Applying the variational principle to (1+1)-dimensional quantum field theories

Understand

We extend the recently introduced continuous matrix product state (cMPS) variational class to the setting of (1+1)-dimensional relativistic quantum field theories.

• This allows one to overcome the difficulties highlighted by Feynman concerning the variational procedure applied to relativistic theories, and provides a new way to regularize quantum field theories.
• A fermionic version of the continuous matrix product state is introduced which is manifestly free from fermion doubling and sign problems.
• We illustrate the power of the formalism with the simulation of free massive Dirac fermions, the Gross-Neveu model, and the Casimir effect.