Tunneling with physics-informed renormalisation group flows in the anharmonic oscillator

The resolution of strongly correlated physical systems is computationally hard, but can be simplified enormously by a formulation in terms of suitable dynamical degrees of freedom. Within the functional renormalisation group framework, physics-informed renormalisation group flows (PIRG flows) [1] implement scale-dependent coordinate transformations that can be used to devise optimal expansion schemes around such degrees of freedom.

Recently, we have applied PIRG flows to the anharmonic oscillator, with an emphasis on the weak coupling regime with its instanton-dominated tunnelling processes [2].
We show that the instanton physics behind the exponential decay of the energy gap is already covered in the first order of the derivative expansion of the PIRG. The crucial new ingredients in the present analysis are the use of the ground state expansion within PIRG flows, as well as precision numerics based on Galerkin methods. Our result a_inst = 1.910(2) for the decay constant is in quantitative agreement with the analytic one, a_inst = 1.886 with a deviation of 1%. This illustrates very impressively the capacity of the PIRG for fully capturing non-perturbative physics already in relatively simple approximations.