Quantum Monte Carlo study of electrons in low dimensions

Abstract

Abstract. We report on a diffusion Monte Carlo investigation of model electron systems in low dimensions, which should be relevant to the physics of systems obtainable nowadays in semiconductor heterostructures. In particular, we present results for a one dimensional electron gas, at selected values of the coupling strength and confinement parameter, briefly analyzing the pair correlations and relating them to predictions by Schulz for a Luttinger liquid with long-range interactions. We find no evidence of the the Bloch instability yielded by approximate treatments such as the STLS and DFT schemes.

Dependence of structure factor and correlation energy on the width of electron wires

“…The correlation energy at high densities r s ≤ 0.1 and b = 0.1, is in agreement with the quantum Monte Carlo simulation [36,37] for polarized fluids.…”

“…Furthermore, the harmonic wire with transverse confinement has been investigated with a lattice regularized diffusion Monte Carlo (LRDMC) technique by Casula et al [36], and by others [37][38][39].…”

Charge and Spin Correlations of a One‐Dimensional Electron Gas on the Continuum

“…However, they also appear to imply the presence of quasi-antiferromagnetic order, that is, a divergence of the spin structure factor at 2k F in the unpolarized state, a result at variance with the findings of the bosonization technique. [8] Rather than being due to the differences between models, [16] such a discrepancy is likely to result from the ergodicity problems encountered in both DMC and VMC simulations at strong coupling, [15,17] as exchange between opposite spin electrons is frozen out by the strong Coulomb repulsion. Whereas in the DMC method a solution of such a problem is not straightforward, [17] in VMC simulations one may devise fairly simple ways of restoring ergodicity, [15,17] [a] Dr. M. We present a variational Monte Carlo study of a model onedimensional electron gas on the continuum, with long-range interaction (1/r decay).…”

Ground-state properties of the one-dimensional electron liquid

“…For the harmonic wire, we used cells with N = 123, 155, and occasionally 255 for the ζ = 1 systems and cells with N = 22 and 102 for the ζ = 0 systems. Previous work encountered difficulties in sampling different spin configurations of the harmonic wire for ζ = 1 due to the presence of pseudonodes at the antiparallel coalescence points, 40 although these problems were largely overcome by the use of lattice-regularized diffusion Monte Carlo (LRDMC) in Ref. 38.…”

“…37,38 An example of this is the harmonic wire, in which the transverse confinement is provided by a parabolic potential, leading to a Gaussian density profile in the transverse plane. The harmonic wire has been studied with quantum Monte Carlo (QMC), [38][39][40] variants of the Singwi-Tosi-Land-Sjölander approach, [41][42][43][44] and the Fermi hypernetted-chain approximation. 45 We have studied both the infinitely thin wire and the harmonic wire using QMC.…”