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/9710164 · Journal of the Physical Society of Japan

Berezinskii-Kosterlitz-Thouless Transition of Spin-1 XXZ Chains in a Staggered Magnetic Field

Masayoshi Tsukano, Kiyohide Nomura

Published Jan 15, 1998• 17 citations
arXivHTMLPDF

Abstract

Phase diagram of S=1 XXZ chain in a staggered magnetic field is obtained numerically. The Berezinskii-Kosterlitz-Thouless transition between the XY and the antiferromagnetic phases is studied by the level-spectroscopy. Moreover we find that there is no distinction between the Haldane and the antiferromagnetic phases, since the Gaussian critical line does not appear, in contrast to the $S=1/2$ case. It is expected that some hidden $Z_2\times Z_2$ symmetry breaking happens not only in the Haldane phase but also in the antiferromagnetic one.

DOI
10.1143/jpsj.67.302

Related papers

Phase Diagram of S=1 Bond-AlternatingXXZChains

Atsuhiro Kitazawa, K. Nomura, Kiyomi Okamoto

Phase transitions between the XY, the dimer, and the Haldane phases of the spin-1 bond-alternating XXZ chain are studied numerically. By use of the ``level spectroscopy'' we overcome the difficulties in treating the Berezinskii-Kosterlitz-Thouless transition which occurs at the XY-dimer and XY-Haldane boundaries. We find that the XY-Haldane boundary lies just on $\ensuremath{\Delta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ (pure XY line). The critical properties can be interpreted as the Ashkin-Teller type reflecting the hidden ${\mathrm{Z}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathrm{Z}}_{2}$ symmetry. We make a conjecture on the phase diagram of the present model for arbitrary $S$.

arXiv:cond-mat/9511122•Physical Review Letters•May 20, 1996•94 citations

Spin-1 XXZ chains in a staggered magnetic field

匡良 塚野, K. Nomura

Phase transitions of the spin-1 $\mathrm{XXZ}$ chain with a single-ion anisotropy in a staggered magnetic field are studied. We obtain interesting phase diagrams consisting of ferromagnetic, partially ferromagnetic, $XY,$ antiferromagnetic (AF) and large-$D$ phases. By using the twist-boundary-condition method, a Gaussian critical line is found between the AF phase and the large-$D$ phase. A multicritical point lies among the $XY,$ AF and large-$D$ phases. An Ashkin-Teller type of bifurcation does not appear.

Physical review. B, Condensed matter•Apr 1, 1998•9 citations

Phase Diagram of S = 1 Bond-Alternating XXZ Chains Reflecting the Hidden Z2 × Z2 Symmetry

Atsuhiro Kitazawa, K. Nomura, Received February

The phase diagram of the spin-1 bond-alternating XXZ chain is studied numerically. This model is appropriate to study the VBS picture and the hidden Z_2\times Z_2 symmetry concerning to the Haldane gap problem. The possible phases are the ferromagnetic, the XY, the Haldane, the dimer, and the Neel ones. The critical properties of this model can be interpreted as the Ashkin-Teller type reflecting the hidden Z_2\times Z_2 symmetry. The phase transitions are of the Berezinskii-Kosterlitz-Thouless type (XY-Haldane and XY-dimer), of the 2D Gaussian type (Haldane-dimer), and of the 2D Ising type (Haldane-Neel and dimer-Neel). We determine the phase boundary and universality class using the recent developed techniques by the authors.

•Jan 1, 2008•0 citations

Phase Diagram of S=1 Bond-Alternating XXZ Chains Reflecting the Hidden Z_2\times Z_2 Symmetry

Atsuhiro Kitazawa, K. Nomura

The phase diagram of the spin-1 bond-alternating XXZ chain is studied numerically. This model is appropriate to study the VBS picture and the hidden Z_2\times Z_2 symmetry concerning to the Haldane gap problem. The possible phases are the ferromagnetic, the XY, the Haldane, the dimer, and the Néel ones. The critical properties of this model can be interpreted as the Ashkin-Teller type reflecting the hidden Z_2\times Z_2 symmetry. The phase transitions are of the Berezinskii-Kosterlitz-Thouless type (XY-Haldane and XY-dimer), of the 2D Gaussian type (Haldane-dimer), and of the 2D Ising type (Haldane-Néel and dimer-Néel). We determine the phase boundary and universality class using the recent developed techniques by the authors.

