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{"ops":[{"insert":"I have just recently been introduced to the Kalmeyer-Laughling wavefunction\n\n$\u00a0\u00a0\u00a0\\psi(s_1,\\dots,s_N) \\propto \\delta_s \\prod_{i<j} (z_i-z_j)^{\\frac{s_is_j}{2}-\\frac{1}{2}}\\prod_k e^{\\frac{i\\pi}{2}(k-1)(s_k+1)}$\n\nwhere we consider a lattice in two dimensions, and on each lattice site there is a spin-1\/2 particles in either state up or state down, $s_i = \\pm 1$. $\\delta_s$ is 1 if the sum of the spin is zero, zero otherwise. I am bit confused about the $k$, but i believe it is simply a product over every lattice site?\n\nI want to rewrite the wavefunction using occupation numbers instead, so $s_j = 2n_j-1$ where $n_j$ is the number of particles on site $j$. I should be able to get the following form:\n\n$\u00a0\u00a0\\psi(n_1,\\dots,n_N) \\propto \\delta_n \\prod_{i<j}(z_i-z_j)^{2n_in_j}\\prod_{i\\neq j}(z_i-z_j)^{\\alpha n_i}$\n\nI tried rewriting the exponential function in the original form:\n\n$\\prod_ke^{\\frac{i\\pi}{2}(k-1)(s_k+1)} = \\prod_ke^{\\frac{i\\pi}{2}(k-1)(2n_k)} =\u00a0\\prod_ke^{i\\pi(k-1)n_k} $\n\n\n"}]}

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