Comment on "Equivalence of the variational matrix product method and the density matrix renormalization group applied to spin chains"

Dukelsky, Mart\'in-Delgado, Nishino and Sierra (Europhys. Lett., 43, 457 (1998) - hereafter referred to as DMNS) investigated the matrix product method (MPM), comparing it with the infinite-size density matrix renormalization group (DMRG). For equivalent basis size, the MPM produces an improved variational energy over that produced by DMRG and, unlike DMRG, produces a translationally-invariant wavefunction. The DMRG results presented were significantly worse than the MPM, caused by a shallow bound state appearing at the join of the two DMRG blocks. They also suggested that the DMRG results can be improved by using an alternate superblock construction $[B] \bullet [B]$ for the last few steps of the calculation. In this comment, we show that the DMRG results presented by DMNS are in error and the artificial bound state produced by the standard superblock configuration is very small even for $m=2$ states kept. In addition, we calculate explicitly the energy and wavefunction for the $[B] \bullet [B]$ superblock structure and verify that the energy coincides with that of the MPM, as conjectured by S. Ostlund and S. Rommer (Phys. Rev. Lett., 75, 3537 (1995)).Comment: 2 pages, 1 eps figure included. eps.cls include

Comment on "Phase separation in a two-species Bose mixture"

In an article in 2007, Mishra, Pai, and Das [Phys. Rev. A 76, 013604 (2007)] investigated the two-component Bose-Hubbard model using the numerical DMRG procedure. In the regime of inter-species repulsion $U^{ab}$ larger than the intra-species repulsion $U$, they found a transition from a uniform miscible phase to phase-separation occurring at a finite value of $U$ , e.g., at around $U = 1.3$ for $\Delta = U^{ab}/U = 1.05$ and $\rho_{a} = \rho_{b} = 1/2$. In this comment, we show that this result is not correct and in fact the two-component Bose-Hubbard model is unstable to phase-separation for any $U^{ab} > U > 0$.Comment: 2 pages, 3 figures, submitted to Phys. Rev.

Particle number conservation in quantum many-body simulations with matrix product operators

Incorporating conservation laws explicitly into matrix product states (MPS) has proven to make numerical simulations of quantum many-body systems much less resources consuming. We will discuss here, to what extent this concept can be used in simulation where the dynamically evolving entities are matrix product operators (MPO). Quite counter-intuitively the expectation of gaining in speed by sacrificing information about all but a single symmetry sector is not in all cases fulfilled. It turns out that in this case often the entanglement imposed by the global constraint of fixed particle number is the limiting factor.Comment: minor changes, 18 pages, 5 figure

U.S.-Japan and U.S.-China trade conflict : export growth, reciprocity, and the international trading system

First Japan and more recently China have pursued export-oriented growth strategies. While other Asian countries have done likewise, Japan and China are of particular interest because their economies are so large and the size of the associated bilateral trade imbalances with the United States so conspicuous. In this paper the authors focus on U.S. efforts to restore the reciprocal GATT/WTO market-access bargain in the face of such large imbalances and the significant spillovers to the international trading system. The paper highlights similarities and differences in the two cases. The authors describe U.S. attempts to reduce the bilateral imbalances through targeted trade policies intended to slow growth of U.S. imports from these countries or increase growth of U.S. exports to them. They then examine how these trade policy responses, as well as U.S. efforts to address what were perceived as underlying causes of the imbalances, influenced the evolution of the international trading system. Finally, the authors compare the macroeconomic conditions associated with the bilateral trade imbalances and their implications for the conclusions of the two episodes.Free Trade,Trade Law,Economic Theory&Research,Trade Policy,Currencies and Exchange Rates

U.S. Trade Policy and the Adjustment Process

This paper focuses on the adjustment environment in the United States as set out by the active U.S. trade remedy laws (antidumping, countervailing duties, and safeguards) and the Trade Adjustment Assistance program. We document U.S. industries' use of these various laws and relate industry use of trade policies to import competition and revealed comparative advantage. We also examine potential effects of U.S. trade policies on adjustment to shifting comparative advantage and give examples of industry outcomes. An important conclusion is that trade policies delaying industry adjustment can promote new entry into the domestic industry and thereby increase rather than alleviate the pressure on existing plants and workers. Copyright 2005, International Monetary Fund