Emergent Moments and Random Singlet Physics in a Majorana Spin Liquid.

We exhibit an exactly solvable example of a SU(2) symmetric Majorana spin liquid phase, in which quenched disorder leads to random-singlet phenomenology of emergent magnetic moments. More precisely, we argue that a strong-disorder fixed point controls the low temperature susceptibility χ(T) of an exactly solvable S=1/2 model on the decorated honeycomb lattice with vacancy and/or bond disorder, leading to χ(T)=C/T+DT^{α(T)-1}, where α(T)→0 slowly as the temperature T→0. The first term is a Curie tail that represents the emergent response of vacancy-induced spin textures spread over many unit cells: it is an intrinsic feature of the site-diluted system, rather than an extraneous effect arising from isolated free spins. The second term, common to both vacancy and bond disorder [with different α(T) in the two cases] is the response of a random singlet phase, familiar from random antiferromagnetic spin chains and the analogous regime in phosphorus-doped silicon (Si:P).

Many-Body Delocalization as Symmetry Breaking.

We present a framework in which the transition between a many-body localized (MBL) phase and an ergodic one is symmetry breaking. We consider random Floquet spin chains, expressing their averaged spectral form factor (SFF) as a function of time in terms of a transfer matrix that acts in the space direction. The SFF is determined by the leading eigenvalues of this transfer matrix. In the MBL phase, the leading eigenvalue is unique, as in a symmetry-unbroken phase, while in the ergodic phase and at late times the leading eigenvalues are asymptotically degenerate, as in a system with degenerate symmetry-breaking phases. We identify the broken symmetry of the transfer matrix, introduce a local order parameter for the transition, and show that the associated correlation functions are long-ranged only in the ergodic phase.

Quantum Hall Network Models as Floquet Topological Insulators.

Network models for equilibrium integer quantum Hall (IQH) transitions are described by unitary scattering matrices that can also be viewed as representing nonequilibrium Floquet systems. The resulting Floquet bands have zero Chern number, and are instead characterized by a chiral Floquet winding number. This begs the question, How can a model without Chern number describe IQH systems? We resolve this puzzle by showing that nonzero Chern number is recovered from the network model via the energy dependence of network model scattering parameters. This relationship shows that, despite their topologically distinct origins, IQH and chiral Floquet topology-changing transitions share identical universal scaling properties.

Does the gene matter? Genotype-phenotype and genotype-outcome associations in congenital melanocytic naevi.

BACKGROUND: Genotype-phenotype studies can identify subgroups of patients with specific clinical features or differing outcomes, which can help shape management. OBJECTIVES: To characterize the frequency of different causative genotypes in congenital melanocytic naevi (CMN), and to investigate genotype-phenotype and genotype-outcome associations. METHODS: We conducted a large cohort study in which we undertook MC1R genotyping from blood, and high-sensitivity genotyping of NRAS and BRAF hotspots in 156 naevus biopsies from 134 patients with CMN [male 40%; multiple CMN 76%; projected adult size (PAS) > 20 cm, 59%]. RESULTS: Mosaic NRAS mutations were detected in 68%, mutually exclusive with BRAF mutations in 7%, with double wild-type in 25%. Two separate naevi were sequenced in five of seven patients with BRAF mutations, confirming clonality. Five of seven patients with BRAF mutations had a dramatic multinodular phenotype, with characteristic histology distinct from classical proliferative nodules. NRAS mutation was the commonest in all sizes of CMN, but was particularly common in naevi with PAS > 60 cm, implying more tolerance to that mutation early in embryogenesis. Facial features were less common in double wild-type patients. Importantly, the incidence of congenital neurological disease, and apparently of melanoma, was not altered by genotype; no cases of melanoma were seen in BRAF-mutant multiple CMN, however, this genotype is rare. CONCLUSIONS: CMN of all sizes are most commonly caused by mutations in NRAS. BRAF is confirmed as a much rarer cause of multiple CMN, and appears to be commonly associated with a multinodular phenotype. Genotype in this cohort was not associated with differences in incidence of neurological disease in childhood. However, genotyping should be undertaken in suspected melanoma, for guidance of treatment. What's already known about this topic? Multiple congenital melanocytic naevi (CMN) have been shown to be caused by NRAS mosaic mutations in 70-80% of cases, by BRAF mosaicism in one case report and by inference in some previous cases. There has been debate about genotypic association with different sizes of CMN, and no data on genotype-outcome. What does this study add? NRAS mosaicism was found in 68%, BRAF in 7% and double wild-type in 25% of cases of CMN. NRAS was the commonest mutation in all sizes of CMN, but was nearly universal in projected adult size > 60 cm. BRAF is often associated with a distinct multinodular clinical/histological phenotype. Adverse outcomes did not differ between genotypes on current numbers.

