Entanglement scaling and criticality with tensor networks

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.