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

Continuum emission associated with 6.7-GHz methanol masers

We have used the Australia Telescope Compact Array (ATCA) to search for continuum emission toward three strong 6.7-GHz methanol maser sources. For two of the sources, G339.88-1.26 and NGC 6334F (G351.42+0.64), we detect continuum emission closely associated with the methanol masers. A further three clusters of masers showed no radio continuum emission above our sensitivity limit of 1-5 mJy. We find the position of the 6.7-GHz methanol masers in G339.88-1.26 to be consistent with the hypothesis that the masers lie in the circumstellar disc surrounding a massive star. We also argue that one of the clusters of methanol masers in NGC 6334F provides indirect observational support for the circumstellar disc hypothesis.Comment: 8 pages including 2 figures, using LaTeX formatted with mn.sty, accepted for publication in MNRA

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

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

Generic Construction of Efficient Matrix Product Operators

Matrix Product Operators (MPOs) are at the heart of the second-generation Density Matrix Renormalisation Group (DMRG) algorithm formulated in Matrix Product State language. We first summarise the widely known facts on MPO arithmetic and representations of single-site operators. Second, we introduce three compression methods (Rescaled SVD, Deparallelisation and Delinearisation) for MPOs and show that it is possible to construct efficient representations of arbitrary operators using MPO arithmetic and compression. As examples, we construct powers of a short-ranged spin-chain Hamiltonian, a complicated Hamiltonian of a two-dimensional system and, as proof of principle, the long-range four-body Hamiltonian from quantum chemistry.Comment: 13 pages, 10 figure

Spin-1 Heisenberg antiferromagnetic chain with exchange and single-ion anisotropies

Using density matrix renormalization group calculations, ground state properties of the spin-1 Heisenberg chain with exchange and single-ion anisotropies in an external field are studied. Our findings confirm and refine recent results by Sengupta and Batista, Physical Review Letters 99, 217205 (2007) (2007), on the same model applying Monte Carlo techniques. In particular, we present evidence for two types of biconical (or supersolid) and for two types of spin-flop (or superfluid) structures. Basic features of the quantum phase diagram may be interpreted qualitatively in the framework of classical spin models.Comment: Ref. 1 corrected (also in the abstract