Eur. Phys. J. B 68, 59-66 (2009)
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

Abstract

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 δ^ν, 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.