Emergent geometry and path integral optimization for a Lifshitz action

Extending the background metric optimization procedure for Euclidean path integrals of two-dimensional conformal field theories, introduced by Caputa et al. [Phys. Rev. Lett. 119, 071602 (2017), J. High Energy Phys. 11 (2017) 097], to a z = 2 anisotropically scale-invariant (2 + 1)-dimensional Lifshitz field theory of a free massless scalar field, we find optimal geometries for static and dynamic correlation functions. For the static correlation functions, the optimal background metric is equivalent to an AdS metric on a Poincare patch, while for dynamical correlation functions, we find Lifshitz like metric. This results suggest that a MERA-like tensor network, perhaps without unitarity, would still be considered an optimal background spacetime configuration for the numerical description of this system, even though the classical action we start with is not a conformal field theory.

Automated summary

By extending the background metric optimization procedure to a Lifshitz field theory, optimal geometries for static and dynamic correlation functions were found. The results suggest that a MERA-like tensor network may still be considered an optimal background spacetime configuration for the numerical description of this system, despite not starting with a conformal field theory.