Pairwise thermal entanglement in Ising-XYZ diamond chain structure in an external magnetic field

Quantum entanglement is one of the most fascinating types of correlation that can be shared only among quantum systems. The Heisenberg chain is one of the simplest quantum chains which exhibits a reach entanglement feature, due to the Heisenberg interaction is quantum coupling in the spin system. The two particles were coupled trough XYZ coupling or simply called as two-qubit XYZ spin, which are the responsible for the emergence of thermal entanglement. These two-qubit operators are bonded to two nodal Ising spins, and this process is repeated infinitely resulting in a diamond chain structure. We will discuss two-qubit thermal entanglement effect on Ising-XYZ diamond chain structure. The concurrence could be obtained straightforwardly in terms of two-qubit density operator elements, using this result, we study the thermal entanglement, as well as the threshold temperature where entangled state vanishes. The present model displays a quite unusual concurrence behavior, such as, the boundary of two entangled regions becomes a disentangled region, this is intrinsically related to the XY-anisotropy in the Heisenberg coupling. Despite a similar property had been found for only two-qubit, here we show in the case of a diamond chain structure, which reasonably represents real materials.Comment: 6 pages, 7 figure

Debt enforcement and the return on money

The rate-of-return-dominance puzzle asks why low-return assets, like fiat money, are used in actual economies given that risk-free higher-return assets are available. As long as this question remains unresolved, most conclusions from monetary models which arbitrarily restrict the marketability properties of alternative assets to make money valuable are difficult to assess. In this paper, I provide a framework in which fiat money has value in equilibrium, even though a higher-return asset is available and there are neither restrictions nor transaction costs in using it. I suggest that the use of money is associated with frictions underlying debt contracts. In an environment where full enforcement is not feasible, the actual rate of return on assets is determined by incentives eliciting voluntary debt repayment. I show that the inflation rate or, more generally, the depreciation rate of an asset in which debts are denominated may function as a commitment device. As a result, money is used in equilibrium and the optimal inflation rate is positive.Money, Inflation, Debt Enforcement, Banking.