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The many-body Hamiltonians and other fermionic physical observables areexpressed in terms of fermionic creation and annihilation operators, which formthe algebra of canonical anti-commutation relations (CAR). In this work we usea canonical isomorphism between CAR and $\mathcal M_{2^\infty}$ algebras toderive analytic matrix representations of many-fermion operators. Code-linesimplementing these matrix representations are supplied and Hubbard-typeHamiltonians are worked out explicitly.

Computational Many-Body Physics via $\mathcal M_{2^q}$ Algebra