  Spin chain Hamiltonians can be written in terms of complex differential
operators using the Bargmann representation of the Jordan-Schwinger map. In
this case, the eigenfunctions are expressed as the product of orthonormal
monomials of the phase-space coordinates $z_{i}=Q_{i}+i P_{i}$ in the complex
plane. Furthermore, the series constructed from each phase-space coordinate
converges uniformly in any compact domain of the complex plane. Formulating
spin chains with respect to the phase-space coordinates helps in discussing
their classical limit and in the calculations of quasi-probability
distributions.
