cMERA for interacting quantum fields

Specialist level
Javier Molina Vilaplana
U. Cartagena

The multiscale entanglement renormalization ansatz (MERA), which was originally proposed as a variational method to obtain the ground state of spin chains systems, consists of a real space renormalization group technique that, iteratively, removes the quantum correlations between small adjacent regions of space at each length scale. A continuous version of MERA (cMERA) was proposed, but it only has been properly understood for free field theories. Motivated, among others, by the conjecture that cMERA is a realization of the AdS/CFT correspondence, a  nonperturbative formalism for interacting theories turns out to be essential to advance in this program.
In this Journal Club, we report on a recent proposal for a non-Gaussian cMERA tensor network for interacting quantum field theories (icMERA) . This consists of a continuous tensor network circuit in which the generator of the entanglement renormalization of the wavefunction is nonperturbatively extended with nonquadratic variational terms. The icMERA circuit non perturbatively implements a set of scale dependent nonlinear transformations on the fields of the theory, which suppose a generalization of the scale dependent linear transformations induced by the Gaussian cMERA circuit.
Here we present these transformations for the case of self-interacting scalar  field theories. We show how the icMERA tensor network can be fully optimized for the self interacting scalar theory in (1+1) dimensions. This allows us to evaluate, nonperturbatively, the connected parts of the two- and four-point correlation functions. 
Our results show that icMERA wavefunctionals encode proper non-Gaussian correlations of the theory, thus providing a new variational tool to study phenomena related with strongly interacting field theories.