Motivated by a number of recent experimental studies we have revisited the problem of the microscopic calculation of the quasiparticle self-energy and many-body effective mass enhancement in an unpolarized two-dimensional electron liquid. Our systematic study is based on the many-body local field theory and takes advantage of the results of the most recent diffusion Monte Carlo calculations of the static charge and spin response of the electron liquid. We report extensive calculations of both the real and imaginary parts of the quasiparticle self-energy. We also present results for the many-body effective mass enhancement and the renormalization constant over a broad range of electron densities. In this respect we critically examine the relative merits of the on-shell approximation, commonly used in weak coupling situations versus the actual self-consistent solution of the Dyson equation. We show that already for r s Ӎ 3 and higher, a solution of the Dyson equation proves necessary in order to obtain a well-behaved effective mass. Finally we find confirmation that the inclusion of both charge-and spin-density fluctuations beyond the random phase approximation is indeed crucial to get reasonable agreement with recent measurements.

We present an analytical expression for the static many-body local field factor G+(q) of a homogeneous two-dimensional electron gas, which reproduces Diffusion Monte Carlo data and embodies the exact asymptotic behaviors at both small and large wave number q. This allows us to also provide a closed-form expression for the exchange and correlation kernel Kxc(r), which represents a key input for density functional studies of inhomogeneous systems.PACS number: 71.10. Ca, 71.15.Mb The static charge-charge response function χ C (q) of a paramagnetic electron gas (EG) can be written in terms of the Lindhard function χ 0 (q) by means of the spin-symmetric many-body local field G + (q) through the relationshipThus G + (q) is a fundamental quantity for the determination of many properties of a general electron system. By definition G + (q) is meant to represent the effects of the exchange and correlation hole surrounding each electron in the fluid and is therefore a key input in the density functional theory (DFT) of the inhomogeneous electron gas 1 and in studies of quasiparticle properties (such as the effective mass and the effective Landè g-factor) in the electronic Fermi liquid 2 . For what concerns DFT calculations, a common approximation to the unknown exchange-correlation energy functional E xc [n] appeals to its second functional derivative,wheren is the average local density of the EG. The local field factor and the exchange-correlation kernel are simply related in Fourier transform bywhere d is the dimensionality of the system and v q is the Fourier transform of the Coulomb potential e 2 /r. In what follows we shall only consider the case of two spatial dimensions, with d = 2 and v q = 2πe 2 /q. The corresponding three-dimensional case was discussed in Ref. [3]. A number of exact asymptotic properties of the static local field factor in two dimensions are readily proven. In particular,withwhere k F = √ 2πn = √ 2/r s a B is the Fermi wave number, r s = πna 2 B is the usual EG density parameter with a B the Bohr radius, κ 0 = πr 4 s /2 is the compressibility of the ideal gas in units of a 2 B /Ryd, while κ is the compressibility of the interacting system. By making use of the thermodynamic definition of κ we can write1 where ǫ c (r s ) is the correlation energy per particle. Once this function is known, it is possible to calculate A + . For the present purpose ǫ c (r s ) can be taken from the Monte Carlo data of Ref. [4]. The asymptotic behavior of G + (q) at large q is also known exactly 5,6 :where C + is proportional to the difference in kinetic energy between the interacting and the ideal gas,Moreover B + = 1 − g(0), g(0) being the value of the pair-correlation function at the origin. For g(0) we use the simple expressionwhich has been derived 7 by an interpolation between the result of a low-r s expansion, including the second order direct and exchange contributions to the energy in the paramagnetic state, and the result of a partial-wave phase-shift analysis near Wigner crystallization. This interpolatio...