Universality of Entropy Scaling in 1D Gap-less Models

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  • 20 November 2003
Abstract
We consider gap-less models in one dimension (in thermodynamic limit). At small temperature these models can be described by conformal field theory. According to the third law of thermodynamics at zero temperature the entropy of the whole infinite ground state is zero. But the entropy can be positive for a subsystem (part of the ground state). Let us consider Bose gas with delta interaction as an example. A gas on a space interval has some entropy, it describes entanglement of the gas on this interval with the rest of the ground state. We study the scaling of the entropy as the size of this subsystem increases. For spin chains we prove the formula, discovered by G.Vidal, J.I. Latorre, E.Rico and A. Kitaev. Our main example is the Hubbard model.

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