Intrinsic and emergent anomalies at deconfined critical points

It is well known that theorems of Lieb-Schultz-Mattis type prohibit the existence of a trivial symmetric gapped ground state in certain systems possessing a combination of internal and lattice symmetries. In the continuum description of such systems the Lieb-Schultz-Mattis theorem is manifested in the form of a quantum anomaly afflicting the symmetry. We demonstrate this phenomenon in the context of the deconfined critical point between a Neel state and a valence bond solid in an $S =1/2$ square lattice antiferromagnet, and compare it to the case of $S=1/2$ honeycomb lattice where no anomaly is present. We also point out that new anomalies, unrelated to the microscopic Lieb-Schultz-Mattis theorem, can emerge prohibiting the existence of a trivial gapped state in the immediate vicinity of critical points or phases. For instance, no translationally invariant weak perturbation of the $S = 1/2$ gapless spin chain can open up a trivial gap even if the spin-rotation symmetry is explicitly broken. The same result holds for the $S =1/2$ deconfined critical point on a square lattice.Comment: 25 pages + Appendice

The danger of subverting students’ views in schools

This paper is firmly grounded in the position that engaging with students’ voices in schools is central to the development of inclusive practices. It explores the tensions that can be created when efforts are made to engage with students’ voices in relation to their experiences of learning and teaching. An example from a three-year research and development project, which worked alongside teachers to use students’ voices as a way of developing inclusive practices, is used to illustrate these tensions. This project, though showing that students’ voices can be a powerful means for understanding learning and teaching in schools, also encountered challenges with these processes. This paper focuses on the experiences of one secondary school which (possibly inadvertently) subverted and undermined students’ voice initiatives and explores the potential negative impacts of this on individual students, on students as a whole, and on teacher development. By doing this, suggestions as to how such tensions can be avoided in schools are offered, with the aim being to allow a genuine engagement with the views of students

Instabilities near the onset of spin density wave order in metals

We discuss the low energy theory of two-dimensional metals near the onset of spin density wave order. It is well known that such a metal has a superconducting instability induced by the formation of spin-singlet pairs of electrons, with the pairing amplitude changing sign between regions of the Fermi surface connected by the spin density wave ordering wavevector. Here we review recent arguments that there is an additional instability which is nearly as strong: towards the onset of a modulated bond order which is locally an Ising-nematic order. This new instability is a consequence of an emergent "pseudospin" symmetry of the low energy theory---the symmetry maps the sign-changing pairing amplitude to the bond order parameter.Comment: 14 pages, 9 figures; contribution to the special issue of the New Journal of Physics on "Fermiology of Cuprates", edited by Mike Norman and Cyril Prous

Spectral Regularisation: Induced Gravity and the Onset of Inflation

Using spectral regularisation, we compute the Weyl anomaly and express the anomaly generating functional of the quantum effective action through a collective scalar degree of freedom of all quantum vacuum fluctuations. Such a formulation allows us to describe induced gravity on an equal footing with the anomaly-induced effective action, in a self-consistent way. We then show that requiring stability of the cosmological constant under loop quantum corrections, Sakharov's induced gravity and Starobinsky's anomaly-induced inflation are either both present or both absent, depending on the particle content of the theory.Comment: 23 pages, 1 figure Slightly amended file to match published versio