1302.6251 (U. Marzolino et al.)

Frustration, Entanglement, and Correlations in Quantum Many Body Systems    [PDF]

U. Marzolino, S. M. Giampaolo, F. Illuminati

We derive an exact lower bound to a universal measure of frustration in globally degenerate ground states of many body systems. The bound results in the sum of two contributions, one due to entanglement and one due to classical correlations after local generalized measurements on arbitrarily selected subsystems. The existence of classical statistical correlations is thus identified as a third necessary source of frustration, beyond geometry and entanglement, in the presence of ground-state degeneracy. We show that the global, on average, frustration properties of quantum systems are characterized by the behavior of the maximally mixed ground state, that is the convex combination with equal a priori probabilities of all the degenerate pure ground states. We determine sufficient conditions for a quantum spin system to saturate the bound, and for models with twofold ground-state degeneracy we prove that the local and on average characterizations of frustration coincide, in the sense that all degenerate ground states possess the same frustration properties of the maximally mixed ground state.

View original: http://arxiv.org/abs/1302.6251