arXiv:cond-mat/0211429 · Physical review. B, Condensed matter

Rung-singlet phase of the S=12 two-leg spin-ladder with four-spin cyclic exchange

Kai Phillip Schmidt, H. Monien, Götz Silvester Uhrig

Published May 22, 2003• 30 citations

Abstract

Using continuous unitary transformations (CUTs) we calculate the one-triplet gap for the antiferromagnetic $S=\frac{1}{2}$ two-leg spin ladder with additional four-spin exchange interactions in a high order series expansion about the limit of isolated rungs. By applying an efficient extrapolation technique we calculate the transition line between the rung-singlet phase and a spontaneously dimerized phase with dimers on the legs. Using this extrapolation technique we are able to analyze the crossover from strong rung coupling to weakly coupled chains.

DOI: 10.1103/physrevb.67.184413

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arXiv:cond-mat/0211429 · Physical review. B, Condensed matter

Rung-singlet phase of the S=12 two-leg spin-ladder with four-spin cyclic exchange

Kai Phillip Schmidt, H. Monien, Götz Silvester Uhrig

Published May 22, 2003• 30 citations

arXiv HTML PDF

Abstract

Using continuous unitary transformations (CUTs) we calculate the one-triplet gap for the antiferromagnetic

S=\frac{1}{2}

two-leg spin ladder with additional four-spin exchange interactions in a high order series expansion about the limit of isolated rungs. By applying an efficient extrapolation technique we calculate the transition line between the rung-singlet phase and a spontaneously dimerized phase with dimers on the legs. Using this extrapolation technique we are able to analyze the crossover from strong rung coupling to weakly coupled chains.

DOI: 10.1103/physrevb.67.184413

Related papers

Singlet quantum phases and magnetization of the frustrated spin-1/2 ladder with ferromagnetic (F) exchange in legs and alternating F-AF exchange in rungs

Chatterjee, Monalisa, Manoranjan Kumar, Z. G. Soos

The magnetization $M(h)$ is used to identify three singlet quantum phases of the ladder with isotropic exchange interactions. The Dimer phase with frustrated F exchanges in rungs and legs has a first-order $M(h)$ transition at $0$ K from singlet to ferromagnetic at the saturation field $h_s$ . The Haldane-DAF phase with strong F exchange in rungs and net AF exchange between rungs has continuous $M(h)$ and is adiabatically connected to the $S = 1$ Heisenberg AF chain. The AF phase with strong F exchange in legs and net AF exchange between legs has continuous $M(h)$ and is adiabatically connected to the spin-1/2 $J_1-J_2$ model with $J_1 > 0$ and $J_2 < 0$ . All three singlet phases have finite gaps to the lowest triplet state.The magnetization $M(h)$ is used to identify three singlet quantum phases of the ladder with isotropic exchange interactions. The Dimer phase with frustrated F exchanges in rungs and legs has a first-order $M(h)$ transition at $0$ K from singlet to ferromagnetic at the saturation field $h_s$. The Haldane-DAF phase with strong F exchange in rungs and net AF exchange between rungs has continuous $M(h)$ and is adiabatically connected to the $S = 1$ Heisenberg AF chain. The AF phase with strong F exchange in legs and net AF exchange between legs has continuous $M(h)$ and is adiabatically connected to the spin-1/2 $J_1-J_2$ model with $J_1 > 0$ and $J_2 < 0$. All three singlet phases have finite gaps to the lowest triplet state.

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Perturbation theories for the S=12 spin ladder with a four-spin ring exchange

M. Müller, T. Vekua, H.-J. Mikeska

The isotropic $S=1/2$ antiferromagnetic spin ladder with additional four-spin ring exchange is studied perturbatively in the strong coupling regime with the help of cluster expansion technique, and by means of bosonization in the weak coupling limit. It is found that a sufficiently large strength of ring exchange leads to a second-order phase transition, and the shape of the boundary in the vicinity of the known exact transition point is obtained. The critical exponent for the gap is found to be $\ensuremath{\eta}\ensuremath{\simeq}1,$ in agreement both with exact results available for the dimer line and with the bosonization analysis. The phase we determined after crossing the critical line is gapped and spontaneously dimerized. The results for the transition line from strong coupling and from weak coupling match with each other naturally.The isotropic $S=1/2$ antiferromagnetic spin ladder with additional four-spin ring exchange is studied perturbatively in the strong coupling regime with the help of cluster expansion technique, and by means of bosonization in the weak coupling limit. It is found that a sufficiently large strength of ring exchange leads to a second-order phase transition, and the shape of the boundary in the vicinity of the known exact transition point is obtained. The critical exponent for the gap is found to be $\ensuremath{\eta}\ensuremath{\simeq}1,$ in agreement both with exact results available for the dimer line and with the bosonization analysis. The phase we determined after crossing the critical line is gapped and spontaneously dimerized. The results for the transition line from strong coupling and from weak coupling match with each other naturally.

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We present the phase diagram of the $S=1/2$ Heisenberg model on the two leg ladder with cyclic four-spin exchange, determined by a combination of exact diagonalization and density-matrix renormalization group techniques. We find six different phases and regimes: the rung singlet phase, a ferromagnetic phase, two symmetry broken phases with staggered dimers and staggered scalar chiralities, and a gapped region with dominant vector chirality, or collinear spin correlations. We localize the phase transitions and investigate their nature.We present the phase diagram of the $S=1/2$ Heisenberg model on the two leg ladder with cyclic four-spin exchange, determined by a combination of exact diagonalization and density-matrix renormalization group techniques. We find six different phases and regimes: the rung singlet phase, a ferromagnetic phase, two symmetry broken phases with staggered dimers and staggered scalar chiralities, and a gapped region with dominant vector chirality, or collinear spin correlations. We localize the phase transitions and investigate their nature.

