Magnetic phase diagram of the dimerized spin $S=1/2$ ladder

Abstract

The ground-state magnetic phase diagram of a spin $S=1/2$ two-leg ladder with alternating rung exchange $J_{\perp }(n)=J_{\perp }[1+(-1{)}^n\delta ]$ is studied using the analytical and numerical approaches. In the limit where the rung exchange is dominant, we have mapped the model onto the effective quantum sine-Gordon model with topological term and identified two quantum phase transitions at magnetization equal to the half of saturation value from a gapped to the gapless regime. These quantum transitions belong to the universality class of the commensurate-incommensurate phase transition. We have also shown that the magnetization curve of the system exhibits a plateau at magnetization equal to the half of the saturation value. We also present a detailed numerical analysis of the low energy excitation spectrum and the ground state magnetic phase diagram of the ladder with rung-exchange alternation using Lanczos method of numerical diagonalizations for ladders with number of sites up to N=28. We have calculated numerically the magnetic field dependence of the low-energy excitation spectrum, magnetization and the on-rung spin-spin correlation function. We have also calculated the width of the magnetization plateau and show that it scales as ${\delta }^{\nu }$, where critical exponent varies from $\nu =0.87\pm 0.01$ in the case of a ladder with isotropic antiferromagnetic legs to $\nu =1.82\pm 0.01$ in the case of ladder with ferromagnetic legs. Obtained numerical results are in an complete agreement with estimations made within the continuum-limit approach.

8 pages, 6 figures. arXiv admin note: text overlap with arXiv:cond-mat/0603153, arXiv:1110.4467

References in corpus (8)

• Bose-Einstein Condensation in Magnetic Insulators
• Quantum magnetism and criticality
• Electron Spin Resonance in sine-Gordon spin chains in the perturbative spinon regime
• Magnetization plateau in the S=1/2 spin ladder with alternating rung exchange
• Field-induced gap in ordered Heisenberg antiferromagnets
• Magnetic field induced phase transitions in spin ladders with ferromagnetic legs
• Scaling behavior of the energy gap of spin-1/2 AF-Heisenberg chain in both uniform and staggered fields
• Spin Ladder with Anisotropic Ferromagnetic Legs in a Transverse Magnetic Field

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• Thermal Properties of Rung Disordered Two-leg Quantum Spin Ladders: Quantum Monte Carlo Study
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