paper

Non-Gaussian Entanglement Renormalization for Quantum Fields

arXiv:2003.08438 · doi:10.1007/JHEP07(2020)149

Abstract

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 theory in 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.

arXiv commentv2: (43 pages) substantial improvement to the optimization procedure of the circuit for the model (Section 5.3). A new appendix is added to illustrate what are the features of the ground state of the theory that captured by the icMERA tensor network. Accepted for publication in JHEP

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