Matrix Product Density Operators: Renormalization Fixed Points and Boundary Theories

We consider the tensors generating matrix product states and density operators in a spin chain. For pure states, we revise the renormalization procedure introduced by F. Verstraete et al. in 2005 and characterize the tensors corresponding to the fixed points. We relate them to the states possessing zero correlation length, saturation of the area law, as well as to those which generate ground states of local and commuting Hamiltonians. For mixed states, we introduce the concept of renormalization fixed points and characterize the corresponding tensors. We also relate them to concepts like finite correlation length, saturation of the area law, as well as to those which generate Gibbs states of local and commuting Hamiltonians. One of the main result of this work is that the resulting fixed points can be associated to the boundary theories of two-dimensional topological states, through the bulk-boundary correspondence introduced by Cirac et al. in 2011.Comment: 63 pages, Annals of Physics (2016). Accepted versio

An antibody raised against a pathogenic serpin variant induces mutant-like behaviour in the wild-type protein.

A monoclonal antibody (mAb) that binds to a transient intermediate may act as a catalyst for the corresponding reaction; here we show this principle can extend on a macro-molecular scale to the induction of mutant-like oligomerisation in a wild-type protein. Using the common, pathogenic Glu342Lys (Z) variant of α1-antitrypsin as antigen - whose native state is susceptible to the formation of a proto-oligomeric intermediate - we have produced a mAb (5E3) that increases the rate of oligomerisation of the wild-type (M) variant. Employing ELISA, gel shift, thermal stability and FRET time-course experiments, we show that mAb5E3 does not bind to the native state of α1-antitrypsin, but recognises a cryptic epitope in the vicinity of the post-helix A loop and strand 4C that is revealed upon transition to the polymerisation intermediate, and which persists in the ensuing oligomer. This epitope is not shared by loop-inserted monomeric conformations. We show the increased amenity to polymerisation by either the pathogenic Glu342Lys mutation or the binding of mAb5E3 occurs without affecting energetic barrier to polymerisation. As mAb5E3 also does not alter the relative stability of the monomer to intermediate, it acts in a manner similar to the Glu342Lys mutation, by facilitating the conformational interchange between these two states

Shapes and Positions of Black Hole Shadows in Accretion Disks and Spin Parameters of Black Holes

Can we determine a spin parameter of a black hole by observation of a black hole shadow in an accretion disk? In order to answer this question, we make a qualitative analysis and a quantitative analysis of a shape and a position of a black hole shadow casted by a rotating black hole on an optically thick accretion disk and its dependence on an angular momentum of a black hole. We have found black hole shadows with a quite similar size and a shape for largely different black hole spin parameters and a same black hole mass. Thus, it is practically difficult to determine a spin parameter of a black hole from a size and a shape of a black hole shadow in an accretion disk. We newly introduce a bisector axis of a black hole shadow named a shadow axis. For a rotating black hole a shape and a position of a black hole shadow are not symmetric with respect to a rotation axis of a black hole shadow. So, in this case the minimum interval between a mass center of a black hole and a shadow axis is finite. An extent of this minimum interval is roughly proportional to a spin parameter of a black hole for a fixed inclination angle between a rotation axis of a black hole and a direction of an observer. In order to measure a spin parameter of a black hole, if a shadow axis is determined observationally, it is crucially important to determine a position of a mass center of a black hole in a region of a black hole shadow.Comment: 13 pages, 6 figures, accepted for publication in Ap

Exploring LGBT resilience and moving beyond a deficit-model: findings from a qualitative study in England

The aim of this study is to critique and extend psychological approaches to resilience by examining retrospective accounts of LGBT people in England who had directly experienced or witnessed events that were salient as significantly negative or traumatic. Pre-screening telephone interviews identified ten individuals who matched inclusion criteria (mean age: 39 years; range 26–62 years) as part of a larger study. Interviews were semi-structured and informed by a literature review undertaken at the start of the study. We identified three themes of that extend the resilience literature for LGBTQ+ people: (1) identifying and foregrounding inherent personal traits – how non-contextual inborn qualities or attributes needed external effort to be recognised and operationalised; (2) describing asymmetric sources of social support and acceptance – the importance of positive environment is unequally available to LGBT people compared to heterosexuals, and uneven within the LGBT group; and (3) blurring distinctions between resilience and coping – experiential approaches to moving beyond distress. We suggest that narratives of resilience in the accounts of LGBT people can inform the development of resilience promotion models for minoritized individuals and support movement away from deficit-focused approaches to health policy

Medium-modified evolution of multiparticle production in jets in heavy-ion collisions

The energy evolution of medium-modified average multiplicities and multiplicity fluctuations in quark and gluon jets produced in heavy-ion collisions is investigated from a toy QCD-inspired model. In this model, we use modified splitting functions accounting for medium-enhanced radiation of gluons by a fast parton which propagates through the quark gluon plasma. The leading contribution of the standard production of soft hadrons is found to be enhanced by the factor $\sqrt{N_s}$ while next-to-leading order (NLO) corrections are suppressed by $1/\sqrt{N_s}$, where the nuclear parameter $N_s>1$ accounts for the induced-soft gluons in the hot medium. The role of next-to-next-to-leading order corrections (NNLO) is studied and the large amount of medium-induced soft gluons is found to drastically affect the convergence of the perturbative series. Our results for such global observables are cross-checked and compared with their limits in the vacuum and a new method for solving the second multiplicity correlator evolution equations is proposed.Comment: 21 pages and 8 figures, typo corrections, references adde

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

An antibody raised against a pathogenic serpin variant induces mutant-like behaviour in the wild-type protein

A monoclonal antibody (mAb) that binds to a transient intermediate may act as a catalyst for the corresponding reaction; here we show this principle can extend on a macro molecular scale to the induction of mutant-like oligomerization in a wild-type protein. Using the common pathogenic E342K (Z) variant of α1-antitrypsin as antigen-whose native state is susceptible to the formation of a proto-oligomeric intermediate-we have produced a mAb (5E3) that increases the rate of oligomerization of the wild-type (M) variant. Employing ELISA, gel shift, thermal stability and FRET time-course experiments, we show that mAb5E3 does not bind to the native state of α1-antitrypsin, but recognizes a cryptic epitope in the vicinity of the post-helix A loop and strand 4C that is revealed upon transition to the polymerization intermediate, and which persists in the ensuing oligomer. This epitope is not shared by loop-inserted monomeric conformations. We show the increased amenity to polymerization by either the pathogenic E342K mutation or the binding of mAb5E3 occurs without affecting the energetic barrier to polymerization. As mAb5E3 also does not alter the relative stability of the monomer to intermediate, it acts in a manner similar to the E342K mutant, by facilitating the conformational interchange between these two states