Topological Phases of One-Dimensional Fermions: An Entanglement Point of View

The effect of interactions on topological insulators and superconductors remains, to a large extent, an open problem. Here, we describe a framework for classifying phases of one-dimensional interacting fermions, focusing on spinless fermions with time-reversal symmetry and particle number parity conservation, using concepts of entanglement. In agreement with an example presented by Fidkowski \emph{et. al.} (Phys. Rev. B 81, 134509 (2010)), we find that in the presence of interactions there are only eight distinct phases, which obey a $\mathbb{Z}_8$ group structure. This is in contrast to the $\mathbb{Z}$ classification in the non-interacting case. Each of these eight phases is characterized by a unique set of bulk invariants, related to the transformation laws of its entanglement (Schmidt) eigenstates under symmetry operations, and has a characteristic degeneracy of its entanglement levels. If translational symmetry is present, the number of distinct phases increases to 16.Comment: 12 pages, 1 figure; journal ref. adde

Management of mental illness by the British Army

Background: The Ministry of Defence has its own hospital for soldiers requiring admission for mental health problems. Aims: To assess the efficiency of the army psychiatric hospital at restoring patients to full active duty. To assess whether a new military training and rehabilitation unit (MTRU) that emphasises military-skills training, improves outcome. Method: A 2-year, inception-cohort outcome study of hospital in-patients. A 12-month, case-matched, ‘before and after’ outcome study compared MTRU patients with hospital in-patients. Results: I (hospital in-patients, n=309): at 2-year follow-up 67 (22%) were fully fit for active duty. Military psychiatrists' success rate at predicting recovery to active duty was 27%. 2: the odds of a soldier in the MTRU cohort (n=35) returning to active duty were 14 times greater than for the hospital cohort (n=35). The odds of remaining in the army while unfit for active duty were 20 times less for the MTRU than for the hospital cohort. Conclusions: The army hospital is inefficient at rehabilitation to active duty. The MTRU significantly increased the odds of returning to active duty and reduced the odds of remaining in the army while still unfit. These findings may be applicable to the emergency services

Symmetry protection of topological order in one-dimensional quantum spin systems

We discuss the characterization and stability of the Haldane phase in integer spin chains on the basis of simple, physical arguments. We find that an odd-$S$ Haldane phase is a topologically non-trivial phase which is protected by any one of the following three global symmetries: (i) the dihedral group of $\pi$-rotations about $x,y$ and $z$ axes; (ii) time-reversal symmetry $S^{x,y,z} \rightarrow - S^{x,y,z}$; (iii) link inversion symmetry (reflection about a bond center), consistently with previous results [Phys. Rev. B \textbf{81}, 064439 (2010)]. On the other hand, an even-$S$ Haldane phase is not topologically protected (i.e., it is indistinct from a trivial, site-factorizable phase). We show some numerical evidence that supports these claims, using concrete examples.Comment: 9 pages, 6 figures, extended version: several new examples and numerical results added. Journal reference adde

Detection of Symmetry Protected Topological Phases in 1D

A topological phase is a phase of matter which cannot be characterized by a local order parameter. It has been shown that gapped phases in 1D systems can be completely characterized using tools related to projective representations of the symmetry groups. We show how to determine the matrices of these representations in a simple way in order to distinguish between different phases directly. From these matrices we also point out how to derive several different types of non-local order parameters for time reversal, inversion symmetry and $Z_2 \times Z_2$ symmetry, as well as some more general cases (some of which have been obtained before by other methods). Using these concepts, the ordinary string order for the Haldane phase can be related to a selection rule that changes at the critical point. We furthermore point out an example of a more complicated internal symmetry for which the ordinary string order cannot be applied.Comment: 12 pages, 9 Figure

Axion Cosmology and the Energy Scale of Inflation

We survey observational constraints on the parameter space of inflation and axions and map out two allowed windows: the classic window and the inflationary anthropic window. The cosmology of the latter is particularly interesting; inflationary axion cosmology predicts the existence of isocurvature fluctuations in the CMB, with an amplitude that grows with both the energy scale of inflation and the fraction of dark matter in axions. Statistical arguments favor a substantial value for the latter, and so current bounds on isocurvature fluctuations imply tight constraints on inflation. For example, an axion Peccei-Quinn scale of 10^16 GeV excludes any inflation model with energy scale > 3.8*10^14 GeV (r > 2*10^(-9)) at 95% confidence, and so implies negligible gravitational waves from inflation, but suggests appreciable isocurvature fluctuations.Comment: 10 PRD pages, 4 figs, V3: updated to match published versio