In this paper we discuss the properties of the reduced density matrix of quantum many body systems with permutational symmetry and present basic quantifications of the entanglement in terms of the von Neumann (VNE). Renyi and Tsallis entropies. In particular we show on the specific example of the spin 1/2 Heisenberg model, how the RDM acquires a block diagonal form with respect to the quantum number k k fixing the polarization in the subsystem conservation of Sz and with respect to the irreducible representations of the Sn group. Analytical expressions for the RDM elements and for the RDM spectrum are derived for states of arbitrary permutational symmetry and for arbitrary polarizations. The temperature dependence and the scaling of the VNE across a finite temperature phase transition is discussed and the RDM moments and the Renyi and Tsallis entropies calculated both for symmetric ground states of the Heisenberg chain and for maximally mixed states.

Reduced density matrix and entanglement entropy of permutationally invariant quantum many body systems - Chap. 9

SALERNO, Mario
2013

Abstract

In this paper we discuss the properties of the reduced density matrix of quantum many body systems with permutational symmetry and present basic quantifications of the entanglement in terms of the von Neumann (VNE). Renyi and Tsallis entropies. In particular we show on the specific example of the spin 1/2 Heisenberg model, how the RDM acquires a block diagonal form with respect to the quantum number k k fixing the polarization in the subsystem conservation of Sz and with respect to the irreducible representations of the Sn group. Analytical expressions for the RDM elements and for the RDM spectrum are derived for states of arbitrary permutational symmetry and for arbitrary polarizations. The temperature dependence and the scaling of the VNE across a finite temperature phase transition is discussed and the RDM moments and the Renyi and Tsallis entropies calculated both for symmetric ground states of the Heisenberg chain and for maximally mixed states.
978-981-4460-31-6
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11386/4530258
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