Scaling of entanglement at a quantum phase transition for a two-dimensional array of quantum dots

The entanglement scaling behavior in a two-dimensional itinerant system was analyzed using the Hubbard model. The critical exponent ν=1 was found, which coincides well with the previous work in studying the charge gap. It was shown that, on the two sides of the critical point denoting an inherent quantum phase transition (QPT), the entanglement follows different scalings with the size, just as an order parameter does. The subtle role played by the entanglement in QPT as a fungible physical resource was revealed by the this shown fact.