arXiv:cond-mat/9909290 · Physical review. B, Condensed matter

Phase diagram of S=12XXZ chain with next-nearest-neighbor interaction

Shunsaku Hirata, K. Nomura

Published Apr 1, 2000• 30 citations

Abstract

The ground-state properties of the one-dimensional $\mathrm{XXZ}$ model with next-nearest-neighbor coupling $\ensuremath{\alpha}$ and anisotropy $\ensuremath{\Delta}$ is studied. A direct transition between the ferromagnetic phase and the spontaneously dimerized phase is found. The effect of bond alternation which arises in realistic systems due to lattice distortion is discussed also. The results suggest that transitions between the ferromagnetic and spin-Peierls phases occur.

DOI: 10.1103/physrevb.61.9453

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arXiv:cond-mat/9909290 · Physical review. B, Condensed matter

Phase diagram of S=12XXZ chain with next-nearest-neighbor interaction

Shunsaku Hirata, K. Nomura

Published Apr 1, 2000• 30 citations

arXiv HTML PDF

Abstract

The ground-state properties of the one-dimensional

\mathrm{XXZ}

model with next-nearest-neighbor coupling

\ensuremath{\alpha}

and anisotropy

\ensuremath{\Delta}

is studied. A direct transition between the ferromagnetic phase and the spontaneously dimerized phase is found. The effect of bond alternation which arises in realistic systems due to lattice distortion is discussed also. The results suggest that transitions between the ferromagnetic and spin-Peierls phases occur.

DOI: 10.1103/physrevb.61.9453

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Ground-state phase diagram of a spin- 12 frustrated ferromagnetic XXZ chain: Haldane dimer phase and gapped/gapless chiral phases

Shunsuke Furukawa, Masahiro Sato, Shigeki Onoda +1 more

The ground-state phase diagram of a spin- $\frac{1}{2}$ XXZ chain with competing ferromagnetic nearest-neighbor ( ${J}_{1}<0$ ) and antiferromagnetic second-neighbor ( ${J}_{2}>0$ ) exchange couplings is studied by means of the infinite time evolving block decimation algorithm and effective field theories. For the SU(2)-symmetric (Heisenberg) case, we show that the nonmagnetic phase in the range $\ensuremath{-}4<{J}_{1}/{J}_{2}<0$ has a small but finite ferromagnetic dimer order. We argue that this spontaneous dimer order is associated with effective spin-1 degrees of freedom on dimerized bonds, which collectively form a valence bond solid state as in the spin-1 antiferromagnetic Heisenberg chain (the Haldane spin chain). We thus call this phase the Haldane dimer phase. With easy-plane anisotropy, the model exhibits a variety of phases including the vector chiral phase with gapless excitations and the even-parity dimer and N\'eel phases with gapped excitations, in addition to the Haldane dimer phase. Furthermore, we show the existence of gapped phases with coexisting orders in narrow regions that intervene between the gapless chiral phase and any one of Haldane dimer, even-parity dimer, and N\'eel phases. Possible implications for quasi-one-dimensional edge-sharing cuprates are discussed.The ground-state phase diagram of a spin-$\frac{1}{2}$ XXZ chain with competing ferromagnetic nearest-neighbor (${J}_{1}<0$) and antiferromagnetic second-neighbor (${J}_{2}>0$) exchange couplings is studied by means of the infinite time evolving block decimation algorithm and effective field theories. For the SU(2)-symmetric (Heisenberg) case, we show that the nonmagnetic phase in the range $\ensuremath{-}4<{J}_{1}/{J}_{2}<0$ has a small but finite ferromagnetic dimer order. We argue that this spontaneous dimer order is associated with effective spin-1 degrees of freedom on dimerized bonds, which collectively form a valence bond solid state as in the spin-1 antiferromagnetic Heisenberg chain (the Haldane spin chain). We thus call this phase the Haldane dimer phase. With easy-plane anisotropy, the model exhibits a variety of phases including the vector chiral phase with gapless excitations and the even-parity dimer and N\'eel phases with gapped excitations, in addition to the Haldane dimer phase. Furthermore, we show the existence of gapped phases with coexisting orders in narrow regions that intervene between the gapless chiral phase and any one of Haldane dimer, even-parity dimer, and N\'eel phases. Possible implications for quasi-one-dimensional edge-sharing cuprates are discussed.