arXiv:cond-mat/9705179•May 19, 1997•0 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

Low Energy Behaviour of XXZ Antiferromagnetic Spin Chain

Bahman Roostaei

Zero temperature phase diagram of XXZ spin chain in external magnetic field is investigated at low energies using path integral approach.It has been shown by spin wave analysis and then by nonlinear sigma model transformation that below some critical field the system undergoes quantum Kosterlitz-Thouless phase transition.Above that critical field for low anisotropies the system is saturated while at strong anisotropy the system has Ising antiferromagnetic order.

arXiv:cond-mat/0108086•Aug 5, 2001•0 citations
Phase diagram of S=1 XXZ chain in a staggered magnetic field is obtained numerically. The Berezinskii-Kosterlitz-Thouless transition between the XY and the antiferromagnetic phases is studied by the level-spectroscopy. Moreover we find that there is no distinction between the Haldane and the antiferromagnetic phases, since the Gaussian critical line does not appear, in contrast to the S=1/2S=1/2S=1/2 case. It is expected that some hidden Z2×Z2Z_2\times Z_2Z2​×Z2​ symmetry breaking happens not only in the Haldane phase but also in the antiferromagnetic one.
Phase transitions between the XY, the dimer, and the Haldane phases of the spin-1 bond-alternating XXZ chain are studied numerically. By use of the ``level spectroscopy'' we overcome the difficulties in treating the Berezinskii-Kosterlitz-Thouless transition which occurs at the XY-dimer and XY-Haldane boundaries. We find that the XY-Haldane boundary lies just on $\ensuremath{\Delta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ (pure XY line). The critical properties can be interpreted as the Ashkin-Teller type reflecting the hidden ${\mathrm{Z}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathrm{Z}}_{2}$ symmetry. We make a conjecture on the phase diagram of the present model for arbitrary SSS.
Phase transitions of the spin-1 XXZ\mathrm{XXZ}XXZ chain with a single-ion anisotropy in a staggered magnetic field are studied. We obtain interesting phase diagrams consisting of ferromagnetic, partially ferromagnetic, XY,XY,XY, antiferromagnetic (AF) and large-DDD phases. By using the twist-boundary-condition method, a Gaussian critical line is found between the AF phase and the large-DDD phase. A multicritical point lies among the XY,XY,XY, AF and large-DDD phases. An Ashkin-Teller type of bifurcation does not appear.
The phase diagram of the spin-1 bond-alternating XXZ chain is studied numerically. This model is appropriate to study the VBS picture and the hidden Z_2\times Z_2 symmetry concerning to the Haldane gap problem. The possible phases are the ferromagnetic, the XY, the Haldane, the dimer, and the Neel ones. The critical properties of this model can be interpreted as the Ashkin-Teller type reflecting the hidden Z_2\times Z_2 symmetry. The phase transitions are of the Berezinskii-Kosterlitz-Thouless type (XY-Haldane and XY-dimer), of the 2D Gaussian type (Haldane-dimer), and of the 2D Ising type (Haldane-Neel and dimer-Neel). We determine the phase boundary and universality class using the recent developed techniques by the authors.
The phase diagram of the spin-1 bond-alternating XXZ chain is studied numerically. This model is appropriate to study the VBS picture and the hidden Z_2\times Z_2 symmetry concerning to the Haldane gap problem. The possible phases are the ferromagnetic, the XY, the Haldane, the dimer, and the Néel ones. The critical properties of this model can be interpreted as the Ashkin-Teller type reflecting the hidden Z_2\times Z_2 symmetry. The phase transitions are of the Berezinskii-Kosterlitz-Thouless type (XY-Haldane and XY-dimer), of the 2D Gaussian type (Haldane-dimer), and of the 2D Ising type (Haldane-Néel and dimer-Néel). We determine the phase boundary and universality class using the recent developed techniques by the authors.
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.