Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/9901195 · Journal of the Physical Society of Japan

Ground State Phase Diagram of the One DimensionalS=1/2XXZ Model with Dimerization and Quadrumerization

Wei Chen, Kazuo Hida

Published Aug 15, 1999• 4 citations
arXivHTMLPDF

Abstract

The one dimensional S=1/2 XXZ model with dimerization (1-j) and quadrumerization δis studied by the numerical exact diagonalization of finite size systems. Using the conformal field theory and the level spectroscopy method, we calculate the ground state phase diagram with XY-like anisotropy Δ(0
DOI
10.1143/jpsj.68.2779

Related papers

Ground State Properties of One DimensionalS=1/2Heisenberg Model with Dimerization and Quadrumerization

Wei Chen, Kazuo Hida

The one dimensional S=1/2 Heisenberg model with dimerization and quadrumerization is studied by means of the numerical exact diagonalization of finite size systems. Using the phenomenological renormalization group and finite size scaling law, the ground state phase diagram is obtained in the isotropic case. It exhibits a variety of the ground states which contains the S=1 Haldane state, S=1 dimer state and S=1/2 dimer state as limiting cases. The gap exponent $ν$ is also calculated which coincides with the value for the dimerization transition of the isotropic Heisenberg chain. In the XY limit, the phase diagram is obtained analytically and the comparison is made with the isotropic case.

arXiv:cond-mat/9804149•Journal of the Physical Society of Japan•Aug 15, 1998•9 citations

Magnetization Plateaus in One DimensionalS=1/2Heisenberg Model with Dimerization and Quadrumerization

Wei Chen, Kazuo Hida, Hiroki Nakano

The one dimensional $S=1/2$ Heisenberg model with dimerization ($1-j$) and quadrumerization ($δ$) in the magnetic field is studied by means of the numerical exact diagonalization of finite size systems and the conformal field theory. It is found that the magnetization plateau at half of the saturation value exists for $δ\neq 0$. For $δ= 0$, this model is described by the conformal field theory with central charge $c=1$ at this value of magnetization. The critical exponent $ν$ which characterizes the $δ$-dependence of the width of the plateau is calculated using the level spectroscopy method. The $j$-dependence of the critical exponent $ν$ is found to be non-monotonic and discontinuous at $j = 0$. The effective theory of the magnetization plateau is also presented for various limiting cases.

arXiv:cond-mat/9808300•Journal of the Physical Society of Japan•Feb 15, 1999•20 citations

Ground-state phase diagram of S=1 XXZ chains with uniaxial single-ion-type anisotropy

Wei Chen, Kazuo Hida, B. C. Sanctuary

One-dimensional $S=1$ $\mathrm{XXZ}$ chains with uniaxial single-ion-type anisotropy are studied by numerical exact diagonalization of finite-size systems. The numerical data are analyzed using conformal field theory, the level spectroscopy, phenomenological renormalization-group, and finite-size scaling method. We thus present a quantitatively reliable ground-state phase diagram of this model. The ground states of this model contain the Haldane phase, large-D phase, N\'eel phase, two $\mathrm{XY}$ phases, and the ferromagnetic phase. There are four different types of transitions between these phases: the Brezinskii-Kosterlitz-Thouless-type transitions, the Gaussian-type transitions, the Ising-type transitions, and the first-order transitions. The locations of these critical lines are accurately determined.

arXiv:cond-mat/0209403•Physical review. B, Condensed matter•Mar 4, 2003•250 citations

Phase Diagram ofS=1 XXZ Chain with Next-Nearest-Neighbor Interaction

Takahiro Murashima, Keigo Hijii, K. Nomura +1 more

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.

arXiv:cond-mat/0405385•Journal of the Physical Society of Japan•May 15, 2005•9 citations

Exact-diagonalization study of the one-dimensional disorderedXXZmodel

Karl J. Runge, Gergely T. Zimányi

We investigate the one-dimensional quantum XXZ model in the presence of diagonal disorder. Recently the model has been analyzed with the help of field-theoretical renormalization-group methods, and a phase diagram has been predicted. We study the model with exact diagonalization techniques up to chain lengths of 16 sites. Using finite-size scaling methods we estimate critical exponents and the phase diagram and find reasonably good agreement with the field-theoretical results, namely, that any amount of disorder destroys the superfluidity for XXZ anisotropy \ensuremath{\Delta} between -1/2 and 1, while the superfluidity persists to finite disorder strength for -1-1/2 and then undergoes a Kosterlitz-Thouless-type transition.

