Entanglement renormalization

Abstract

In the context of real-space renormalization group methods, we propose a novel scheme for quantum systems defined on a D-dimensional lattice. It is based on a coarse-graining transformation that attempts to reduce the amount of entanglement of a block of lattice sites before truncating its Hilbert space. Numerical simulations involving the ground state of a 1D system at criticality show that the resulting coarse-grained site requires a Hilbert space dimension that does not grow with successive rescaling transformations. As a result we can address, in a quasi-exact way, tens of thousands of quantum spins with a computational effort that scales logarithmically in the system's size. The calculations unveil that ground state entanglement in extended quantum systems is organized in layers corresponding to different length scales. At a quantum critical point, each rellevant length scale makes an equivalent contribution to the entanglement of a block with the rest of the system.