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Abstract |
Describing full unitary dynamics of a many-body system is difficult and also unpractical. Focusing on a
coarse-grained dynamics, or few select smooth 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 that is not in the spectrum of any finite transfer matrix. Resolution of this seeming paradox will
involve a spectrum that is completely discontinuous in the thermodynamic limit. When dealing with finite non-
Hermitian matrices it can turn out that being exact is actually wrong, while being slightly wrong is correct. |