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Shunsuke Furukawa, Masahiro Sato, Akira Furusaki

We study the ground-state phase diagram of a one-dimensional spin- $\frac{1}{2}$ easy-plane XXZ model with a ferromagnetic nearest-neighbor (NN) coupling ${J}_{1}$ and a competing next-nearest-neighbor (NNN) antiferromagnetic coupling ${J}_{2}$ in the parameter range $0<{J}_{2}/|{J}_{1}|<0.4$ . When ${J}_{2}/|{J}_{1}|\ensuremath{\lesssim}1/4$, the model is in a Tomonaga-Luttinger liquid phase which is adiabatically connected to the critical phase of the XXZ model of ${J}_{2}=0$ . On the basis of the effective (sine-Gordon) theory and numerical analyses of low-lying energy levels of finite-size systems, we show that the NNN coupling induces phase transitions from the Tomonaga-Luttinger liquid to gapped phases with either N\'eel or dimer order. Interestingly, these two types of ordered phases appear alternately as the easy-plane anisotropy is changed toward the isotropic limit. The appearance of the antiferromagnetic (N\'eel) order in this model is remarkable, as it is strongly unfavored by both the easy-plane ferromagnetic NN coupling and the antiferromagnetic NNN coupling in the classical-spin picture. We argue that emergent trimer degrees of freedom play a crucial role in the formation of the N\'eel order.We study the ground-state phase diagram of a one-dimensional spin-$\frac{1}{2}$ easy-plane XXZ model with a ferromagnetic nearest-neighbor (NN) coupling ${J}_{1}$ and a competing next-nearest-neighbor (NNN) antiferromagnetic coupling ${J}_{2}$ in the parameter range $0<{J}_{2}/|{J}_{1}|<0.4$. When ${J}_{2}/|{J}_{1}|\ensuremath{\lesssim}1/4$, the model is in a Tomonaga-Luttinger liquid phase which is adiabatically connected to the critical phase of the XXZ model of ${J}_{2}=0$. On the basis of the effective (sine-Gordon) theory and numerical analyses of low-lying energy levels of finite-size systems, we show that the NNN coupling induces phase transitions from the Tomonaga-Luttinger liquid to gapped phases with either N\'eel or dimer order. Interestingly, these two types of ordered phases appear alternately as the easy-plane anisotropy is changed toward the isotropic limit. The appearance of the antiferromagnetic (N\'eel) order in this model is remarkable, as it is strongly unfavored by both the easy-plane ferromagnetic NN coupling and the antiferromagnetic NNN coupling in the classical-spin picture. We argue that emergent trimer degrees of freedom play a crucial role in the formation of the N\'eel order.

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Phase diagram of the one-dimensional S=12 XXZ model with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions

Rouhollah Jafari, A. Langari

We have studied the phase diagram of the one-dimensional $S=\frac{1}{2}$ $XXZ$ model with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions. We have applied the quantum renormalization group (QRG) approach to obtain stable fixed points and the scaling of coupling constants. The QRG prescription has to be implemented to the second order of interblock interactions to obtain a self-similar Hamiltonian after each step of the QRG. This model shows a rich phase diagram which includes quantum spin-fluid and dimer phases in addition to the classical N\'eel and ferromagnetic ones. We have found the border between different phases by tracing the scaling of coupling constants.We have studied the phase diagram of the one-dimensional $S=\frac{1}{2}$ $XXZ$ model with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions. We have applied the quantum renormalization group (QRG) approach to obtain stable fixed points and the scaling of coupling constants. The QRG prescription has to be implemented to the second order of interblock interactions to obtain a self-similar Hamiltonian after each step of the QRG. This model shows a rich phase diagram which includes quantum spin-fluid and dimer phases in addition to the classical N\'eel and ferromagnetic ones. We have found the border between different phases by tracing the scaling of coupling constants.

