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

The many-body Hamiltonians and other fermionic physical observables are expressed in terms of fermionic creation and annihilation operators, which form the algebra of canonical anti-commutation relations (CAR). In this work we use a canonical isomorphism between CAR and $\mathcal M_{2^\infty}$ algebras to derive analytic matrix representations of many-fermion operators. Code-lines implementing these matrix representations are supplied and Hubbard-type Hamiltonians are worked out explicitly.