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

Unchecked and unbalanced? The politics and policy of US nuclear launch authority

Presidential control of U.S. nuclear launch authority lacks robust checks and balances. Recent congressional attempts to restrict sole presidential control over first use of nuclear weapons are the latest expression of periodic concern over this exception to the constitutional system of fragmented authority and mutual veto powers. Such attempts to limit the Commander-in-Chief's discretion nonetheless raise serious constitutional and strategic issues that, on balance, argue against a stronger congressional role. A better option that applies the constitutional spirit of checks and balances while preserving necessary strategic flexibility is executive concurrence. Requiring the President to obtain concurrent authorization from the Secretary of Defense and Attorney General for nuclear first use would offer a double security in offering political and legal cover to Presidents for their decision while protecting the uniformed military from having to make independent assessments of the legality of a presidential launch order