Dielectric Response of Periodic Systems from Quantum Monte Carlo Calculations

We present a novel approach that allows us to calculate the dielectric response of periodic systems in the quantum Monte Carlo formalism. We employ a many-body generalization for the electric-enthalpy functional, where the coupling with the field is expressed via the Berry-phase formulation for the macroscopic polarization. A self-consistent local Hamiltonian then determines the ground-state wave function, allowing for accurate diffusion quantum Monte Carlo calculations where the polarization’s fixed point is estimated from the average on an iterative sequence, sampled via forward walking. This approach has been validated for the case of an isolated hydrogen atom and then applied to a periodic system, to calculate the dielectric susceptibility of molecular-hydrogen chains. The results found are in excellent agreement with the best estimates obtained from the extrapolation of quantum-chemistry calculations.

Figure 1

(a) Polarization of an isolated H atom in the absence of an electric field as a function of the forward walking parameter $\Delta t$, using a trial wave function expressed by a GGA orbital calculated in the presence of an electric field of 0.005 a.u. The dashed line is a guide to the eye. (b) Polarizability of an isolated H atom, for each of the self-consistent DMC runs in the iterative sequence (see text). The dashed line is a guide to the eye.

Figure 2

(a) Linear polarizability per ${\mathrm{H}}_2$ unit for a periodic linear chain of 22 ${\mathrm{H}}_2$ dimers in PBCs, for each of the self-consistent DMC runs in the iterative sequence (see text). The dashed line is a guide to the eye. (b) Last ten $z_i$ values (thin lines) and estimate of the fixed point of $f(z)$ (bold lines).