  In this work, a non-Gaussian cMERA tensor network for interacting quantum
field theories (icMERA) is presented. 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 nonperturbatively 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 and fermionic field theories. Finally, the icMERA
tensor network is fully optimized for the $\lambda \phi^4$ 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.
