  Understanding extreme non-locality in many-body quantum systems can help
resolve questions in thermostatistics and laser physics. The existence of
symmetry selection rules for Hamiltonians with non-decaying terms on
infinite-size lattices can lead to finite energies per site, which deserves
attention. Here, we present a tensor network approach to construct the ground
states of nontrivial symmetric infinite-dimensional spin Hamiltonians based on
constrained optimizations of their infinite matrix product states description,
which contains no truncation step, offers a very simple mathematical structure,
and other minor advantages at the cost of slightly higher polynomial complexity
in comparison to an existing method. More precisely speaking, our proposed
algorithm is in part equivalent to the more generic and well-established
solvers of infinite density-matrix renormalization-group and variational
uniform matrix product states, which are, in principle, capable of accurately
representing the ground states of such infinite-range-interacting many-body
systems. However, we employ some mathematical simplifications that would allow
for efficient brute-force optimizations of tensor-network matrices for the
specific cases of highly-symmetric infinite-size infinite-range models. As a
toy-model example, we showcase the effectiveness and explain some features of
our method by finding the ground state of the U(1)-symmetric
infinite-dimensional antiferromagnetic $XX$ Heisenberg model.
