Entanglement and avoided crossing dynamics in the disordered Majumdar-Ghosh model

We study the ground and first excited state of the finite one dimensional Majumdar-Ghosh model with quenched disorder about the avoided crossings. We find a relation between the shift of the first avoided crossing and average value of random numbers. For low disorder regime, the two-qubit, odd and even partition entanglement gets exchanged at avoided crossings for low spin, and former two for any value of spin. This effect has a deep relation with the dimerization nature of these states. We develop an expression sans entanglement measures to detect and study these crossings. (paper)