arXiv:cond-mat/9812330 · Physical review. B, Condensed matter

Excitation spectrum and ground-state properties of the S = 1 2 Heisenberg ladder with staggered dimerization

Valeri N. Kotov, J. Oitmaa, Zheng Weihong

Published May 1, 1999• 16 citations

Abstract

We study the excitation spectrum and ground-state properties of the two-leg $S=\frac{1}{2}$ quantum spin ladder with staggered dimerization. Two massive phases separated by a critical line are found, as predicted by previous analysis, based on the nonlinear sigma model. We have used dimer series expansions, exact diagonalization of small clusters, and diagrammatic analysis of an effective interacting Bose gas Hamiltonian, obtained by using the bond operator representation for spins. We compute the excitation spectrum in the phase, dominated by strong rungs in the parameter regimes far away and close to the point of instability. The exact location of the phase boundary is determined.

DOI: 10.1103/physrevb.59.11377

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arXiv:cond-mat/9812330 · Physical review. B, Condensed matter

Excitation spectrum and ground-state properties of the S = 1 2 Heisenberg ladder with staggered dimerization

Valeri N. Kotov, J. Oitmaa, Zheng Weihong

Published May 1, 1999• 16 citations

arXiv HTML PDF

Abstract

We study the excitation spectrum and ground-state properties of the two-leg

S=\frac{1}{2}

quantum spin ladder with staggered dimerization. Two massive phases separated by a critical line are found, as predicted by previous analysis, based on the nonlinear sigma model. We have used dimer series expansions, exact diagonalization of small clusters, and diagrammatic analysis of an effective interacting Bose gas Hamiltonian, obtained by using the bond operator representation for spins. We compute the excitation spectrum in the phase, dominated by strong rungs in the parameter regimes far away and close to the point of instability. The exact location of the phase boundary is determined.

DOI: 10.1103/physrevb.59.11377

Related papers

Phase diagram of the S=12 two-leg spin ladder with staggered bond alternation

Kiyomi Okamoto

The ground state of the $S=1/2$ two-leg ladder with the staggered bond alternations is investigated. We have determined the precise phase diagram on the $\ensuremath{\delta}\ensuremath{-}{J}^{\ensuremath{'}}$ plane $(\ensuremath{\delta}$ and ${J}^{\ensuremath{'}}$ are the magnitudes of the bond alternation and the rung interaction, respectively), employing the level spectroscopic analysis of the numerical diagonalization data obtained by the Lanczos algorithm with the twisted boundary condition. The phase boundary between the leg-dimer state and the rung-dimer state near $(\ensuremath{\delta}{,J}^{\ensuremath{'}})=(0,0)$ is of the form ${J}^{\ensuremath{'}}\ensuremath{\propto}{\ensuremath{\delta}}^{0.69},$ which is consistent with the prediction ${J}^{\ensuremath{'}}\ensuremath{\propto}{\ensuremath{\delta}}^{2/3}$ by Mart\'{\i}n-Delgado, Duleksky, and Sierra, and also by Wang and Nersesyan, but not with ${J}^{\ensuremath{'}}\ensuremath{\propto}{\ensuremath{\delta}}^{2}$ by Cabra and Grynberg.The ground state of the $S=1/2$ two-leg ladder with the staggered bond alternations is investigated. We have determined the precise phase diagram on the $\ensuremath{\delta}\ensuremath{-}{J}^{\ensuremath{'}}$ plane $(\ensuremath{\delta}$ and ${J}^{\ensuremath{'}}$ are the magnitudes of the bond alternation and the rung interaction, respectively), employing the level spectroscopic analysis of the numerical diagonalization data obtained by the Lanczos algorithm with the twisted boundary condition. The phase boundary between the leg-dimer state and the rung-dimer state near $(\ensuremath{\delta}{,J}^{\ensuremath{'}})=(0,0)$ is of the form ${J}^{\ensuremath{'}}\ensuremath{\propto}{\ensuremath{\delta}}^{0.69},$ which is consistent with the prediction ${J}^{\ensuremath{'}}\ensuremath{\propto}{\ensuremath{\delta}}^{2/3}$ by Mart\'{\i}n-Delgado, Duleksky, and Sierra, and also by Wang and Nersesyan, but not with ${J}^{\ensuremath{'}}\ensuremath{\propto}{\ensuremath{\delta}}^{2}$ by Cabra and Grynberg.

Physical review. B, Condensed matterJun 24, 200317 citations

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Dimerized spin-1/2 ladders exhibit a variety of phase structures, which depend on the intra-chain and inter-chain spin exchange energies as well as on the dimerization pattern of the ladder. Using the density matrix renormalization group (DMRG) algorithm, we study critical properties of the bond-alternating two-leg Heisenberg spin ladder with diagonal interaction J ×. Two types of spin systems, staggered dimerized antiferromagnetic ladder and columnar dimerized ferro-antiferromagnetic couplings ladder, are investigated. To clarify the phase transition behaviors, we simultaneously analyze the string order parameter (SOP), the twisted order parameter (TOP), as well as a measurement of the quantum information analysis. Based on measuring this different observables, we establish the phase diagram accurately and give the fitting functions of the phase boundaries. In addition, the phase transition of cross-coupled spin ladder (in the absence of intrinsic dimerization) is also discussed.Dimerized spin-1/2 ladders exhibit a variety of phase structures, which depend on the intra-chain and inter-chain spin exchange energies as well as on the dimerization pattern of the ladder. Using the density matrix renormalization group (DMRG) algorithm, we study critical properties of the bond-alternating two-leg Heisenberg spin ladder with diagonal interaction J ×. Two types of spin systems, staggered dimerized antiferromagnetic ladder and columnar dimerized ferro-antiferromagnetic couplings ladder, are investigated. To clarify the phase transition behaviors, we simultaneously analyze the string order parameter (SOP), the twisted order parameter (TOP), as well as a measurement of the quantum information analysis. Based on measuring this different observables, we establish the phase diagram accurately and give the fitting functions of the phase boundaries. In addition, the phase transition of cross-coupled spin ladder (in the absence of intrinsic dimerization) is also discussed.

