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DTSTAMP:20261014T204707Z
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DESCRIPTION:Quantum phase transitions manifest as an abrupt change in the g
 round state of a many-body system\; yet it is an open question whether thi
 s sudden change necessarily precludes a continuous dynamical connection be
 tween the two phases. We introduce a classification of quantum phase trans
 itions based on this geometric aspect of the ground-state manifold\, that 
 differs from known classifications. By leveraging the framework of counter
 diabatic driving\, we explicitly construct schedules that dynamically conn
 ect one phase to another. This strategy allows us to uncover a large class
  of quantum phase transitions\, where the states on both sides are separat
 ed only by a finite geometric distance in the thermodynamic limit. We term
  such transitions traversable\, since exact counterdiabatic driving links 
 the two phases via a finite dynamical protocol in the thermodynamic limit.
 \nWe show that multiple known transitions fall into this class—e.g.\, sy
 mmetry-breaking transitions obeying hyperscaling and discontinuous transit
 ions with an enhanced continuous symmetry. We further show the existence o
 f quantum phase transitions that cannot be crossed dynamically even with t
 he help of nonlocal counterdiabatic driving\, as they would require diverg
 ent amplitudes and frequencies. Geometrically\, these nontraversable trans
 itions correspond to an infinite distance separating the two phases of mat
 ter\; we show that the class comprises continuous transitions exhibiting m
 ean-field universality—including long-range interacting systems\, and di
 scontinuous transitions arising from the competition between metastable mi
 nima.\nOur geometric classification goes beyond the known taxonomy\, is in
 dependent of local order parameters and renormalization group fixed points
 \, and has direct implications for quantum sensing\, the complexity of sta
 te preparation\, and adiabatic quantum computing.\n\nReference: https://ar
 xiv.org/abs/2605.31472
LOCATION:ETH Zürich\, Hönggerberg HIT E 41.1
ORGANIZER:Marin Bukov
SUMMARY:(Non-)Traversable Quantum Phase Transitions
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