ap.analysis of pdes – Non-isolated ground state of a Schrödinger operator

Question. Is there a dimension $$d in mathbb {N}$$ and a measurable function $$V: mathbb {R} ^ d to[0infty)[0infty)[0infty)[0infty)$$ such as the smallest spectral value $$lambda$$ of the Schrödinger operator $$– Delta + V$$ sure $$L ^ 2 ( mathbb {R} ^ d)$$ is a proper value, but not an isolated point of the spectrum?

I would expect this to be known, but I could not give an example (neither myself nor by browsing scripts about Schrödinger operators).