Phase shift, the Marshall sign, and the Luttinger-liquid behavior in one dimension

The phase shift as a key concept to understand the Luttinger liquid behavior in one dimension is explored in the strong-coupling regime of the Hubbard model, where a simple charge-spin separation picture exists. We demonstrate an explicit connection between the phase shift upon doping and the Marshall sign hidden in the spin background. The obtained many-body phase-shift field reproduces the known non-Fermi-liquid behavior where the phase-shift effect also plays a crucial role to shift the Fermi surface to satisfy the Luttinger volume. The connection of the phase shift and the fractional statistics transformation is also discussed