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Résumé |
I will provide a framework for computing time-averaged dynamics in locally interacting systems in any
dimension. It
is based on pseudolocal dynamical symmetries generalising pseudolocal charges and unifies seemingly
disparate
manifestations of quantum non-ergodic dynamics including quantum many-body scars, continuous, discrete
and
dissipative time crystals, Hilbert space fragmentation, lattice gauge theories, and disorder-free localization.
Using
the theory two novel types of phase transitions are introduced: 1) The « scarring phase transition » where the
order
parameter is the locality of the projected local quantities – for certain initial states persistent oscillations are
present. 2) The « fragmentation phase transition » for which long-range order is established in an entire
phase due
to presence of certain non-local strings. Two prototypical, but otherwise mostly intractable, models are
solved using
the theory: 1) a spin 1 scarred model and 2) the t-J_z model with fragmentation.
References:
Berislav Buca. Unified theory of local quantum many-body dynamics: Eigenoperator thermalization theorems.
Phys.
Rev. X 13, 031013 (2023).
Benjamin Doyon. Thermalization and pseudolocality in extended quantum systems. Commun. Math. Phys.
351: 155-
200 (2017). |
