Evaluation of vorticity expansion approximation of current-density functional theory by means of Levy’s asymptotic bound

Abstract

We evaluate the vorticity expansion approximation ͑VEA͒ of the current-density functional theory ͑CDFT͒ by means of the derived Levy's asymptotic bound. The VEA formula exactly satisfies Levy's asymptotic bound, though the local-density approximation of the CDFT does not. The validity of the VEA formula is thus confirmed successfully.

Sum rules for the exchange-correlation energy functional of the extended constrained-search theory: Application to checking the validity of the vorticity expansion approximation of the current-density functional theory

“…This approximate form is developed to fulfill the gauge invariance and nineteen sum rules. The VEA formula for a homogeneous system is in quite good agreement with the exchange and correlation energies [34] of the homogeneous electron liquid applied by a uniform magnetic field [31][32][33].…”

“…For the purpose of checking the validity of the VEA formula, the CDFT version of Levy's asymptotic bounds has been derived [32]. It is confirmed that the VEA formula fulfils the bounds, whereas the LDA of the CDFT does not.…”

“…In this section, we evaluate the VEA formula of the CDFT [31][32][33] by using various kinds of sum rules including the four kinds of sum rules derived in the previous section. In Sec.…”

“…These include the set of sum rules that are derived by using the gauge invariance, the virial theorem, the coordinate scaling of electrons, the adiabatic connection, and so on [1,2,9,10,29,30]. Using such sum rules as constraints, we have recently proposed the vorticity expansion approximation (VEA) for the xc energy functional of the CDFT [31][32][33]. This approximate form is developed to fulfill the gauge invariance and nineteen sum rules.…”

Calculation of magnetic oscillations via the magnetic-field-containing relativistic tight-binding approximation method: Revisiting the de Haas–van Alphen effect

“…Therefore, it is expected that the MFRTB method can revisit the dHvA effect from the viewpoint of the first-principles calculation. Besides the description of the dHvA effect, the MFRTB method is also expected to be used for revealing the mechanism of the elastic softening of the boron-doped silicon immersed in the magnetic field [12][13][14][15], and for solving the Kohn-Sham equations of the current-density functional theories [16][17][18][19][20][21][22]. In the previous paper, we have applied this method to the crystalline silicon immersed in the magnetic field and revealed the specific structures of the energy spectrum [11].…”