The k-commutant of free fermions is the Grassmannian manifold of fermionic Gaussian states on 2k sites, exposing a real-replica space duality.
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Disorder does not alter the presence or absence of measurement-induced phase transitions in noninteracting fermions; the long-time behavior is controlled by the same nonlinear sigma model with renormalized parameters.
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Geometry of Free Fermion Commutants
The k-commutant of free fermions is the Grassmannian manifold of fermionic Gaussian states on 2k sites, exposing a real-replica space duality.
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Measurement-induced phase transitions in disordered fermions
Disorder does not alter the presence or absence of measurement-induced phase transitions in noninteracting fermions; the long-time behavior is controlled by the same nonlinear sigma model with renormalized parameters.