Entanglement scaling for $\lambda {\varphi }_2^4$

We study the $\lambda {\varphi }^4$ model in $0+2$ dimensions at criticality, and effectuate a simultaneous scaling of UV and IR physics. We demonstrate that the order parameter $\varphi$, the correlation length $\xi$ and quantities like ${\varphi }^3$ and the entanglement entropy exhibit useful double scaling properties. The calculations are performed with boundary matrix product state methods on tensor network representations of the partition function, though the technique is equally applicable outside the realm of tensor networks. We find the value ${\alpha }_c=11.09698(31)$ for the critical point, improving on previous results.