  We consider critical models in one dimension. We study the ground state in
thermodynamic limit [infinite lattice]. Following Bennett, Bernstein, Popescu,
and Schumacher, we use the entropy of a sub-system as a measure of
entanglement. We calculate the entropy of a part of the ground state. At zero
temperature it describes entanglement of this part with the rest of the ground
state. We obtain an explicit formula for the entropy of the subsystem at low
temperature. At zero temperature we reproduce a logarithmic formula of Holzhey,
Larsen and Wilczek. Our derivation is based on the second law of
thermodynamics. The entropy of a subsystem is calculated explicitly for Bose
gas with delta interaction, the Hubbard model and spin chains with arbitrary
value of spin.
