagnetic leg couplings under the influence of a symmetry-breaking transverse magnetic field by the exact diagonalization technique. In the case of antiferromagnetic coupling between legs we identified two phase transitions in the plane of magnetic field versus interchain coupling strength. The first corresponds to the transition from the gapped rung-singlet phase to the gapped stripe-ferromagnetic phase. The second represents the transition from the gapped stripe-ferromagnetic phase into the fully polarized ferromagnetic phase.We have studied the ground-state phase diagram of a two-leg spin ladder with anisotropic ferromagnetic leg couplings under the influence of a symmetry-breaking transverse magnetic field by the exact diagonalization technique. In the case of antiferromagnetic coupling between legs we identified two phase transitions in the plane of magnetic field versus interchain coupling strength. The first corresponds to the transition from the gapped rung-singlet phase to the gapped stripe-ferromagnetic phase. The second represents the transition from the gapped stripe-ferromagnetic phase into the fully polarized ferromagnetic phase.

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Ningsheng Zhu, Xiaoqun Wang, Changfeng Chen

Using the density matrix renormalization group method, we have obtained the ground-state phase diagram of a spin-1/2 two-leg antiferromagnetic Heisenberg ladder with a ferromagnetic diagonal interaction ${J}_{\ifmmode\times\else\texttimes\fi{}}.$ The boundary between the two phases found in the system, the Haldane phase and the singlet phase, lies in the frustrated area of the parameter space, i.e., both the rung coupling ${J}_{\ensuremath{\perp}}$ and the diagonal coupling ${J}_{\ifmmode\times\else\texttimes\fi{}}$ are ferromagnetic. The spin gap is found to be insensitive to the change of the ferromagnetic diagonal coupling strength when the ratio of the rung coupling constant ${J}_{\ensuremath{\perp}}$ to the leg coupling constant ${J}_{\ensuremath{\Vert}}$ is 0.5, in agreement with the analysis of recent experimental spin susceptibility data.Using the density matrix renormalization group method, we have obtained the ground-state phase diagram of a spin-1/2 two-leg antiferromagnetic Heisenberg ladder with a ferromagnetic diagonal interaction ${J}_{\ifmmode\times\else\texttimes\fi{}}.$ The boundary between the two phases found in the system, the Haldane phase and the singlet phase, lies in the frustrated area of the parameter space, i.e., both the rung coupling ${J}_{\ensuremath{\perp}}$ and the diagonal coupling ${J}_{\ifmmode\times\else\texttimes\fi{}}$ are ferromagnetic. The spin gap is found to be insensitive to the change of the ferromagnetic diagonal coupling strength when the ratio of the rung coupling constant ${J}_{\ensuremath{\perp}}$ to the leg coupling constant ${J}_{\ensuremath{\Vert}}$ is 0.5, in agreement with the analysis of recent experimental spin susceptibility data.

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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

h_{c_{1}}

and

h_{c_{2}}

, corresponding to the transition between different magnetic phases of the system. It is found that the intermediate state ($h_{c_{1}}

S

σ

-type spins) are aligned in the same direction. Whereas, in anisotropic antiferromagnetic phase, both

S

and

σ

-type of spins are anti-ferromagnetically aligned with each other, two nearest

S

spins along the rung form an anisotropic singlet bond whereas two nearest

σ

spins form an Ising bond. In large Heisenberg rung exchange interaction limit, spins on each leg are ferromagnetically aligned, but spins on different legs are anti-ferromagnetically aligned. The thermodynamic quantities like

Cv(T)

χ(T)

and

S(T)

are also calculated using the transfer matrix method for different phase. The magnetic gap in the SRFM and the SLFM can be notice from

χ(T)

and

Cv(T)

curves.

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.