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.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- General Physics and Astronomy