Truncation effects in the charge representation of the O(2) model

Understand

The O(2) model in Euclidean space-time is the zero-gauge-coupling limit of the compact scalar quantum electrodynamics.

• We obtain a dual representation of it called the charge representation.
• We study the quantum phase transition in the charge representation with a truncation to ``spin $S$," where the quantum numbers have an absolute value less than or equal to $S$.
• The charge representation preserves the gapless-to-gapped phase transition even for the smallest spin truncation $S = 1$.