Variational density matrix optimization using semidefinite programming

TL;DR

This paper presents a method for optimizing the second-order density matrix directly via semidefinite programming, enabling more efficient quantum many-body calculations with demonstrated results on Beryllium series.

Contribution

It introduces a variational approach using semidefinite programming to determine N-representable density matrices, with detailed formulation and solution methods.

Findings

Successfully applied to Beryllium isoelectronic series

Formulated the problem as a standard SDP

Discussed interior point methods for solving SDP

Abstract

We discuss how semidefinite programming can be used to determine the second-order density matrix directly through a variational optimization. We show how the problem of characterizing a physical or N -representable density matrix leads to matrix-positivity constraints on the density matrix. We then formulate this in a standard semidefinite programming form, after which two interior point methods are discussed to solve the SDP. As an example we show the results of an application of the method on the isoelectronic series of Beryllium.