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Zbl 0821.46087
Fannes, M.; Nachtergaele, B.; Werner, R.F.
Entropy estimates for finitely correlated states. (English)
[J] Ann. Inst. Henri Poincaré, Phys. Théor. 57, No.3, 259-277 (1992). ISSN 0246-0211

Summary: We study in this paper the Rényi entropy densities of integer order for the class of finitely correlated states on a quantum spin chain and obtain in this way explicit lower bounds for the usual entropy density. We apply this technique to obtain good bounds on the entropy density of a certain state on a spin-3/2 chain.\par This state is a ground state of a translation invariant nearest neighbour SU(2)-invariant interaction, which is thus shown to possess a residual entropy as $T\to 0$. Breaking the translation symmetry by adding a small SU(2)-invariant interaction of period two removes the ground state degeneracy and produces a non-zero spectral gap above the ground state.

MSC 2000:: *46L60 Appl. of selfadjoint operator algebras to physics
46L30 States of C*-algebras
82B10 Quantum equilibrium statistical mechanics (general)

Keywords: Rényi entropy densities of integer order; finitely correlated states on a quantum spin chain; SU(2)-invariant interaction; ground state degeneracy; non-zero spectral gap above the ground state

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