arXiv:0710.3239Physical Review BJul 10, 200764 citations

The ground-state properties of the one-dimensional

\mathrm{XXZ}

model with next-nearest-neighbor coupling

\ensuremath{\alpha}

and anisotropy

\ensuremath{\Delta}

The ground-state phase diagram of a spin-

\frac{1}{2}

XXZ chain with competing ferromagnetic nearest-neighbor (

{J}_{1}<0

) and antiferromagnetic second-neighbor (

{J}_{2}>0

) exchange couplings is studied by means of the infinite time evolving block decimation algorithm and effective field theories. For the SU(2)-symmetric (Heisenberg) case, we show that the nonmagnetic phase in the range $\ensuremath{-}4<{J}_{1}/{J}_{2}<0$ has a small but finite ferromagnetic dimer order. We argue that this spontaneous dimer order is associated with effective spin-1 degrees of freedom on dimerized bonds, which collectively form a valence bond solid state as in the spin-1 antiferromagnetic Heisenberg chain (the Haldane spin chain). We thus call this phase the Haldane dimer phase. With easy-plane anisotropy, the model exhibits a variety of phases including the vector chiral phase with gapless excitations and the even-parity dimer and N\'eel phases with gapped excitations, in addition to the Haldane dimer phase. Furthermore, we show the existence of gapped phases with coexisting orders in narrow regions that intervene between the gapless chiral phase and any one of Haldane dimer, even-parity dimer, and N\'eel phases. Possible implications for quasi-one-dimensional edge-sharing cuprates are discussed.

The one dimensional S=1 XXZ model with next-nearest-neighbor interaction

α

and Ising-type anisotropy

Δ

is studied by using a numerical diagonalization technique. We discuss the ground state phase diagram of this model numerically by the twisted-boundary-condition level spectroscopy method and the phenomenological renormalization group method, and analytically by the spin wave theory. We determine the phase boundaries among the XY phase, the Haldane phase, the ferromagnetic phase and the Néel phase, and then we confirm the universality class. Moreover, we map this model onto the non-linear

σ

model and analyze the phase diagram in the

α

\ll

-1 and

Δ

\sim

1 region by using the renormalization group method.

We study the ground-state phase diagram of a one-dimensional spin-

\frac{1}{2}

easy-plane XXZ model with a ferromagnetic nearest-neighbor (NN) coupling

{J}_{1}

and a competing next-nearest-neighbor (NNN) antiferromagnetic coupling

{J}_{2}

in the parameter range

0<{J}_{2}/|{J}_{1}|<0.4

. When ${J}_{2}/|{J}_{1}|\ensuremath{\lesssim}1/4$, the model is in a Tomonaga-Luttinger liquid phase which is adiabatically connected to the critical phase of the XXZ model of

{J}_{2}=0

. On the basis of the effective (sine-Gordon) theory and numerical analyses of low-lying energy levels of finite-size systems, we show that the NNN coupling induces phase transitions from the Tomonaga-Luttinger liquid to gapped phases with either N\'eel or dimer order. Interestingly, these two types of ordered phases appear alternately as the easy-plane anisotropy is changed toward the isotropic limit. The appearance of the antiferromagnetic (N\'eel) order in this model is remarkable, as it is strongly unfavored by both the easy-plane ferromagnetic NN coupling and the antiferromagnetic NNN coupling in the classical-spin picture. We argue that emergent trimer degrees of freedom play a crucial role in the formation of the N\'eel order.

We have studied the phase diagram of the one-dimensional

S=\frac{1}{2}

XXZ

model with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions. We have applied the quantum renormalization group (QRG) approach to obtain stable fixed points and the scaling of coupling constants. The QRG prescription has to be implemented to the second order of interblock interactions to obtain a self-similar Hamiltonian after each step of the QRG. This model shows a rich phase diagram which includes quantum spin-fluid and dimer phases in addition to the classical N\'eel and ferromagnetic ones. We have found the border between different phases by tracing the scaling of coupling constants.