03-489 Vladimir Korepin

Universality of Scaling of Entropy in 1D Gap-less Models (103K, PS) Nov 7, 03

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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 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. We study the scaling of the entropy as the size of this subsystem increases. Our main example is the Hubbard model. For spin chains we prove the formula, discovered by G.Vidal, J.I. Latorre, E.Rico and A. Kitaev. Our proof is based on the second law of thermodynamics.

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