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

Article

关键词: RENORMALIZATION-GROUP ANALYSIS;    PHASE-TRANSITIONS;    HUBBARD-MODEL;    FIELD-THEORY;    XY MODEL;    QUANTUM;    CHAINS;    CONFINEMENT;    DYNAMICS;    BEHAVIOR;   

DOI  :  10.1103/PhysRevB.103.245137

来源: SCIE

【 摘 要 】

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.

【 授权许可】

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