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We show that topological phases of the Dirac system in arbitral evendimensional space are simulated by $LC$ electric circuits with operationalamplifiers. The lattice Hamiltonian for the hypercubic lattice in $2n$dimensional space is characterized by the $n$-th Chern number. The boundarystate is described by the Weyl theory in $2n-1$ dimensional space. They arewell observed by measuring the admittance spectrum. They are different from thedisentangled $n$-th Chern insulators previously reported, where the $n$-thChern number is a product of the first Chern numbers. The results are extendedto non-Hermitian systems with complex Dirac masses. The non-Hermitian $n$-thChern number remains to be quantized for the complex Dirac mass.

Electric circuit simulations of $n$th-Chern insulators in $2n$-dimensional space and their non-Hermitian generalizations for arbitral $n$