Physical observable for one-dimensional the spin-1 Blume–Capel model

We carry out an extensive study, within the infinite matrix product state algorithm, one-dimensional spin-1 Blume–Capel model on the spin-chain and subject to a changeable external magnetic field. The phase transition points are obtained by investigating the behavior of physical observable and as well as exacting the critical exponent from the scaling relationship. The final results are achieved for the physical observable-quantum entanglement entropy, local order parameter and its scaling: the scaling relationship between quantum entanglement entropy and truncation dimension, the scaling of Schmidt decomposition coefficient λmax and truncation dimension, the critical exponent of local order parameter near the phase transition point is extracted with the scaling behavior for the model with exchange coupling γ=0.6. These techniques are an easy way to exact the critical exponent for quantum phase transitions.