From Symmetries to Commutant Algebras in Standard Hamiltonians

Understand

In this work, we revisit several families of standard Hamiltonians that appear in the literature and discuss their symmetries and conserved quantities in the language of commutant algebras.

• In particular, we start with families of Hamiltonians defined by parts that are local, and study the algebra of operators that separately commute with each part.
• The families of models we discuss include the spin-1/2 Heisenberg model and its deformations, several types of spinless and spinful free-fermion models, and the Hubbard model.
• This language enables a decomposition of the Hilbert space into dynamically disconnected sectors that reduce to the conventional quantum number sectors for regular symmetries.