  In this paper we rigorously construct a finite volume representation for the
height-one field of the Abelian sandpile model and the degree field of the
uniform spanning tree in terms of the fermionic Gaussian free field. This
representation can be seen as the lattice representation of a free symplectic
fermion field. It allows us to compute cumulants of those fields, both in
finite volume and in the scaling limit, including determining the explicit
normalizing constants for fields in the corresponding logarithmic field theory.
Furthermore, our results point towards universality of the height-one and
degree fields, as we prove that the scaling limits of the cumulants agree (up
to constants) in the square and triangular lattice. We also recover the
equivalent scaling limits for the hypercubic lattice in higher dimensions, and
discuss how to adapt the proofs of our results to general graphs.
