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

Abstract

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.