Path-integral Monte Carlo study on SUSY isospectrality in quartic double-well potential

Abstract

In this paper, we apply Path-integral Monte Carlo (PIMC) to compute the ground-state densities of a quartic double-well potential V₀(x) and its SUSY partner V₁(x), parametrised by barrier height h and well-separation b. Each density was characterized by its peak separation d mapped across the (h, b) parameter space, providing a non-perturbative numerical test of the SUSY isospectrality relation. The energy of the ground-state density of V₁ is confirmed to be degenerate with the first excited state of V₀, confirming this relation. Moreover, it was found that the peak separation d grows monotonically with b. However, this behavior breaks down when h → 0, which can be explained by the histograms of the ground-state densities in these regions, which were broad and relatively flat. Given these results, it was demonstrated that PIMC can be a direct numerical probe of ground-state SUSY QM.