Universality of entropy scaling in one dimensional gapless models

The universal properties of the entropy in one dimensional gapless models were investigated using the conformal field theory. The Hubbard model, the entropy in spin chains, and a Bose gas with delta interaction were also studied. A cross-over formula for the entropy of the subsystem was discovered. The formula mediated between a logarithmic function for zero temperature, a linear function for large temperature indicating that the entropy of a large subsystem could be described at any temperature. The entanglement of the part of the ground state from a space interval with the rest of the ground state was also described at zero temperature.