Breakdown of the coherent state path integral: two simple examples

TL;DR

This paper demonstrates the failure of the time-continuous coherent state path integral in specific quantum models, highlighting issues that do not occur in the discretized version, thus questioning its reliability in certain cases.

Contribution

It provides explicit examples showing the breakdown of the continuous path integral approach for the Bose-Hubbard and spin models with quadratic Hamiltonians.

Findings

Time-continuous path integral fails for specific models.

Discretized path integral remains valid in these cases.

Highlights limitations of the continuous approach in quantum path integrals.

Abstract

We show how the time-continuous coherent state path integral breaks down for both the single-site Bose-Hubbard model and the spin path integral. Specifically, when the Hamiltonian is quadratic in a generator of the algebra used to construct coherent states, the path integral fails to produce correct results following from an operator approach. As suggested by previous authors, we note that the problems do not arise in the time-discretized version of the path integral.