Physical review. B, Condensed matter•Jun 1, 1994•24 citations

Exact Diag. Study of the 1D Disordered XXZ Model

Karl J. Runge, Gergely T. Zimányi

We investigate the one-dimensional quantum $XXZ$ model in the presence of diagonal disorder. Recently the model has been analyzed with the help of field-theoretical renormalization group methods, and a phase diagram has been predicted. We study the model with exact diagonalization techniques up to chain lengths of 16 sites. Using finite-size scaling methods we estimate critical exponents and the phase diagram and find reasonably good agreement with the field-theoretical results, namely, that any amount of disorder destroys the superfluidity for $XXZ$ anisotropy $Δ$ between $ -1/2 $ and $1$, while the superfluidity persists to finite disorder strength for $ -1 < Δ< -1/2$ and then undergoes a Kosterlitz-Thouless type transition.

arXiv:cond-mat/9312002•Dec 1, 1993•0 citations
The one dimensional S=1/2 Heisenberg model with dimerization and quadrumerization is studied by means of the numerical exact diagonalization of finite size systems. Using the phenomenological renormalization group and finite size scaling law, the ground state phase diagram is obtained in the isotropic case. It exhibits a variety of the ground states which contains the S=1 Haldane state, S=1 dimer state and S=1/2 dimer state as limiting cases. The gap exponent ννν is also calculated which coincides with the value for the dimerization transition of the isotropic Heisenberg chain. In the XY limit, the phase diagram is obtained analytically and the comparison is made with the isotropic case.
The one dimensional S=1/2S=1/2S=1/2 Heisenberg model with dimerization (1−j1-j1−j) and quadrumerization (δδδ) in the magnetic field is studied by means of the numerical exact diagonalization of finite size systems and the conformal field theory. It is found that the magnetization plateau at half of the saturation value exists for δ≠0δ\neq 0δ=0. For δ=0δ= 0δ=0, this model is described by the conformal field theory with central charge c=1c=1c=1 at this value of magnetization. The critical exponent ννν which characterizes the δδδ-dependence of the width of the plateau is calculated using the level spectroscopy method. The jjj-dependence of the critical exponent ννν is found to be non-monotonic and discontinuous at j=0j = 0j=0. The effective theory of the magnetization plateau is also presented for various limiting cases.
One-dimensional S=1S=1S=1 XXZ\mathrm{XXZ}XXZ chains with uniaxial single-ion-type anisotropy are studied by numerical exact diagonalization of finite-size systems. The numerical data are analyzed using conformal field theory, the level spectroscopy, phenomenological renormalization-group, and finite-size scaling method. We thus present a quantitatively reliable ground-state phase diagram of this model. The ground states of this model contain the Haldane phase, large-D phase, N\'eel phase, two XY\mathrm{XY}XY phases, and the ferromagnetic phase. There are four different types of transitions between these phases: the Brezinskii-Kosterlitz-Thouless-type transitions, the Gaussian-type transitions, the Ising-type transitions, and the first-order transitions. The locations of these critical lines are accurately determined.
The one dimensional S=1 XXZ model with next-nearest-neighbor interaction ααα and Ising-type anisotropy ΔΔΔ 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 σσσ model and analyze the phase diagram in the ααα ≪\ll≪ -1 and ΔΔΔ ∼\sim∼ 1 region by using the renormalization group method.
We investigate the one-dimensional quantum XXZ model in the presence of diagonal disorder. Recently the model has been analyzed with the help of field-theoretical renormalization-group methods, and a phase diagram has been predicted. We study the model with exact diagonalization techniques up to chain lengths of 16 sites. Using finite-size scaling methods we estimate critical exponents and the phase diagram and find reasonably good agreement with the field-theoretical results, namely, that any amount of disorder destroys the superfluidity for XXZ anisotropy \ensuremath{\Delta} between -1/2 and 1, while the superfluidity persists to finite disorder strength for -1-1/2 and then undergoes a Kosterlitz-Thouless-type transition.
We investigate the one-dimensional quantum XXZXXZXXZ model in the presence of diagonal disorder. Recently the model has been analyzed with the help of field-theoretical renormalization group methods, and a phase diagram has been predicted. We study the model with exact diagonalization techniques up to chain lengths of 16 sites. Using finite-size scaling methods we estimate critical exponents and the phase diagram and find reasonably good agreement with the field-theoretical results, namely, that any amount of disorder destroys the superfluidity for XXZXXZXXZ anisotropy ΔΔΔ between $ -1/2 $ and 111, while the superfluidity persists to finite disorder strength for $ -1 < Δ< -1/2$ and then undergoes a Kosterlitz-Thouless type transition.