Coupled-cluster summation of the particle-particle ladder diagrams for the two-dimensional electron gas

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Abstract
The correlation energy and antiparallel spin pair correlation function of the two-dimensional electron gas are studied within the particle-particle ladder approximation of the coupled-cluster equations. Unlike the three-dimensional electron gas the correlation energy is shown to be convergent in the particle-particle ladder approximation for the two-dimensional system. The coupled-cluster particle-particle ladder equations are cast into the form of singular integral equations. Using a product integration technique the integral equations are solved numerically. The correlation energy and r=0 value of the antiparallel spin pair correlation function are calculated from the numerical coupled-cluster coefficients for a range of electron densities from rs=0 to 16. The antiparallel spin pair correlation function at r=0 is shown to be positive for all electron densities when a wavefunction accurate to first order in the coupled-cluster particle-particle ladder coefficients is used. The calculated correlation energy is compared with dielectric results of Jonson (1976) and ring results of Freeman (1977, 1978). Good agreement between the dielectric results and the particle-particle ladder results are found for intermediate to low electron densities. The particle-particle ladder coupled-cluster correlation energy is shown to be exact in the high-density limit, although the approach to the limit is not correct owing to the neglect of ring contributions. It is suggested that simultaneous inclusion of particle-particle ladder and ring diagrams will give correlation energies accurate over the entire range of calculated densities.