Conceitos essenciais
While entanglement entropy fails to differentiate between dynamical phases in fermionic systems on regular graphs with varying degrees, Krylov complexity provides a more sensitive measure, revealing distinct complexity phases.
Estatísticas
Entanglement entropy scales as S ~ N for both d = 2 and d = 3 regular graphs.
For free fermions, the Krylov dimension scales as D ~ N for d = 2 and D ~ N^2 for d = 3.
For interacting fermions, the Krylov dimension scales as D ~ 4^(N^α) for d = 2 (0.38 ≤ α ≤ 0.59) and D ~ 4^N for d = 3.
In the interacting case with d = 3, the Lyapunov exponent extracted from OTOC is λL = 0.31(2).