Wigner crystallization of electrons in a 2D quantum dots is reported. It proceeds in two stages: I) via radial ordering of electrons on shells and II) freezing of the inter-shell rotation. The phase boundary of the crystal is computed in the whole temperature-density plane, and the influence of quantum effects and of the particle number is analyzed.In recent years there is growing interest in finite quantum systems at high density or/and low temperature. In particular, the behavior of a small number of electrons in quantum dots is actively investigated both experimentally [1] and theoretically [2,3]. The limiting behavior oftwo-dimensional (2D) finite quantum systems at zero temperature has been studied by unrestricted Hartree-Fock calculations [2] which revealed a transition from a Fermi liquid to an ordered state called "Wigner molecule". The same crossover at finite temperature has been recently demonstrated by fermionic path integral Monte Carlo [3].It has to be expected that further increase of correlations (increase of the Brueckner parameter r s ) will lead to a still higher ordered quantum state resembling the Wigner crystal (WC) [4,5].On the other hand, for finite classical systems, Monte Carlo simulations have shown evidence of crystallization for sufficiently large values of the coupling parameter Γ. These classical clusters consist of well separated shells [6,7,8,9], and melting proceeds in two stages: first, orientational disordering of shells takes place -neighbouring shells may rotate relative to each other while retaining their internal order. Further growth of thermal fluctuations leads to shell broadening and overlap -radial melting. The temperature of radial melting T r may be many orders of magnitude higher than the orientational melting temperature T o [8]. Large clusters with N > 100 have a regular triangular lattice structure and exhibit only radial melting. Now the question arises, how does the behavior of finite electron clusters change at low temperature, i.e. in the quantum regime? In this Letter we demonstrate that, indeed, Wigner crystallization in 2D quantum electron clusters exists and that it is accompanied by two distinctradial and orientiational -ordering transitions too. However, in contrast to classical clusters, we observe a new melting scenario which is caused by quantum fluctuations and exists even at zero temperature ("cold" melting [10]). We present a detailed analysis of the two-stage quantum melting process and provide numerical data for the phase boundaries of both crystal phases, for particle numbers in the range N = 10 . . . 20.Model and characteristic parameters. The theoretical analysis of quantum confined electrons at finite temperature requires the simultaneous account of strong correlations and quantum effects which excludes e.g. perturbation or mean field methods. We, therefore, use a path integral Monte Carlo (PIMC) approach. We consider a finite unpolarized [11] 2D system of N electrons at temperature T . The electrons interact via the repulsive Coulomb poten...

Small three-dimensional strongly coupled charged particles in a spherical confinement potential arrange themselves in a nested shell structure. By means of experiments, computer simulations, and theoretical analysis, the sensitivity of their structural properties to the type of interparticle forces is explored. While the normalized shell radii are found to be independent of shielding, the shell occupation numbers are sensitive to screening and are quantitatively explained by an isotropic Yukawa model.

Correlated fermions are of high interest in condensed matter (Fermi liquids, Wigner molecules), cold atomic gases and dense plasmas. Here we propose a novel approach to path integral Monte Carlo (PIMC) simulations of strongly degenerate non-ideal fermions at finite temperature by combining a fourth-order factorization of the density matrix with antisymmetric propagators, i.e., determinants, between all imaginary time slices. To efficiently run through the modified configuration space, we introduce a modification of the widely used continuous space worm algorithm, which allows for an efficient sampling at arbitrary system parameters. We demonstrate how the application of determinants achieves an effective blocking of permutations with opposite signs, leading to a significant relieve of the fermion sign problem. To benchmark the capability of our method regarding the simulation of degenerate fermions, we consider multiple electrons in a quantum dot and compare our results with other ab initio techniques, where they are available. The present permutation blocking PIMC approach allows us to obtain accurate results even for N = 20 electrons at low temperature and arbitrary coupling, where no other ab initio results have been reported, so far.