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

The ground-state magnetic phase diagram of a spin S = 1/2 two-leg ladder with alternating rung exchange J⊥(n) = J⊥[1 + (−1) nδ] 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 sineGordon 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 spinspin correlation function. We have also calculated the width of the magnetization plateau and show that it scales as δν , where critical exponent varies from ν = 0.87 ± 0.01 in the case of a ladder with isotropic antiferromagnetic legs to ν = 1.82±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. PACS. 75.10.Jm Quantized spin models; 75.10.PqSpin chain models