Absence of ground states at large total momentum in translation-invariant polaron models

Determine whether, for translation-invariant polaron models at fixed total momentum P (including the Fröhlich polaron and the Bose polaron without ultraviolet regularization), ground states are absent at sufficiently large |P|, thereby proving the conjectured nonexistence of ground states in that regime.

Background

The authors situate their results within non-relativistic quantum field theory and discuss analogous phase-transition phenomena in polaron models. For fixed total momentum, ground states at small |P| are known to exist, but the expected absence at large |P| remains mostly unproven.

They highlight that only in the ultraviolet-regularized Fröhlich polaron has absence at large momentum been established, leaving a broader open question in the field.

References

Especially, when one turns to translation-invariant polaron models such as the Fr\"ohlich polaron or the Bose polaron at fixed total momentum $P$, then the existence of ground states at small total momentum is well-known and the absence of ground states at large total momentum is at least conjectured, but except for the ultraviolet regularized Fr\"ohlich polaron not proven.

— On the Ising Phase Transition in the Infrared-Divergent Spin Boson Model  (2501.19362 - Betz et al., 31 Jan 2025) in Introduction, broader context paragraph