Entanglement Spectrum, Critical Exponents and Order Parameters in Quantum Spin Chains

We investigate the entanglement spectrum near criticality in finite quantum spin chains. Using finite size scaling we show that when approaching a quantum phase transition, the Schmidt gap, i.e., the difference between the two largest eigenvalues of the reduced density matrix ?1, ?2, signals the critical point and scales with universal critical exponents related to the relevant operators of the corresponding perturbed conformal field theory describing the critical point. Such scaling behavior allows us to identify explicitly the Schmidt gap as a local order parameter.

Nonequilibrium critical scaling from quantum thermodynamics

The emerging field of quantum thermodynamics is contributing important results and insights into archetypal many-body problems, including quantum phase transitions. Still, the question whether out-of-equilibrium quantities, such as fluctuations of work, exhibit critical scaling after a sudden quench in a closed system has remained elusive. Here, we take a novel approach to the problem by studying a quench across an impurity quantum critical point. By performing density matrix renormalization group computations on the two-impurity Kondo model, we are able to establish that the irreversible work produced in a quench exhibits finite-size scaling at quantum criticality. This scaling faithfully predicts the equilibrium critical exponents for the crossover length and the order parameter of the model, and, moreover, implies a new exponent for the rescaled irreversible work. By connecting the irreversible work to the two-impurity spin correlation function, our findings can be tested experimentally.

Sex Education in Northern Ireland Schools: a Critical Evaluation.

To date there has been little research on young people and sexuality in Northern Ireland. This paper draws on the first major study in this area to analyse the delivery of formal sex education in schools. Both quantitative and qualitative methods were used to access young people's opinions about the quality of the sex education they had received at school. Overall, they reported high levels of dissatisfaction, with notable variations in relation to both gender and religious affiliation. In one sense their opinions mesh well with those of young people in other parts of these islands. At the same time the specificity of sexuality in Ireland plays a key role in producing the moral system that underlies much of formal sex education in schools. Underpinned by a particularly traditional and conservative strain of Christian morality, sex education in Northern Ireland schools is marked by conservatism and silence and by the avoidance of opportunities for informed choice in relation to sexuality on the part of young people.