Complexity Functionals and Complexity Growth Limits in Continuous MERA Circuits

Understand

Using the path integral associated to a cMERA tensor network, we provide an operational definition for the complexity of a cMERA circuit/state which is relevant to investigate the complexity of states in quantum field theory.

• In this framework, it is possible to explicitly establish the correspondence (Minimal) Complexity $=$ (Least) Action.
• Remarkably, it is also shown how the cMERA complexity action functional can be seen as the action of a Liouville field theory, thus establishing a connection with two dimensional quantum gravity.
• Concretely, the Liouville mode is identified with the variational parameter defining the cMERA circuit.