Effective non-Hermitian systems with interactions are incompatible with direct inclusion of anti-Hermitian terms in Matsubara Green's functions and are instead described by pseudo-Hermitian quantum mechanics.
( 12) (suppressing momentum index), we have χAB (t − t′) = − iθ(t − t′) ∑ αβγδ ei(ξα− ξβ )(t− t′)ïLα|ˆA|RβðïLγ|ˆB|Rδðï[c R α cL β , c R γ cL δ ]ð
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Physical constraints on effective non-Hermitian systems
Effective non-Hermitian systems with interactions are incompatible with direct inclusion of anti-Hermitian terms in Matsubara Green's functions and are instead described by pseudo-Hermitian quantum mechanics.