Bose one-component plasma in 2D: a Monte Carlo study

TL;DR

This study investigates the low-temperature phase diagram of a two-dimensional Bose one-component plasma with a $1/r$ interaction and a uniform neutralizing background using finite-temperature Quantum Monte Carlo with the Worm Algorithm and Modified Periodic Coulomb treatment for long-range forces. System sizes up to $N=2304$ and densities characterized by $r_s$ in the range $1\le r_s \le 80$ are analyzed, enabling a robust extrapolation to the ground state and a KT analysis of the superfluid transition. The authors find a superfluid ground state persisting up to $r_s\approx70$, with a Wigner crystallization threshold near $r_W\approx71$, and observe no re-entrant crystalline phase or crystalline bubbles when quantum exchanges are included; the superfluid transition temperature $T_c$ shows only a weak dependence on density, lying roughly between $0.6T^\star$ and $0.9T^\star$. These results reconcile differences with prior works that neglected exchanges and validate the Modified Periodic Coulomb approach for long-range Coulomb bosons, offering insights relevant to layered superconductors and bipolaron theories.

Abstract

The low-temperature properties of a 2D Bose fluid of charged particles interacting through a 1/r potential, moving in the presence of a uniform neutralizing background, is studied by Quantum Monte Carlo simulations. We make use of the Modified Periodic Coulomb potential formalism to account for the long-range character of the interaction, and explore a range of density corresponding to average interparticle separation $1 \le r_s\le 80$. We report numerical results based on simulations of system comprising up to 2304 particles. We find a superfluid ground state for $r_s$ as large as 70, i.e., significantly above the most recent numerical estimate of the Wigner crystallization threshold, which we estimate at $r_W \approx 71$. Furthermore, no thermally re-entrant crystalline phase nor any evidence of metastable bubbles is observed near the transition, in contrast with a previous theoretical study in which quantum statistics was neglected. The computed superfluid transition temperature depends remarkably weakly on density.

Figures (5)

• Figure 1: Computed energy per particle (in Hartree) as a function of temperature for a system with $r_s=1$. Data are shown for two different system sizes, comprising $N=36$ and $N=576$ particles. Lines through the data are fits to the data obtained as explained in the text. Statistical errors are smaller than symbol sizes.
• Figure 2: Extrapolation of the ground state energy per particle (in Hartree) to the thermodynamic limit for two different values of $r_s$, namely $r_s=1$ (top) and $r_s=80$ (bottom). Statistical errors are smaller than symbol sizes.
• Figure 3: Pair correlation function computed in the low temperature limit for $r_s=1, 10, 20, 68, 80$. Higher values of $r_s$ correspond to higher peaks. Inset shows the behavior of the correlation function for $r\to 0$ for the case $r_s=1$.
• Figure 4: Superfluid fraction $\rho_S(T)$ for $r_s=64$ for a system comprising $N=576$ particles. When not shown, statistical errors are smaller than symbol size. Solid line through the data is obtained by solving the recursive KT equations (see text), whereas the dotted line represents the extrapolation to the thermodynamic limit. Dotted-dashed line corresponds to $T/T^\star=1$. Inset shows the one-body density matrix $n(r)$ computed at $T/T^\star=0.41$.
• Figure 5: Superfluid transition temperature $T_c$ (in units of $T^\star$) computed as a function of $r_s$.