Entanglement renormalization in noninteracting fermionic systems

Abstract

We demonstrate, in the context of quadratic fermion lattice models in one and two spatial dimensions, the potential of entanglement renormalization (ER) to define a proper real-space renormalization group transformation. Our results show the validity of the multiscale entanglement renormalization ansatz to describe certain ground states in two dimensions, including quantum critical states. They also unveil a connection between the performance of ER and the logarithmic violations of the boundary law for entanglement in systems with a one-dimensional Fermi surface. ER is recast in the language of creation/annihilation operators and correlation matrices. © 2010 The American Physical Society.