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Keigo Hijii, K. Nomura

We study a phase transition and critical properties of the quantum spin ladder system with a four-spin interaction. We determine a phase boundary between a rung singlet and a staggered dimer phases numerically. This phase transition is of a second order in the weak-coupling region. We confirm that this universality class is described by the $k=2$ SU(2) Wess-Zumino-Witten model, analyzing the central charge and scaling dimensions. In the strong-coupling region, phase transition becomes of a first order.We study a phase transition and critical properties of the quantum spin ladder system with a four-spin interaction. We determine a phase boundary between a rung singlet and a staggered dimer phases numerically. This phase transition is of a second order in the weak-coupling region. We confirm that this universality class is described by the $k=2$ SU(2) Wess-Zumino-Witten model, analyzing the central charge and scaling dimensions. In the strong-coupling region, phase transition becomes of a first order.

Physical Review BJul 23, 20099 citations

Numerical Study of Magnetic Raman Scattering Spectra in Ladder Antiferromagnets –Exchange Scatterings from the Singlet Ground State–

Shinichiro Tada, Yuhei Natsume, Toshihiko Suzuki

The exchange-scattering spectra are reproduced by the numerical calculation for the finite Heisenberg ladder, in which two-legs with antiferromagnetic bond J c is connected by rungs with antiferromagnetic bond J r . The numerical calculation is made for the system of 12 ×2 sites by Lanczos method. The ratio of J c / J r is considered to be 0.6–1.0 in order to discuss the experimental work for ladders of Cu 2+ ions in oxide compounds Sr 14- x Ca x Cu 24 O 41 . In addition to the Raman edge about J r corresponding twice the singlet-triplet spin gap, the characteristic structure appears around 2 or 3 times of J r i.e. 3 or 5 times the spin-gap. We concentrate our attention on characteristic features of excited levels, transitions to which are Raman-active. In particular, the relationship between correlations for spins in those states and corresponding Raman intensities is discussed in the picture of triplet pairs excited from singlet dimers. By the perturbation theory, the essential dependence of those intensities on distances between triplet dimers is investigated.The exchange-scattering spectra are reproduced by the numerical calculation for the finite Heisenberg ladder, in which two-legs with antiferromagnetic bond J c is connected by rungs with antiferromagnetic bond J r . The numerical calculation is made for the system of 12 ×2 sites by Lanczos method. The ratio of J c / J r is considered to be 0.6–1.0 in order to discuss the experimental work for ladders of Cu 2+ ions in oxide compounds Sr 14- x Ca x Cu 24 O 41 . In addition to the Raman edge about J r corresponding twice the singlet-triplet spin gap, the characteristic structure appears around 2 or 3 times of J r i.e. 3 or 5 times the spin-gap. We concentrate our attention on characteristic features of excited levels, transitions to which are Raman-active. In particular, the relationship between correlations for spins in those states and corresponding Raman intensities is discussed in the picture of triplet pairs excited from singlet dimers. By the perturbation theory, the essential dependence of those intensities on distances between triplet dimers is investigated.

Journal of the Physical Society of JapanAug 15, 20011 citation

Using continuous unitary transformations (CUTs) we calculate the one-triplet gap for the antiferromagnetic

S=\frac{1}{2}

The magnetization

M(h)

is used to identify three singlet quantum phases of the ladder with isotropic exchange interactions. The Dimer phase with frustrated F exchanges in rungs and legs has a first-order

M(h)

transition at

0

K from singlet to ferromagnetic at the saturation field

h_s

. The Haldane-DAF phase with strong F exchange in rungs and net AF exchange between rungs has continuous

M(h)

and is adiabatically connected to the

S = 1

Heisenberg AF chain. The AF phase with strong F exchange in legs and net AF exchange between legs has continuous

M(h)

and is adiabatically connected to the spin-1/2

J_1-J_2

model with

J_1 > 0

and

J_2 < 0

. All three singlet phases have finite gaps to the lowest triplet state.

The isotropic

S=1/2

antiferromagnetic spin ladder with additional four-spin ring exchange is studied perturbatively in the strong coupling regime with the help of cluster expansion technique, and by means of bosonization in the weak coupling limit. It is found that a sufficiently large strength of ring exchange leads to a second-order phase transition, and the shape of the boundary in the vicinity of the known exact transition point is obtained. The critical exponent for the gap is found to be $\ensuremath{\eta}\ensuremath{\simeq}1,$ in agreement both with exact results available for the dimer line and with the bosonization analysis. The phase we determined after crossing the critical line is gapped and spontaneously dimerized. The results for the transition line from strong coupling and from weak coupling match with each other naturally.

We present the phase diagram of the

S=1/2

Heisenberg model on the two leg ladder with cyclic four-spin exchange, determined by a combination of exact diagonalization and density-matrix renormalization group techniques. We find six different phases and regimes: the rung singlet phase, a ferromagnetic phase, two symmetry broken phases with staggered dimers and staggered scalar chiralities, and a gapped region with dominant vector chirality, or collinear spin correlations. We localize the phase transitions and investigate their nature.

k=2

SU(2) Wess-Zumino-Witten model, analyzing the central charge and scaling dimensions. In the strong-coupling region, phase transition becomes of a first order.