Crossover from Fermi liquid to Wigner molecule behavior in quantum dots

It was recently argued that in small quantum dots the electrons could crystallize at much higher densities than in the infinite two-dimensional electron gas. We compare predictions that the onset of spin polarization and the formation of Wigner molecules occurs at a density parameter $r_s\approx 4 a_B^*$ to the results of a straight-forward diagonalization of the Hamiltonian matrix.

The transport properties of quantum dots with up to N=7 electrons ranging from the weak to the strong interacting regime are investigated via the projected Hartree-Fock technique. As interactions increase radial order develops in the dot, with the formation of ring and centered-ring structures. Subsequently, angular correlations appear, signalling the formation of a Wigner molecule state. We show striking signatures of the emergence of Wigner molecules, detected in transport....

The ab initio thermodynamic simulation of correlated Fermi systems is of central importance for many applications, such as warm dense matter, electrons in quantum dots, and ultracold atoms. Unfortunately, path integral Monte Carlo (PIMC) simulations of fermions are severely restricted by the notorious fermion sign problem (FSP). In this work, we present a hands-on discussion of the FSP and investigate in detail its manifestation with respect to temperature, system size, inter...

We present an extensive comparative study of ground-state densities and pair distribution functions for electrons confined in two-dimensional parabolic quantum dots over a broad range of coupling strength and electron number. We first use spin-density-functional theory to determine spin densities that are compared with Diffusion Monte Carlo (DMC) data. This accurate knowledge of one-body properties is then used to construct and test a local approximation for the electron-pair...

It is well known that the use of the primitive second-order propagator in Path Integral Monte Carlo calculations of many-fermion systems leads to the sign problem. In this work, we show that by using the similarity-transformed Fokker-Planck propagator, it is possible to solve for the ground state of a large quantum dot, with up to 100 polarized electrons, without solving the sign problem. These similarity-transformed propagators naturally produce rotational symmetry-breaking ...

We present a method for performing path integral molecular dynamics (PIMD) simulations for fermions and address its sign problem. PIMD simulations are widely used for studying many-body quantum systems at thermal equilibrium. However, they assume that the particles are distinguishable and neglect bosonic and fermionic exchange effects. Interacting fermions play a key role in many chemical and physical systems, such as electrons in quantum dots and ultracold trapped atoms. A d...

We argue that Coulomb blockade phenomena are a useful probe of the cross-over to strong correlation in quantum dots. Through calculations at low density using variational and diffusion quantum Monte Carlo (up to r_s ~ 55), we find that the addition energy shows a clear progression from features associated with shell structure to those caused by commensurability of a Wigner crystal. This cross-over (which occurs near r_s ~ 20 for spin-polarized electrons) is, then, a signature...

Conditional probability distributions from exact diagonalization are used to investigate the crystalline or liquid character of the downward cusp states in parabolic quantum dots (QD's) at high magnetic fields. These states are crystalline in character for fractional fillings covering both low and high values, unlike the liquid Jastrow-Laughlin wave functions, but in remarkable agreement with the rotating-electron-molecule ones [Phys. Rev. B 66, 115315 (2002)]. The cusp state...

Currents in a few-electron parabolic quantum dot placed into a perpendicular magnetic field are considered. We show that traditional ways of investigating the Wigner crystallization by studying the charge density correlation function can be supplemented by the examination of the density-current correlator. However, care must be exercised when constructing the correct projection of the multi-dimensional wave function space. The interplay between the magnetic field and Euler-li...

Second order perturbation theory and a Lipkin-Nogami scheme combined with an exact Monte Carlo projection after variation are applied to compute the ground-state energy of $6\le N\le 210$ electron-hole pairs confined in a parabolic two-dimensional quantum dot. The energy shows nice scaling properties as N or the confinement strength is varied. A crossover from the high-density electron-hole phase to the BCS excitonic phase is found at a density which is roughly four times the...