The description of critical phenomena in terms of the renormalization group forms the cornerstone of our modern understanding of strongly-correlated systems. It leads to effective Hamiltonians that can be studied using numerical methods such as Monte Carlo, and the success of those methods relies heavily on scaling ideas for the interpretation of the data. Based on the density matrix renormalization group (DMRG) and insights from the theory of
entanglement in quantum information, tensor networks have recently emerged as a viable and wider applicable alternative for the numerical study of strongly-correlated systems. In essence, tensor networks describe many-body wavefunctions in terms of local tensors expressing how entanglement is routed. Although critical phenomena have been studied successfully using tensor networks and finiteentanglement scaling ideas have been formulated, the full problem of scaling has never been addressed in its full power and generality. The central goal of this proposal is to put the renormalization group into DMRG and tensor networks. We will develop a comprehensive theoretical and computational framework for entanglement renormalization, and formulate a scaling ansatz in terms of the novel length scales appearing in the tensor-network description. This research is a fusion of the two groups’ research interests, the Ghent group providing the expertise on tensor networks and the Innsbruck group on scaling and CFTs in strongly-correlated systems.