We identify a fundamental challenge for non-perturbative linked cluster expansions (NLCEs) resulting from the reduced symmetry on graphs, most importantly the breaking of translational symmetry, when targeting the properties of excited states. A gene
ralized notion of cluster additivity is introduced, which is used to formulate an optimized scheme of graph-based continuous unitary transformations (gCUTs) allowing to solve and to physically understand this fundamental challenge. Most importantly, it demands to go beyond the paradigm of using the exact eigenvectors on graphs.
We present specific-heat and neutron-scattering results for the emph{S}=1/2 quantum antiferromagnet (dimethylammonium)(3,5-dimethylpyridinium)CuBr$_4$. The material orders magnetically at emph{T}$_N$=1.99(2),K, and magnetic excitations are accompanie
d by an energy gap of 0.30(2) meV due to spin anisotropy. The system is best described as coupled two-leg spin-1/2 ladders with the leg exchange $J_{rm leg}$=0.60(2)~meV, rung exchange $J_{rm rung}$=0.64(9)~meV, interladder exchange $J_{rm int}$=0.19(2)~meV, and an interaction-anisotropy parameter $lambda$=0.93(2), according to inelastic neutron-scattering measurements. In contrast to most spin ladders reported to date, the material is a rare example in which the interladder coupling is very near the critical value required to drive the system to a Neel-ordered phase without an assistance of a magnetic field.
