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

Zhang, Jin; Meurice, Y.; Tsai, S.-W.

doi:10.1103/physrevb.103.245137

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

Journal Article · Thu Jun 24 00:00:00 EDT 2021 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.103.245137· OSTI ID:1852862

^[1];

^[2]

Univ. of Iowa, Iowa City, IA (United States)
Univ. of California, Riverside, CA (United States)

The O(2) model in Euclidean space-time is the zero-gauge-coupling limit of the compact scalar quantum electrodynamics. In this work, 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 $$\textit{S}$$," where the quantum numbers have an absolute value less than or equal to $$\textit{S}$$. The charge representation preserves the gapless-to-gapped phase transition even for the smallest spin truncation $$\textit{S}$$ = 1. The phase transition for $$\textit{S}$$ = 1 is an infinite-order Gaussian transition with the same critical exponents $$\textit{δ}$$ and $$\textit{η}$$ as the Berezinskii-Kosterlitz-Thouless (BKT) transition, while there are true BKT transitions for $$\textit{S}$$ ≥ 2 . The essential singularity in the correlation length for $$\textit{S}$$ = 1 is different from that for $$\textit{S}$$ ≥ 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 $$\hat{U}^±$$ = exp ($$± i\hat{θ}$$) operators by the spin ladder operators $$\hat{S}^±$$ in the Hamiltonian. The marginal operators vanish at the Gaussian transition point for $$\textit{S}$$ = 1, which allows us to extract the $$\textit{η}$$ exponent with high accuracy.

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Research Organization:: Univ. of Iowa, Iowa City, IA (United States)

Sponsoring Organization:: USDOE Office of Science (SC); National Science Foundation (NSF); National Institutes of Health (NIH)

Grant/Contract Number:: SC0019139; 1839153; MRI-1429826; 1S10OD016290-01A1

OSTI ID:: 1852862

Journal Information:: Physical Review. B, Vol. 103, Issue 24; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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

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