Entanglement and fidelity signatures of quantum phase transitions in spin liquid models

We consider a spin ladder model which is known to have matrix product states as exact ground states with spin liquid characteristics. The model has two critical-point transitions at the parameter values u=0 and infinity. We study the variation of entanglement and fidelity measures in the ground states as a function of u and specially look for signatures of quantum phase transitions at u=0 and infinity. The two different entanglement measures used are S(i) (the single-site von Neumann entropy) and S(i, j) (the two-body entanglement). At the quantum critical point (QCP) u=infinity, the entanglement measure E (=S(i) ,S(i, j)) vanishes but remains nonzero at the other QCP u=0. The first and second derivatives of E with respect to the parameter u and the entanglement length associated with S(i, j) are further calculated to identify special features, if any, near the QCPs. We further determine the GS fidelity F and a quantity ln(D) related to the second derivative of F and show that these quantities calculated for finite-sized systems are good indicators of QPTs occurring in the infinite system.