  The correlation between electrons in different quantum wires is expected to
affect the electronic properties of quantum electron-electron biwire systems.
Here, we use the variational Monte Carlo method to study the ground-state
properties of parallel, infinitely thin electron-electron biwires for several
electron densities ($r_\text{s}$) and interwire separations ($d$).
Specifically, the ground-state energy, the correlation energy, the interaction
energy, the pair-correlation function (PCF), the static structure factor (SSF),
and the momentum distribution (MD) function are calculated. We find that the
interaction energy increases as $\ln(d)$ for $d\to 0$ and it decreases as
$d^{-2}$ when $d\to \infty$. The PCF shows oscillatory behavior at all
densities considered here. As two parallel wires approach each other, interwire
correlations increase while intrawire correlations decrease as evidenced by the
behavior of the PCF, SSF, and MD. The system evolves from two monowires of
density parameter $r_\text{s}$ to a single monowire of density parameter
$r_\text{s}/2$ as $d$ is reduced from infinity to zero. The MD reveals
Tomonaga-Luttinger (TL) liquid behavior with a power-law nature near
$k_\text{F}$ even in the presence of an extra interwire interaction between the
electrons in biwire systems. It is observed that when $d$ is reduced the MD
decreases for $k<k_\text{F}$ and increases for $k>k_\text{F}$, similar to its
behavior with increasing $r_\text{s}$. The TL liquid exponent is extracted by
fitting the MD data near $k_\text{F}$, from which the TL liquid interaction
parameter $K_{\rho}$ is calculated. The value of the TL parameter is found to
be in agreement with that of a single wire for large separation between the two
wires.
