Asymptotic scars arising from the remnants of quantum phase transitions

arXiv:2610.32037v1 Announce Type: new Abstract: Many-body localisation, Hilbert space fragmentation and quantum many-body scars (QMBS) are well-established mechanisms of ergodicity breaking in quantum systems. Recently, asymptotic quantum many-body scars (AQMBS), non-thermal states whose stability grows with system size, have been proposed theoretically and probed experimentally. Here, we show that AQMBS arise naturally as remnants of certain quantum phase transitions. For a broad class of frustration-free Hamiltonians, we prove that their gapless excitations survive deformation into a scarred Hamiltonian as states whose energy variance is bounded by the excitation gap. Consequently, the gapless excitations at a quantum critical point become AQMBS of the scarred Hamiltonian.