The area law and real-space renormalization

Understand

Real-space renormalization-group techniques for quantum systems can be divided into two basic categories - those capable of representing correlations following a simple boundary (or area) law, and those which are not.

• I discuss the scaling of the accuracy of gapped systems in the latter case and analyze the resultant spatial anisotropy.
• It is apparent that particular points in the system, that are somehow `central' in the renormalization, have local quantities that are much closer to the exact results in the thermodynamic limit than the system-wide average.
• Numerical results from the tree-tensor network and tensor renormalization-group approaches for the 2D transverse-field Ising model and 3D classical Ising model, respectively, clearly demonstrate this effect.