From the lecture notes https://canvas.harvard.edu/courses/39684/files/folder/Lectures?preview=5387008 by Subir Sachdev,
the path-integral of 1D XY-model is given by
Z=∫Dθexp{−K2∫dx(dθdx)2}
Introducing a complex order parameter
ψ=eiθ, the correlation function is given by
⟨ψ(x)ψ∗(0)⟩=exp(−1K∫dk2π1−cos(kx)k2)
My question is how I should perform the path-integral to obtain the above correlation function. I also posted my question at
https://physics.stackexchange.com/questions/395511/correlation-function-of-one-dimensional-xy-model