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We investigate the ground-state phase diagram and critical properties of the $S=1/2$ two-leg Heisenberg spin ladder system with a negative four-spin interaction using a numerical exact diagonalization method. Using the perturbation theory in the strong negative rung-coupling limit, we derive an $S=1$ bilinear-biquadratic chain as an effective model. We discuss the ground-state phase diagram in this limit. Next we numerically determine a phase boundary between the rung singlet phase and the columnar dimer (CD) phase by the phenomenological renormalization group method, and one between the CD phase and the Haldane phase by the twisted boundary condition method. We confirm that the phase transition between the CD phase and the Haldane phase is of second order and this universality class is described by the $k=2$ $SU(2)$ Wess-Zumino-Novikov-Witten nonlinear $\ensuremath{\sigma}$ model, calculating the central charge and scaling dimensions.We investigate the ground-state phase diagram and critical properties of the $S=1/2$ two-leg Heisenberg spin ladder system with a negative four-spin interaction using a numerical exact diagonalization method. Using the perturbation theory in the strong negative rung-coupling limit, we derive an $S=1$ bilinear-biquadratic chain as an effective model. We discuss the ground-state phase diagram in this limit. Next we numerically determine a phase boundary between the rung singlet phase and the columnar dimer (CD) phase by the phenomenological renormalization group method, and one between the CD phase and the Haldane phase by the twisted boundary condition method. We confirm that the phase transition between the CD phase and the Haldane phase is of second order and this universality class is described by the $k=2$ $SU(2)$ Wess-Zumino-Novikov-Witten nonlinear $\ensuremath{\sigma}$ model, calculating the central charge and scaling dimensions.

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We study a two-leg antiferromagnetic spin-1/2 ladder in the presence of a staggered magnetic field. We consider two parameter regimes: strong (weak) coupling along the legs and weak (strong) coupling along the rungs. In both cases, the staggered field drives the Haldane spin-liquid phase of the ladder towards a Gaussian quantum criticality. In a generalized spin ladder with a non-Haldane, spontaneously dimerized phase, the staggered magnetic field induces an Ising quantum critical regime. In the vicinity of the critical lines, we derive low-energy effective field theories and use these descriptions to determine the dynamical response functions, the staggered spin susceptibility, and the string order parameter.We study a two-leg antiferromagnetic spin-1/2 ladder in the presence of a staggered magnetic field. We consider two parameter regimes: strong (weak) coupling along the legs and weak (strong) coupling along the rungs. In both cases, the staggered field drives the Haldane spin-liquid phase of the ladder towards a Gaussian quantum criticality. In a generalized spin ladder with a non-Haldane, spontaneously dimerized phase, the staggered magnetic field induces an Ising quantum critical regime. In the vicinity of the critical lines, we derive low-energy effective field theories and use these descriptions to determine the dynamical response functions, the staggered spin susceptibility, and the string order parameter.

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Phase diagram of a spin ladder with cyclic four-spin exchange

Andreas Martin Läuchli, Guido Schmid, Matthias Troyer

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.

arXiv:cond-mat/0206153Physical review. B, Condensed matterMar 31, 200388 citations

We study the excitation spectrum and ground-state properties of the two-leg

S=\frac{1}{2}

The ground state of the

S=1/2

two-leg ladder with the staggered bond alternations is investigated. We have determined the precise phase diagram on the $\ensuremath{\delta}\ensuremath{-}{J}^{\ensuremath{'}}$ plane $(\ensuremath{\delta}$ and ${J}^{\ensuremath{'}}$ are the magnitudes of the bond alternation and the rung interaction, respectively), employing the level spectroscopic analysis of the numerical diagonalization data obtained by the Lanczos algorithm with the twisted boundary condition. The phase boundary between the leg-dimer state and the rung-dimer state near $(\ensuremath{\delta}{,J}^{\ensuremath{'}})=(0,0)$ is of the form ${J}^{\ensuremath{'}}\ensuremath{\propto}{\ensuremath{\delta}}^{0.69},$ which is consistent with the prediction ${J}^{\ensuremath{'}}\ensuremath{\propto}{\ensuremath{\delta}}^{2/3}$ by Mart\'{\i}n-Delgado, Duleksky, and Sierra, and also by Wang and Nersesyan, but not with ${J}^{\ensuremath{'}}\ensuremath{\propto}{\ensuremath{\delta}}^{2}$ by Cabra and Grynberg.

We investigate the ground-state phase diagram and critical properties of the

S=1/2

two-leg Heisenberg spin ladder system with a negative four-spin interaction using a numerical exact diagonalization method. Using the perturbation theory in the strong negative rung-coupling limit, we derive an

S=1

bilinear-biquadratic chain as an effective model. We discuss the ground-state phase diagram in this limit. Next we numerically determine a phase boundary between the rung singlet phase and the columnar dimer (CD) phase by the phenomenological renormalization group method, and one between the CD phase and the Haldane phase by the twisted boundary condition method. We confirm that the phase transition between the CD phase and the Haldane phase is of second order and this universality class is described by the

k=2

SU(2)

Wess-Zumino-Novikov-Witten nonlinear $\ensuremath{\sigma}$ model, calculating the central charge and scaling dimensions.

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 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.