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WORLD SCIENTIFIC eBooks

Cluster-effective-field approximations in frustrated quantum spin systems: CAM analysis of Néel-dimer transition in the S =½ frustrated XXZ chain at the ground state

Yoshihiko Nonomura, Masuo Suzuki

Published Sep 1, 1995• 0 citations
Publisher
DOI
10.1142/9789812797087_0034

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Improved cluster-effective-field study on frustrated quantum spin systems in 2D

Yoshihiko Nonomura

Bulletin of the American Physical Society•Mar 19, 2013•0 citations

Cluster-effective-field approximations in frustrated quantum spin systems: CAM analysis of Neel-dimer transition in the S= 1/2 frustrated XXZ chain at the ground state

Yoshihiko Nonomura, Masuo Suzuki

How to impose boundary conditions is crucial to finite-cluster calculations of quantum spin systems, but only open-boundary clusters have been used in cluster-effective-field approximations up to now. In the present paper, periodic-boundary clusters are also considered for the formulation of cluster-effective-field approximations in frustrated quantum spin systems. Namely, the open-boundary-condition double-cluster approximation (OBC-DCA) and the periodic-boundary-condition double-cluster approximation (PBC-DCA) are applied to the one-dimensional S= 1/2 frustrated XXZ model at the ground state. These two approximations are compared using the coherent-anomaly method (CAM). Within the limitation of cluster sizes in exact-diagonalization calculations, the PBC-DCA can reproduce the true phase boundary of the Neel-dimer transition. On the other hand, the OBC-DCA severely underestimates the existence of magnetic orders as quantum fluctuation is increased. These findings suggest that previous cluster-effective-field studies based on open-boundary clusters should be reconsidered.

Journal of Physics A Mathematical and General•Feb 21, 1994•9 citations

Ground-state phase diagram of a spin- 1 2 frustrated XXZ ladder

Takuhiro Ogino, Ryui Kaneko, Satoshi Morita +1 more

We study the ground-state phase diagram of a spin-$\frac{1}{2}$ frustrated XXZ ladder, in which two antiferromagnetic chains are coupled by competing rung and diagonal interactions, ${J}_{\ensuremath{\perp}}$ and ${J}_{\ifmmode\times\else\texttimes\fi{}}$. Previous studies on the isotropic model have revealed that a fluctuation-induced effective dimer attraction between the legs stabilizes the columnar dimer (CD) phase in the highly frustrated regime ${J}_{\ensuremath{\perp}}\ensuremath{\approx}2{J}_{\ifmmode\times\else\texttimes\fi{}}$, especially for ferromagnetic ${J}_{\ensuremath{\perp},\ifmmode\times\else\texttimes\fi{}}<0$. By means of effective field theory and numerical analyses, we extend this analysis to the XXZ model, and we obtain a rich phase diagram. The diagram includes four gapped featureless phases with no symmetry breaking: the rung singlet (RS) and Haldane phases as well as their twisted variants, the RS* and Haldane* phases, which are all distinct in the presence of certain symmetries. Significantly, the Haldane-CD transition point in the isotropic model turns out to be a crossing point of two transition lines in the XXZ model, and the stripe N\'eel and RS* phases appear between these lines. This indicates a nontrivial interplay between the effective dimer attraction and the exchange anisotropy. In the easy-plane regime, the four featureless phases and two critical phases are found to compete in a complex manner depending on the signs of ${J}_{\ensuremath{\perp},\ifmmode\times\else\texttimes\fi{}}$.

arXiv:2206.13048•Physical review. B./Physical review. B•Oct 3, 2022•13 citations

Excitation structure of frustrated spin chains with dimerization and the description by the effective field theory

Shintaro Takayoshi, Masaki Oshikawa

Bulletin of the American Physical Society•Feb 27, 2012•0 citations

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.

arXiv:1207.1059•Physical Review B•Sep 12, 2012•120 citations

Cluster-effective-field study on ground-state properties of quantum spin systems

禎彦 野々村

•Jan 1, 1994•1 citation
How to impose boundary conditions is crucial to finite-cluster calculations of quantum spin systems, but only open-boundary clusters have been used in cluster-effective-field approximations up to now. In the present paper, periodic-boundary clusters are also considered for the formulation of cluster-effective-field approximations in frustrated quantum spin systems. Namely, the open-boundary-condition double-cluster approximation (OBC-DCA) and the periodic-boundary-condition double-cluster approximation (PBC-DCA) are applied to the one-dimensional S= 1/2 frustrated XXZ model at the ground state. These two approximations are compared using the coherent-anomaly method (CAM). Within the limitation of cluster sizes in exact-diagonalization calculations, the PBC-DCA can reproduce the true phase boundary of the Neel-dimer transition. On the other hand, the OBC-DCA severely underestimates the existence of magnetic orders as quantum fluctuation is increased. These findings suggest that previous cluster-effective-field studies based on open-boundary clusters should be reconsidered.
We study the ground-state phase diagram of a spin-12\frac{1}{2}21​ frustrated XXZ ladder, in which two antiferromagnetic chains are coupled by competing rung and diagonal interactions, ${J}_{\ensuremath{\perp}}$ and ${J}_{\ifmmode\times\else\texttimes\fi{}}$. Previous studies on the isotropic model have revealed that a fluctuation-induced effective dimer attraction between the legs stabilizes the columnar dimer (CD) phase in the highly frustrated regime ${J}_{\ensuremath{\perp}}\ensuremath{\approx}2{J}_{\ifmmode\times\else\texttimes\fi{}}$, especially for ferromagnetic ${J}_{\ensuremath{\perp},\ifmmode\times\else\texttimes\fi{}}<0$. By means of effective field theory and numerical analyses, we extend this analysis to the XXZ model, and we obtain a rich phase diagram. The diagram includes four gapped featureless phases with no symmetry breaking: the rung singlet (RS) and Haldane phases as well as their twisted variants, the RS* and Haldane* phases, which are all distinct in the presence of certain symmetries. Significantly, the Haldane-CD transition point in the isotropic model turns out to be a crossing point of two transition lines in the XXZ model, and the stripe N\'eel and RS* phases appear between these lines. This indicates a nontrivial interplay between the effective dimer attraction and the exchange anisotropy. In the easy-plane regime, the four featureless phases and two critical phases are found to compete in a complex manner depending on the signs of ${J}_{\ensuremath{\perp},\ifmmode\times\else\texttimes\fi{}}$.
The ground-state phase diagram of a spin-12\frac{1}{2}21​ XXZ chain with competing ferromagnetic nearest-neighbor (J1<0{J}_{1}<0J1​<0) and antiferromagnetic second-neighbor (J2>0{J}_{2}>0J2​>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.