(University of Ljubljana)
Describing full unitary dynamics of a many-body system is difficult and also unpractical. Focusing on a coarse-grained dynamics or few select observables often results in a more compact non-unitary evolution. Studying bipartite entanglement dynamics in random circuits one can derive a Markovian transfer matrix description that harbors rather intriguing many-body non-Hermitian physics. The speed of generating entanglement is not given by the 2nd largest eigenvalue of the transfer matrix, but rather by a phantom eigenvalue -- an eigenvalue that is not in the spectrum of any finite transfer matrix. Resolution of this paradox will lead to a pseudospectrum and a realization that, when dealing with finite non-Hermitian matrices it can be that being exact is actually wrong, while being slightly wrong is correct.
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