A Gaussian Variational Approach to cMERA for Interacting Fields

TL;DR

This work develops a Gaussian-variational formulation of cMERA to extend continuum multiscale entanglement renormalization (cMERA) to interacting quantum field theories in arbitrary dimensions. By identifying the first two terms in the variational expansion with the Gaussian Effective Potential, the authors reduce the problem to solving a gap equation for an effective mass, enabling analytic or semi-analytic non-perturbative results. They demonstrate the approach with scalar $\varphi^4$ theory and the Gross-Neveu model, obtaining non-perturbative masses and clarifying the RG interpretation of the cMERA flow, including the quasi-local nature of the renormalized Hamiltonian. The work establishes a practical bridge between cMERA and Gaussian wavefunctionals, paving the way for beyond-quadratic extensions and potential connections to holography and conformal field theories.

Abstract

We use the Gaussian variational principle to apply cMERA to interacting quantum field theories in arbitrary spacetime dimensions. By establishing a correspondence between the first two terms in the variational expansion and the Gaussian Effective Potential, we can exactly solve for a variational approximation to the cMERA entangler. As examples, we treat scalar $\varphi^4$ theory and the Gross-Neveu model and extract non-perturbative behavior. We also comment on the connection between generalized squeezed coherent states and more generic entanglers.