Efficient Tree Tensor Network States (TTNS) for Quantum Chemistry: Generalizations of the Density Matrix Renormalization Group Algorithm

We investigate tree tensor network states for quantum chemistry. Tree tensor network states represent one of the simplest generalizations of matrix product states and the density matrix renormalization group. While matrix product states encode a one-dimensional entanglement structure, tree tensor network states encode a tree entanglement structure, allowing for a more flexible description of general molecules. We describe an optimal tree tensor network state algorithm for quantum chemistry. We introduce the concept of half-renormalization which greatly improves the efficiency of the calculations. Using our efficient formulation we demonstrate the strengths and weaknesses of tree tensor network states versus matrix product states. We carry out benchmark calculations both on tree systems (hydrogen trees and \pi-conjugated dendrimers) as well as non-tree molecules (hydrogen chains, nitrogen dimer, and chromium dimer). In general, tree tensor network states require much fewer renormalized states to achieve the same accuracy as matrix product states. In non-tree molecules, whether this translates into a computational savings is system dependent, due to the higher prefactor and computational scaling associated with tree algorithms. In tree like molecules, tree network states are easily superior to matrix product states. As an ilustration, our largest dendrimer calculation with tree tensor network states correlates 110 electrons in 110 active orbitals.Comment: 15 pages, 19 figure

Japanese growth and stagnation: a Keynesian perspective

This paper uses a modified Harrodian model to understand both the long period of rapid Japanese growth and the recent period of stagnation. The model has multiple steady-growth solutions when the labour supply is highly elastic, and government intervention, we argue, took the Japanese economy onto a high-growth trajectory. Labour constraints began to ap- pear around 1970, and a combination of high saving rates and slow popu- lation growth account for the stagnation of the 1990s. This combination produces a structural liquidity trap and threatens the sustainability of at- tempts to ensure near full employment through fiscal policy or by running a persistent trade surplus. JEL Categories: E12, E63, O53Japan, growth, stagnation, liquidity trap, public debt, multiple equilibria

Welcome Home to Japan: Repatriation of Foreign Profits by Japanese Multinationals

The empirical literature suggests that repatriation decisions of U.S. multinational corporations are influenced by taxes. Although the U.S. and Japan adopt the same foreign tax credit system, we have found no evidence that corporate taxes have significantly affected dividend repatriation of Japanese multinationals. Instead, we have found that almost half of Japanese foreign affiliates pay dividends and their average marginal dividend payout rate is about twenty percent. The results also suggest that the repatriation behavior varies across industries and countries. Furthermore, parent companies' financial status is found to influence the profit remittance of their foreign affiliates.Japanese multinationals, repatriation, foreign tax credits