Truncation effects in the charge representation of the O(2) model
- URL: http://arxiv.org/abs/2104.06342v3
- Date: Thu, 1 Jul 2021 04:26:55 GMT
- Title: Truncation effects in the charge representation of the O(2) model
- Authors: Jin Zhang, Yannick Meurice, Shan-Wen Tsai
- Abstract summary: We study the quantum phase transition in the charge representation with a truncation to spin $S$.
The exponential convergence of the phase-transition point is studied in both Lagrangian and Hamiltonian formulations.
- Score: 3.770141864638074
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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 $S \ge 2$. The essential singularity in the
correlation length for $S = 1$ is different from that for $S \ge 2$. The
exponential convergence of the phase-transition point is studied in both
Lagrangian and Hamiltonian formulations. We discuss the effects of replacing
the truncated $\hat{U}^{\pm} = \exp(\pm i \hat{\theta})$ operators by the spin
ladder operators $\hat{S}^{\pm}$ 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.
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