Spectral Statistics and Many-Body Quantum Chaos with Conserved Charge.

We investigate spectral statistics in spatially extended, chaotic many-body quantum systems with a conserved charge. We compute the spectral form factor K(t) analytically for a minimal Floquet circuit model that has a U(1) symmetry encoded via spin-1/2 degrees of freedom. Averaging over an ensemble of realizations, we relate K(t) to a partition function for the spins, given by a Trotterization of the spin-1/2 Heisenberg ferromagnet. Using Bethe ansatz techniques, we extract the "Thouless time" t_{Th} demarcating the extent of random matrix behavior, and find scaling behavior governed by diffusion for K(t) at t≲t_{Th}. We also report numerical results for K(t) in a generic Floquet spin model, which are consistent with these analytic predictions.

Eigenstate Correlations, Thermalization, and the Butterfly Effect.

We discuss eigenstate correlations for ergodic, spatially extended many-body quantum systems, in terms of the statistical properties of matrix elements of local observables. While the eigenstate thermalization hypothesis (ETH) is known to give an excellent description of these quantities, the phenomenon of scrambling and the butterfly effect imply structure beyond ETH. We determine the universal form of this structure at long distances and small eigenvalue separations for Floquet systems. We use numerical studies of a Floquet quantum circuit to illustrate both the accuracy of ETH and the existence of our predicted additional correlations.

Magnetic Excitations of the Classical Spin Liquid MgCr_{2}O_{4}.

We report a comprehensive inelastic neutron-scattering study of the frustrated pyrochlore antiferromagnet MgCr_{2}O_{4} in its cooperative paramagnetic regime. Theoretical modeling yields a microscopic Heisenberg model with exchange interactions up to third-nearest neighbors, which quantitatively explains all of the details of the dynamic magnetic response. Our work demonstrates that the magnetic excitations in paramagnetic MgCr_{2}O_{4} are faithfully represented in the entire Brillouin zone by a theory of magnons propagating in a highly correlated paramagnetic background. Our results also suggest that MgCr_{2}O_{4} is proximate to a spiral spin-liquid phase distinct from the Coulomb phase, which has implications for the magnetostructural phase transition in MgCr_{2}O_{4}.

Spectral Statistics in Spatially Extended Chaotic Quantum Many-Body Systems.

We study spectral statistics in spatially extended chaotic quantum many-body systems, using simple lattice Floquet models without time-reversal symmetry. Computing the spectral form factor K(t) analytically and numerically, we show that it follows random matrix theory (RMT) at times longer than a many-body Thouless time, t_{Th}. We obtain a striking dependence of t_{Th} on the spatial dimension d and size of the system. For d>1, t_{Th} is finite in the thermodynamic limit and set by the intersite coupling strength. By contrast, in one dimension t_{Th} diverges with system size, and for large systems there is a wide window in which spectral correlations are not of RMT form. Lastly, our Floquet model exhibits a many-body localization transition, and we discuss the behavior of the spectral form factor in the localized phase.

Emergent SO(5) Symmetry at the Néel to Valence-Bond-Solid Transition.

We show numerically that the "deconfined" quantum critical point between the Néel antiferromagnet and the columnar valence-bond solid, for a square lattice of spin 1/2, has an emergent SO(5) symmetry. This symmetry allows the Néel vector and the valence-bond solid order parameter to be rotated into each other. It is a remarkable (2+1)-dimensional analogue of the SO(4)=[SU(2)×SU(2)]/Z(2) symmetry that appears in the scaling limit for the spin-1/2 Heisenberg chain. The emergent SO(5) symmetry is strong evidence that the phase transition in the (2+1)-dimensional system is truly continuous, despite the violations of finite-size scaling observed previously in this problem. It also implies surprising relations between correlation functions at the transition. The symmetry enhancement is expected to apply generally to the critical two-component Abelian Higgs model (noncompact CP(1) model). The result indicates that in three dimensions there is an SO(5)-symmetric conformal field theory that has no relevant singlet operators, so is radically different from conventional Wilson-Fisher-type conformal field theories.

IMPLEMENTING TOOLS TO PROMOTE ADHERENCE TO ANTIRETROVIRAL THERAPY AT FACILITIES IN KENYA.

