Correlation density matrices for 1- dimensional quantum chains based on the density matrix renormalization group

A useful concept for finding numerically the dominant correlations of a given ground state in an interacting quantum lattice system in an unbiased way is the correlation density matrix. For two disjoint, separated clusters, it is defined to be the density matrix of their union minus the direct product of their individual density matrices and contains all correlations between the two clusters. We show how to extract from the correlation density matrix a general overview of the correlations as well as detailed information on the operators carrying long-range correlations and the spatial dependence of their correlation functions. To determine the correlation density matrix, we calculate the ground state for a class of spinless extended Hubbard models using the density matrix renormalization group. This numerical method is based on matrix product states for which the correlation density matrix can be obtained straightforwardly. In an appendix, we give a detailed tutorial introduction to our variational matrix product state approach for ground state calculations for 1- dimensional quantum chain models. We show in detail how matrix product states overcome the problem of large Hilbert space dimensions in these models and describe all techniques which are needed for handling them in practice.Comment: 50 pages, 34 figures, to be published in New Journal of Physic

Horizontal gene transfer contributed to the evolution of extracellular surface structures

The single-cell layered ectoderm of the fresh water polyp Hydra fulfills the function of an epidermis by protecting the animals from the surrounding medium. Its outer surface is covered by a fibrous structure termed the cuticle layer, with similarity to the extracellular surface coats of mammalian epithelia. In this paper we have identified molecular components of the cuticle. We show that its outermost layer contains glycoproteins and glycosaminoglycans and we have identified chondroitin and chondroitin-6-sulfate chains. In a search for proteins that could be involved in organising this structure we found PPOD proteins and several members of a protein family containing only SWT (sweet tooth) domains. Structural analyses indicate that PPODs consist of two tandem β-trefoil domains with similarity to carbohydrate-binding sites found in lectins. Experimental evidence confirmed that PPODs can bind sulfated glycans and are secreted into the cuticle layer from granules localized under the apical surface of the ectodermal epithelial cells. PPODs are taxon-specific proteins which appear to have entered the Hydra genome by horizontal gene transfer from bacteria. Their acquisition at the time Hydra evolved from a marine ancestor may have been critical for the transition to the freshwater environment

Anderson Orthogonality in the Dynamics After a Local Quantum Quench

We present a systematic study of the role of Anderson orthogonality for the dynamics after a quantum quench in quantum impurity models, using the numerical renormalization group. As shown by Anderson in 1967, the scattering phase shifts of the single-particle wave functions constituting the Fermi sea have to adjust in response to the sudden change in the local parameters of the Hamiltonian, causing the initial and final ground states to be orthogonal. This so-called Anderson orthogonality catastrophe also influences dynamical properties, such as spectral functions. Their low-frequency behaviour shows nontrivial power laws, with exponents that can be understood using a generalization of simple arguments introduced by Hopfield and others for the X-ray edge singularity problem. The goal of this work is to formulate these generalized rules, as well as to numerically illustrate them for quantum quenches in impurity models involving local interactions. As a simple yet instructive example, we use the interacting resonant level model as testing ground for our generalized Hopfield rule. We then analyse a model exhibiting population switching between two dot levels as a function of gate voltage, probed by a local Coulomb interaction with an additional lead serving as charge sensor. We confirm a recent prediction that charge sensing can induce a quantum phase transition for this system, causing the population switch to become abrupt. We elucidate the role of Anderson orthogonality for this effect by explicitly calculating the relevant orthogonality exponents.Comment: 21 pages, 14 figure