Phase diagram of a quantum Coulomb wire

Abstract

We report the quantum phase diagram of a one-dimensional Coulomb wire obtained using the path integral Monte Carlo (PIMC) method. The exact knowledge of the nodal points of this system permits us to find the energy in an exact way, solving the sign problem which spoils fermionic calculations in higher dimensions. The results obtained allow for the determination of the stability domain, in terms of density and temperature, of the one-dimensional Wigner crystal. At low temperatures, the quantum wire reaches the quantum-degenerate regime, which is also described by the diffusion Monte Carlo method. Increasing the temperature the system transforms to a classical Boltzmann gas which we simulate using classical Monte Carlo. At large enough density, we identify a one-dimensional ideal Fermi gas which remains quantum up to higher temperatures than in twoand three-dimensional electron gases. The obtained phase diagram as well as the energetic and structural properties of this system are relevant to experiments with electrons in quantum wires and to Coulomb ions in one-dimensional confinement.PACS numbers: 71.10. Pm, 71.10.Hf, 73.21.Hb Few systems are more universal than electron gases. Their study started long-time ago and the compilation of knowledge that we have now at hand is very wide, with impressive quantitative and qualitative results [1]. Phase diagrams for the electron gas in two and three dimensions appear now quite well understood thanks to progressively more accurate many-body calculations using mainly quantum Monte Carlo methods [2]. However, the theoretical knowledge of the electron gas in the onedimensional (1D) geometry is more scarce and a full determination of the density-temperature phase diagram is still lacking. The present work is intended as a contribution towards filling this gap by means of a microscopic approach based on the path integral Monte Carlo (PIMC) method.The quasiparticle concept introduced by Landau in his Fermi liquid theory is able to account for the excitations of the electron gas in two and three dimensions. This is not the case in one dimension where the enhancement of correlations makes all excitations, even at low energy, to be collective. The appropriate theoretical framework is an effective low-energy Tomonaga-Luttinger (TL) theory [3][4][5], properly modified by Schulz [6] to account for the long-range nature of the Coulomb interaction. Probably, the most noticeable prediction of the TL theory is the separation between spin and charge degrees of freedom, whose excitations are predicted to travel at different velocities. At the same time, a Coulomb wire is fundamentally different from other TL systems in that at low densities it forms a Wigner crystal, as manifested by the emergence of quasi-Bragg peaks [6]. Also the strongly repulsive nature of interactions might lead to a formation of a Coulomb Tonks-Girardeau gas [7]. In spite of the experimental difficulties in getting real 1D environments, strong evidences of having reached the TL liquid and the 1D Wigner crystal have...

One-dimensional few-electron effective Wigner crystal in quantum and classical regimes

“…In contrast to Ref. [31], however, which finds two disjointed classical solid phases, we find only a small sliver of a classical effective Wigner phase between the quantum Wigner crystal and the classical liquid.…”

“…The fragility of a classical 1D Wigner crystal phase arises from the fact that the existence of a classical crystal requires very low average density corresponding to very low Fermi temperature -thus the classical crystal is constrained by the Fermi temperature on the one hand (indicating classical to quantum crossover) and the low melting temperature on the other hand (indicating the solid to liquid crossover). This fragility of the classical Wigner crystal was also found to be the case in a completely different calculation [31] employing the static structure factor as the diagnostic to distinguish between the classical and the quantum regime in contrast to our use of the Lindemann criterion. In contrast to Ref.…”

“…As a result, we show that there is an isolated phase of observable 1D Wigner crystal and this phase shrinks extremely slowly with increasing number of particles, which is consistent with the fact that is there is no true long-range order in 1D systems. Again we note that rigorous simulations have been done to study the effect of temperature and produce the classical phase diagrams of Wigner crystal formation [31,32]. However, our simple phase diagram can be readily adapted and fine-tuned for a wide range of experimental parameters.…”

One dimensional1H,2H and3H

“…As a result, dipoles [30,31,46] and HRs [47,48] form a TG/ideal Fermi gas at small density, pass through sTG phase and form a quasi-crystal at large densities. On the opposite, for Coulomb charges, the Wigner quasi-crystal is formed at low densities and TG/IFG at large ones [34,49]. Calogero-Sutherland model permits to access all regimes with K>0 [33].…”

The Inverse-Square Interaction Phase Diagram: Unitarity in the Bosonic Ground State

“…In this sense we refer to the low-lying excitations as plasmons. Instead, 1/r 3 interaction in 3D is similar to one-dimensional chain of Coulomb 1/r charges featuring a "weak" logarithmic prefactor in front of the linear dispersion term [65][66][67], E(k) ∝ | ln(k)||k|, being still a long-range potential. Instead, for the short-range potentials (1/r 4 , 1/r 5 , etc) the dispersion relation obtained with Eq.…”