Use of Schwinger-Dyson equation in constructing an approximate trivializing map

TL;DR

This paper introduces an approximate trivializing map constructed via Schwinger-Dyson equations, offering flexibility in kernel choice and applicability to general actions, with preliminary results showing improved control but high computational overhead.

Contribution

It presents a novel method for constructing trivializing maps using Schwinger-Dyson equations, adaptable to various actions and based on lattice estimates, with initial promising results.

Findings

Better control of the effective action compared to t-expansion

Faster decorrelation observed for some long-range observables

High algorithmic overhead limits practical efficiency

Abstract

We construct an approximate trivializing map by using a Schwinger-Dyson equation. The advantage of this method is that: (1) The basis for the flow kernel can be chosen arbitrarily by hand. (2) It can be applied to the general action of interest. (3) The coefficients in the kernel are determined by lattice estimates of the observables, which does not require analytic calculations beforehand. We perform the HMC with the effective action obtained by the Schwinger-Dyson method, and show that we can have better control of the effective action than the known $t$-expansion construction. However, the algorithmic overhead is still large and overwhelming the gain though faster decorrelation is observed for long-range observables in some cases. This contribution reports the preliminary results of this attempt.