Density matrix renormalisation group Lagrangians
We introduce a Lagrangian formulation of the density matrix renormalisation group (DMRG). We present Lagrangians which, when minimised, yield the optimal DMRG wavefunction in a variational sense, both within the general matrix product ansatz and 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.
This journal is © the Owner Societies 2008. Received 28th March 2008, Accepted 25th April 2008. We would like to thank the referees for their detailed comments on the manuscript. The author acknowledges support from the US Department of Energy under award #DE-FG02-07ER46432.
Submitted - 0804.1755v1.pdf
Published - b805292c.pdf