Density Matrix Renormalization Group Lagrangians

Understand

We introduce a Lagrangian formulation of the Density Matrix Renormalization Group (DMRG).

• We present Lagrangians which when minimised yield the optimal DMRG wavefunction in a variational sense, both within the general matrix product ansatz, as well as within the canonical form of the matrix product that is constructed within the DMRG sweep algorithm.
• Some of the results obtained are similar to elementary expressions in Hartree-Fock theory, and we draw attention to such analogies.
• The Lagrangians introduced here will be useful in developing theories of analytic response and derivatives in the DMRG.