Introduction to Configuration Path Integral Monte Carlo

In low-temperature high-density plasmas quantum effects of the electrons are becoming increasingly important. This requires the development of new theoretical and computational tools. Quantum Monte Carlo methods are among the most successful approaches to first-principle simulations of many-body quantum systems. In this chapter we present a recently developed method---the configuration path integral Monte Carlo (CPIMC) method for moderately coupled, highly degenerate fermions at finite temperatures. It is based on the second quantization representation of the $N$-particle density operator in a basis of (anti-)symmetrized $N$-particle states (configurations of occupation numbers) and allows to tread arbitrary pair interactions in a continuous space. We give a detailed description of the method and discuss the application to electrons or, more generally, Coulomb-interacting fermions. As a test case we consider a few quantum particles in a one-dimensional harmonic trap. Depending on the coupling parameter (ratio of the interaction energy to kinetic energy), the method strongly reduces the sign problem as compared to direct path integral Monte Carlo (DPIMC) simulations in the regime of strong degeneracy which is of particular importance for dense matter in laser plasmas or compact stars. In order to provide a self-contained introduction, the chapter includes a short introduction to Metropolis Monte Carlo methods and the second quantization of quantum mechanics.Comment: chapter in book "Introduction to Complex Plasmas: Scientific Challenges and Technological Opportunities", Michael Bonitz, K. Becker, J. Lopez and H. Thomsen (Eds.) Springer Series "Atomic, Optical and Plasma Physics", vol. 82, Springer 2014, pp. 153-194 ISBN: 978-3-319-05436-0 (Print) 978-3-319-05437-7 (Online

Correlation Induced Inhomogeneity in Circular Quantum Dots

Properties of the "electron gas" - in which conduction electrons interact by means of Coulomb forces but ionic potentials are neglected - change dramatically depending on the balance between kinetic energy and Coulomb repulsion. The limits are well understood. For very weak interactions (high density), the system behaves as a Fermi liquid, with delocalized electrons. In contrast, in the strongly interacting limit (low density), the electrons localize and order into a Wigner crystal phase. The physics at intermediate densities, however, remains a subject of fundamental research. Here, we study the intermediate-density electron gas confined to a circular disc, where the degree of confinement can be tuned to control the density. Using accurate quantum Monte Carlo techniques, we show that the electron-electron correlation induced by an increase of the interaction first smoothly causes rings, and then angular modulation, without any signature of a sharp transition in this density range. This suggests that inhomogeneities in a confined system, which exist even without interactions, are significantly enhanced by correlations.Comment: final version, modified introduction and clarifications, 4 page