Matrix product states and the nonabelian rotor model

Understand

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.