Thermodynamic behavior near the quantum orders in dimerized spin SÂ =Â 1/2 two-leg ladders

Thermodynamic properties of spin-1/2 Heisenberg antiferromagnetic (AFM) two-leg ladder with alternating strong rung interactions are investigated by numerical and analytical approaches. Two gapless Luttinger Liquid (LL) and two gapped symmetry protected topological (SPT) phases are observed in this type of spin structure. As a low temperature characteristic of the first LL gapless regime, a maximum and a minimum are observed in the magnetization curve. The magnetization of the system in the second LL phase is completely different and shows only a maximum in the temperature behavior. In the SPT Haldane phase, the value of magnetization increases with single broad peak, while apparently anomalous behavior is observed in the SPT 1/2-plateau phase. In fact, we have argued that the magnetization shows a complex logical temperature behavior in the 1/2-plateau phase. In the second LL phase, there is a novel three peaks structure in the temperature behavior of the specific heat whereas in the first LL phase, specific heat shows a double peaks structure. The temperature dependence of thermodynamic quantities like the magnetization, the susceptibility and the specific heat are also studied to specify various SPT and LL phases.