Transient-estimate Monte Carlo in the two-dimensional electron gas

Efficient algorithm for "on-the-fly" error analysis of local or distributed serially correlated data

We describe the Dynamic Distributable Decorrelation Algorithm (DDDA) which efficiently calculates the true statistical error of an expectation value obtained from serially correlated data "on-the-fly," as the calculation progresses. DDDA is an improvement on the Flyvbjerg-Petersen renormalization group blocking method (Flyvberg and Peterson, J Chem Phys 1989, 91, 461). This "on-the-fly" determination of statistical quantities allows dynamic termination of Monte Carlo calculations once a specified level of convergence is attained. This is highly desirable when the required precision might take days or months to compute, but cannot be accurately estimated prior to the calculation. Furthermore, DDDA allows for a parallel implementation which requires very low communication, O(log(2)N), and can also evaluate the variance of a calculation efficiently "on-the-fly." Quantum Monte Carlo calculations are presented to illustrate "on-the-fly" variance calculations for serial and massively parallel Monte Carlo calculations.

Correlation energy and spin polarization in the 2D electron gas

The ground-state energy of the two-dimensional uniform electron gas has been calculated with a fixed-node diffusion Monte Carlo method, including backflow correlations, for a wide range of electron densities as a function of spin polarization. We give a simple analytic representation of the correlation energy which fits our simulation data and includes several known high- and low-density limits. This parametrization provides a reliable local spin density energy functional for two-dimensional systems and an estimate for the spin susceptibility. Within the proposed model for the correlation energy, a weakly first-order polarization transition occurs shortly before Wigner crystallization as the density is lowered.

Excitonic condensation in a symmetric electron-hole bilayer

Using diffusion Monte Carlo simulations we have investigated the ground state of a symmetric electron-hole bilayer and determined its phase diagram at T = 0. We find clear evidence of an excitonic condensate, whose stability however is affected by an in-layer electronic correlation. This stabilizes the electron-hole plasma at large values of the density or interlayer distance, and the Wigner crystal at low density and large distance. We have also estimated pair correlation functions and low-order density matrices to give a microscopic characterization of correlations as well as to try and estimate the condensate fraction.