Uses the extension of the Ma RG approach (1973) to quantum functionals in the limit n to infinity to obtain non-perturbative information for quantum systems at T=O, restricting oneself to the n-vector paramagnon problem.
A differential formulation of the dynamic renormalisation group in the large-n limit is presented for the time-dependent generalisation of the n-vector classical model with purely relaxational dynamics for both conserved and non-conserved order parameter. A discussion of the dynamical properties with the same steps used in the traditional perturbative approaches is made in terms of which known and new explicit results are obtained. Furthermore, a mechanical analogy is introduced which may give new information about the structure of the dynamic renormalisation group in the large-n limit. This relies on the possibility of using the well known geometrical and mathematical techniques from the Hamilton-Jacobi theory for classical mechanics.
We solve the anharmonic oscillator using physics-informed renormalisation group (PIRG) flows, focusing on the weak coupling regime dominated by instanton-induced tunnelling processes. We demonstrate that the instanton physics underlying the exponential suppression of the energy gap is already captured at the first order of the derivative expansion within the PIRG framework. The key advances of this work are the implementation of a ground-state expansion in the PIRG flow and the adoption of high-precision Galerkin-based numerics. Our determination of the decay constant, $ a_{} = 1.910(2) $, agrees quantitatively with the analytic value $ a_{} = 1.886 $, differing by only 1\% 1 % . While the present formulation relies on a heuristic mapping that will be systematically refined in future extensions of the PIRG approach, these results already highlight the remarkable ability of the method to capture non-perturbative quantum phenomena within relatively simple truncations.