Abstract
We attempt to construct U(1) conformal field theory (CFT) in the Tomonaga–Luttinger (TL) liquid with the 1/rβ long-range interaction (LRI). Treating the long-range forward scattering as a perturbation and applying CFT to it, we derive finite size scalings which depend on the power of the LRI. The obtained finite size scalings give nontrivial behaviours when β is odd and is close to 2. We find consistency between the analytical arguments and numerical results in the finite size scaling of energy.
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