Finite-Size Geometric Entanglement from Tensor Network Algorithms

Understand

The global geometric entanglement is studied in the context of newly-developed tensor network algorithms for finite systems.

• For one-dimensional quantum spin systems it is found that, at criticality, the leading finite-size correction to the global geometric entanglement 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 geometric entanglement 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.