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

Abstract

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 or equal to S. The charge representation preserves the gapless-to-gapped phase transition even for the smallest spin truncation S = 1. The phase transition for S = 1 is an infinite-order Gaussian transition with the same critical exponents δ and η as the Berezinskii-Kosterlitz-Thouless (BKT) transition, while there are true BKT transitions for S ≥ 2. The essential singularity in the correlation length for S = 1 is different from that for S ≥ 2. The exponential convergence of the phase transition point is studied in both Lagrangian and Hamiltonian formulations. We discuss the effects of replacing the truncated Û ± = exp(±i θ) operators by the spin ladder operators Ŝ± in the Hamiltonian. The marginal operators vanish at the Gaussian transition point for S = 1, which allows us to extract the η exponent with high accuracy.

Clock model interpolation and symmetry breaking in O(2) models

“…However, this exponent should be the same as the power-law scaling of β p of χ M in a weak external field for all clock models with integer q ≥ 5, where there is always an emergent O(2) symmetry [40,62]. In the limit of O(2) model, this exponent is found to be around 0.162 [63][64][65].…”

Prospects for Simulating a Qudit Based Model of (1+1)d Scalar QED

“…s ≈ 1, a truncation of n max = 2 appears to be sufficient. One key feature that is evident is that there seems to be a stark difference between the spin-1 and spin-2 truncation at all couplings; this was seen as well in [81]. The discrepancy is not unexpected, for Z n theories there is a marked discrepancy between n ≤ 4 and n ≥ 5 accurate representations of U (1) [82].…”