Finite-size geometric entanglement from tensor network algorithms

The global geometric entanglement (GE) is studied in the context of newly developed tensor network algorithms for finite systems. For onedimensional quantum spin systems it is found that, at criticality, the leading finite-size correction to the global GE per site behaves as b/n, where n is the size of the system and b a given coefficient. Our conclusion is based on the computation of the GE per spin for the quantum Ising model in a transverse magnetic field and for the spin-1/2 XXZ model. We also discuss the possibility of coefficient b being universal