Entanglement renormalization

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  • 8 December 2005
Abstract
In the context of real-space renormalization group methods for quantum lattice systems in D spatial dimensions, we propose a coarse-graining transformation that renormalizes the amount of entanglement of a block prior to truncating its Hilbert space. Numerical simulations in D=1 spatial dimensions show that the resulting coarse-grained site requires a Hilbert space dimension that does not grow with successive scale transformations. This feature allows us to analyze, through quasi-exact calculations, the ground state of a critical system comprising 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, all length scales make an equivalent contribution to the entanglement in the system.

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