a_1} = al (1,0)$ and ${\bf a_2} = bl (\cos \theta,\sin \theta)$, and $\phi_n ({\bf r})$ vanish at $m_1 {\bf a_1} + m_2 {\bf a_1}$ when $m_1$ and $m_2$ are integers. This requires $$\begin{aligned}
k_m &=& 2\pi (m-1/2)/a = (m-1/2)\sqrt{2\pi \sigma}\nonumber\\
q_m &=&  e^{i\pi m (\varsigma + 1 - m\varsigma)},\end{aligned}$$ where $\sigma = (b/a)\sin \theta$ and $\varsigma = (b/a)\cos\theta$. Note that we used the flux quantization condition $ab \sin\theta = 2\pi$. For a lattice of HQV’s we need to consider a second lattice that is translated by $l{\bm \tau} = l (\tau_x, \tau_y)$ with respect to the first lattice. For the wave function of this lattice, we can use [@superRev] $$\tilde{\phi}_n ({\bf r}) = e^{i \tau_y x} \phi_n ({\bf r} - {\bm
\tau}),$$ the phase factor being chosen so that $\Pi_- \tilde{\phi}_0 ({\bf r}) = 0$. This latter condition ensures that the translated eigenstates have the same gauge as the untranslated eigenstates.

The formalism considered here gives us not only the energy due to interaction between vortices but also the core energy of vortices as well. This is because our vortex lattice wave function gives full description of the core regions. From the linearized GL equation we use here, a 