https://doi.org/10.1140/epjb/e2009-00077-7
Magnetic phase diagram of the dimerized spin S = 1/2 ladder
1
Institut für Theoretische Physik, Universität zu Köln, Zülpicher Str. 77, 50937 Köln, Germany and Andronikashvili Institute of Physics, Tamarashvili 6, 0177 Tbilisi, Georgia
2
Department of Physics, University of Guilan, 41335-1914, Rasht, Iran
Corresponding author: a mahdavifar@guilan.ac.ir
Received:
25
November
2008
Revised:
3
February
2009
Published online:
3
March
2009
The ground-state magnetic phase diagram of a spin S=1/2 two-leg ladder with alternating rung exchange J⊥(n)=J⊥[1 + (-1)n δ] 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 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.Pq – Spin chain models
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2009