Conformal field theory in Tomonaga-Luttinger model with $1/r^{\beta }$ type long-range interactions

Abstract

The validity of the CFT in the Tomonaga-Luttinger liquid with the $1/r^{\beta }$ type long-range interactions is discussed. The arguments by CFT for long-range forward scatterings predict the finite size corrections which depend on the power of the long-range interactions. Especially from finite size corrections in the ground state, we find the effective central charge deviates from $c=1$. These conformal arguments are numerically tested in the one particle excitations and the ground state.

arXiv commentThis paper is the final version. 23 pages, 11 figures

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• Ground states of long-range interacting fermions in one spatial dimension
• Phase diagram of two-component dipolar fermions in one-dimensional optical lattices
• Wigner crystal versus Fermionization for one-dimensional Hubbard models with and without long-range interactions
• Wigner crystal induced by dipole-dipole interaction in one-dimensional optical lattices
• Quantum criticality of dipolar spin chains
• Long-range Order in One-dimensional Spinless Fermi Gas with Attractive Dipole-Dipole Interaction
• One dimensional Bose-Hubbard model with long range hopping