  We use uniform matrix product states (MPS) to study the (1+1)D $O(2)$ and
$O(4)$ rotor models, which are equivalent to the Kogut-Susskind formulation of
matter-free nonabelian lattice gauge theory on a "hawaiian earring" graph for
$U(1)$ and $SU(2)$, respectively. Applying tangent space methods to obtain
ground states and determine the mass gap and the $\beta$ function, we find
excellent agreement with known results, locating the BKT transition for $O(2)$
and successfully entering the asymptotic weak-coupling regime for $O(4)$. To
obtain a finite local Hilbert space, we truncate in the space of generalized
Fourier modes of the gauge group, comparing the effects of different cutoff
values. We find that higher modes become important in the crossover and
weak-coupling regimes of the nonabelian theory, where entanglement also
suddenly increases. This could have important consequences for TNS studies of
Yang-Mills on higher dimensional graphs.
