The logic induced by effect algebras

Effect algebras form an algebraic formalization of the logic of quantum mechanics. For lattice effect algebras $${\mathbf {E}}$$ E , we investigate a natural implication and prove that the implication reduct of $${\mathbf {E}}$$ E is term equivalent to $${\mathbf {E}}$$ E . Then, we present a simple axiom system in Gentzen style in order to axiomatize the logic induced by lattice effect algebras. For effect algebras which need not be lattice-ordered, we introduce a certain kind of implication which is everywhere defined but whose result need not be a single element. Then, we study effect implication algebras and prove the correspondence between these algebras and effect algebras satisfying the ascending chain condition. We present an axiom system in Gentzen style also for not necessarily lattice-ordered effect algebras and prove that it is an algebraic semantics for the logic induced by finite effect algebras.

Disentangling lattice and electronic contributions to the metal–insulator transition from bulk vs. layer confined RNiO3

In complex oxide materials, changes in electronic properties are often associated with changes in crystal structure, raising the question of the relative roles of the electronic and lattice effects in driving the metal–insulator transition. This paper presents a combined theoretical and experimental analysis of the dependence of the metal–insulator transition of NdNiO3 on crystal structure, specifically comparing properties of bulk materials to 1- and 2-layer samples of NdNiO3 grown between multiple electronically inert NdAlO3 counterlayers in a superlattice. The comparison amplifies and validates a theoretical approach developed in previous papers and disentangles the electronic and lattice contributions, through an independent variation of each. In bulk NdNiO3, the correlations are not strong enough to drive a metal–insulator transition by themselves: A lattice distortion is required. Ultrathin films exhibit 2 additional electronic effects and 1 lattice-related effect. The electronic effects are quantum confinement, leading to dimensional reduction of the electronic Hamiltonian and an increase in electronic bandwidth due to counterlayer-induced bond-angle changes. We find that the confinement effect is much more important. The lattice effect is an increase in stiffness due to the cost of propagation of the lattice disproportionation into the confining material.