Lipkin translational-symmetry restoration in the mean-field and energy-density-functional methods

TL;DR

This paper discusses a method to restore translational symmetry in mean-field and energy-density functional calculations using Lipkin's approach, involving the Peierls-Yoccoz mass, enabling systematic symmetry restoration.

Contribution

It introduces a systematic, approximate method for restoring translational symmetry in energy-density functional methods based on Lipkin's idea and the Peierls-Yoccoz mass.

Findings

Peierls-Yoccoz mass can be calculated from energy and overlap kernels.

The method allows systematic symmetry restoration within energy-density formalism.

Applicable to all broken symmetries in principle.

Abstract

Based on the 1960 idea of Lipkin, the minimization of energy of a symmetry-restored mean-field state is equivalent to the minimization of a corrected energy of a symmetry-broken state with the Peierls-Yoccoz mass. It is interesting to note that the "unphysical" Peierls-Yoccoz mass, and not the true mass, appears in the Lipkin projected energy. The Peierls-Yoccoz mass can be easily calculated from the energy and overlap kernels, which allows for a systematic, albeit approximate, restoration of translational symmetry within the energy-density formalism. Analogous methods can also be implemented for all other broken symmetries.