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Truncation effects in the charge representation of the O(2) model
Journal article   Open access   Peer reviewed

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

Jin Zhang, Y. Meurice and S-W Tsai
Physical review. B, Vol.103(24), 245137
06/24/2021
DOI: 10.1103/PhysRevB.103.245137
url
https://arxiv.org/pdf/2104.06342View
Open Access

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 than 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 delta and eta 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 (U) over cap (+/-) = exp(i (theta) over cap) operators by the spin ladder operators (S) over cap (+/-) in the Hamiltonian. The marginal operators vanish at the Gaussian transition point for S = 1, which allows us to extract the eta exponent with high accuracy.
 Materials Science Physical Sciences Physics Technology Materials Science, Multidisciplinary Physics, Applied Physics, Condensed Matter Science & Technology

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