IQI Weekly Seminar

  Tensor networks, such as the matrix product state (MPS) or the multi-scale entanglement renormalization ansatz (MERA), offer an efficient representation of the ground state wave-function of local Hamiltonians on the lattice. Their continuous counterparts (e.g. cMPS and cMERA), aim similarly to efficiently represent the vacuum state wave-functional of quantum field theories. In this talk I will first review the continuous MERA as proposed by Haegeman, Osborne, Verschelde and Verstraete  [Phys. Rev. Lett. 110, 100402 (2013), arXiv:1102.5524], which is based on a fully reversible, unitary evolution in scale -- in sharp contrast with the lattice MERA, where an isometric evolution in scale is responsible for the loss of information along the renormalization group flow. I will then argue that, for both conceptual and computational reasons, the cMERA should also consist of an isometric evolution in scale, and will propose the use of a projector on local operators to this aim. Finally, I will illustrate the proposal by (1) re-writing some of the free-particle conformal filed theory (CFT) examples of cMERA provided by Haegeman et al. so as to make scale invariance explicit and (2) use the proposed projector to identify the scaling operators of the theory and other conformal data of the CFT.     This is work done in collaboration with Qi Hu [in preparation].