Validity of the ESQPT–DPT connection in nonintegrable models with limited system sizes

Determine whether the direct connection between excited-state quantum phase transitions and dynamical phase transitions (DPT-I and DPT-II) established in the Lipkin–Meshkov–Glick model persists in nonintegrable quantum many-body models where only small system sizes and incomplete spectral information are accessible, making it difficult to reliably discern criticality.

Background

The paper demonstrates, in the Lipkin–Meshkov–Glick (LMG) model, a direct connection between excited-state quantum phase transitions (ESQPTs) and two major notions of dynamical phase transitions (DPT-I and DPT-II), including at finite temperature. This connection links the dynamical phases to ESQPT critical energies and associated conservation laws, and aligns with known relationships between DPT-I and DPT-II.

Extending these findings to nonintegrable models is nontrivial. In such systems, computational access is typically limited to small system sizes, hindering reliable identification of ESQPT signatures and criticality in the spectrum, even though a direct connection between DPT-I and DPT-II has been established in various nonintegrable settings. The authors explicitly raise whether the ESQPT–DPT connection they establish in the LMG model also holds under these more constrained, nonintegrable conditions.