Finite Density Matrix Renormalisation Group Algorithm for Anyonic Systems

The numerical study of anyonic systems is known to be highly challenging due to their non-bosonic, non-fermionic particle exchange statistics, and with the exception of certain models for which analytical solutions exist, very little is known about their collective behaviour as a result. Meanwhile, the density matrix renormalisation group (DMRG) algorithm is an exceptionally powerful numerical technique for calculating the ground state of a low-dimensional lattice Hamiltonian, and has been applied to the study of bosonic, fermionic, and group-symmetric systems. The recent development of a tensor network formulation for anyonic systems opened up the possibility of studying these systems using algorithms such as DMRG, though this has proved challenging both in terms of programming complexity and computational cost. This paper presents the implementation of DMRG for finite anyonic systems, including a detailed scheme for the implementation of anyonic tensors with optimal scaling of computational cost. The anyonic DMRG algorithm is demonstrated by calculating the ground state energy of the Golden Chain, which has become the benchmark system for the numerical study of anyons, and is shown to produce results comparable to those of the anyonic TEBD algorithm and superior to the variationally optimised anyonic MERA, at far lesser computational cost.Comment: 24 pages, 37 figure files (25 floating figures). RevTeX 4.1. Minor changes for clarity in Figs. 9 & 11, matching published versio

Economic Growth, International Technological Spillovers and Public Policy: Theory and Empirical Evidence from Asia

This paper examines, within the new growth theory framework, the contribution of international technological spillovers using panel data for eleven Asian countries over the period 1970-93. A country's productivity growth is shown to depend not only on its domestic R&D investment but also on the R&D investment of its trading partners. The evidence for such positive international technological spillovers is strong. This paper also shows that the beneficial effects of international technological spillovers on productivity growth are stronger in South East Asian countries than that of of South Asian countries.Economic Growth, Technology Spillovers, Asia

Tensor network states and algorithms in the presence of a global U(1) symmetry

Tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. In a recent paper [arXiv:0907.2994v1] we discussed how to incorporate a global internal symmetry, given by a compact, completely reducible group G, into tensor network decompositions and algorithms. Here we specialize to the case of Abelian groups and, for concreteness, to a U(1) symmetry, often associated with particle number conservation. We consider tensor networks made of tensors that are invariant (or covariant) under the symmetry, and explain how to decompose and manipulate such tensors in order to exploit their symmetry. In numerical calculations, the use of U(1) symmetric tensors allows selection of a specific number of particles, ensures the exact preservation of particle number, and significantly reduces computational costs. We illustrate all these points in the context of the multi-scale entanglement renormalization ansatz.Comment: 22 pages, 25 figures, RevTeX

The contribution of dormant origins to genome stability:from cell biology to human genetics

AbstractThe ability of a eukaryotic cell to precisely and accurately replicate its DNA is crucial to maintain genome stability. Here we describe our current understanding of the process by which origins are licensed for DNA replication and review recent work suggesting that fork stalling has exerted a strong selective pressure on the positioning of licensed origins. In light of this, we discuss the complex and disparate phenotypes observed in mouse models and humans patients that arise due to defects in replication licensing proteins

Barack Obama's Post-American Foreign Policy

This book is available as open access through the Bloomsbury Open Access programme and is available on www.bloomsburycollections.com. After one of the most controversial and divisive periods in the history of American foreign policy under President George W. Bush, the Obama administration was expected to make changes for the better in US relations with the wider world. Now, international problems confronting Obama appear more intractable, and there seems to be a marked continuity in policies between Obama and his predecessor. Robert Singh argues that Obama's approach of 'strategic engagement' was appropriate for a new era of constrained internationalism, but it has yielded modest results. Obama's search for the pragmatic middle has cost him political support at home and abroad, whilst failing to make decisive gains. Singh suggests by calibrating his foreign policies to the emergence of a 'post-American'world, the president has yet to preside over a renaissance of US global leadership. Ironically,Obama's policies have instead hastened the arrival of a post-American world