BACKGROUND: Lack of effective systems and tools to identify and track defaulters are some of the factors that pose challenges in adherence monitoring for patients on anti-retroviral treatment (ART). An intervention was performed to introduce a facility-based appointment keeping system, and a revised clinic form to monitor patients' adherence to ART. OBJECTIVE: To assess facility staff perceptions of, motivation for and self-reported practice in the implementation, and on the use of adherence-based indicators to inform decisions for performance improvement. DESIGN: Qualitative explorative study aiming to evaluate a quasi-experimental intervention. SETTINGS: Six conveniently sampled health facilities in Kenya located in Central, Eastern and Rift Valley provinces. SUBJECTS: Thirty-six clinic staff members were interviewed, six at each facility, including facility managers, clinicians, nursing and pharmacy staff, counsellors, health records information officers and social workers. Analysis was performed in line with the Pettigrew and Whipp framework. RESULTS: Providers perceived that the intervention had empowered them to assess their clinic's daily workload and to identify those patients who missed their appointments. Factors enhancing the positive uptake of the intervention included the availability of tools to monitor appointment keeping, training on adherence principles and supervisory support. Early detection of treatment defaulters helped the providers design targeted patient support to enhance appointment keeping. CONCLUSION: The effect of the intervention led to implementation of changes within the clinic to enhance patients' appointment keeping and improve adherence to treatment. We expect the reported and observed changes to be sustainable as data generation and calculation of indicators to inform decision-making were performed by the providers themselves.

Length distributions in loop soups.

Statistical lattice ensembles of loops in three or more dimensions typically have phases in which the longest loops fill a finite fraction of the system. In such phases it is natural to ask about the distribution of loop lengths. We show how to calculate moments of these distributions using CP(n-1) or RP(n-1) and O(n) σ models together with replica techniques. The resulting joint length distribution for macroscopic loops is Poisson-Dirichlet with a parameter θ fixed by the loop fugacity and by symmetries of the ensemble. We also discuss features of the length distribution for shorter loops, and use numerical simulations to test and illustrate our conclusions.

Relaxation in driven integer quantum Hall edge states.

A highly nonthermal electron distribution is generated when quantum Hall edge states originating from sources at different potentials meet at a quantum point contact. The relaxation of this distribution to a stationary form as a function of distance downstream from the contact has been observed in recent experiments [C. Altimiras et al., Phys. Rev. Lett. 105, 056803 (2010)]. Here we present an exact treatment of a minimal model for the system at filling factor ν=2, with results that account well for the observations.

Universal statistics of vortex lines.

We study the vortex lines that are a feature of many random or disordered three-dimensional systems. These show universal statistical properties on long length scales, and geometrical phase transitions analogous to percolation transitions but in distinct universality classes. The field theories for these problems have not previously been identified, so that while many numerical studies have been performed, a framework for interpreting the results has been lacking. We provide such a framework with mappings to simple supersymmetric models. Our main focus is on vortices in short-range-correlated complex fields, which show a geometrical phase transition that we argue is described by the CP(k|k) model (essentially the CP(n-1) model in the replica limit n→1). This can be seen by mapping a lattice version of the problem to a lattice gauge theory. A related field theory with a noncompact gauge field, the 'NCCP(k|k) model', is a supersymmetric extension of the standard dual theory for the XY transition, and we show that XY duality gives another way to understand the appearance of field theories of this type. The supersymmetric descriptions yield results relevant, for example, to vortices in the XY model and in superfluids, to optical vortices, and to certain models of cosmic strings. A distinct but related field theory, the RP(2l|2l) model (or the RP(n-1) model in the limit n→1) describes the unoriented vortices that occur, for instance, in nematic liquid crystals. Finally, we show that in two dimensions, a lattice gauge theory analogous to that discussed in three dimensions gives a simple way to see the known relation between two-dimensional percolation and the CP(k|k) σ model with a θ term.

3D loop models and the CP(n-1) sigma model.

Many statistical mechanics problems can be framed in terms of random curves; we consider a class of three-dimensional loop models that are prototypes for such ensembles. The models show transitions between phases with infinite loops and short-loop phases. We map them to CP(n-1) sigma models, where n is the loop fugacity. Using Monte Carlo simulations, we find continuous transitions for n=1, 2, 3, and first order transitions for n≥5. The results are relevant to line defects in random media, as well as to Anderson localization and (2+1)-dimensional quantum magnets.

Disorder in a quantum spin liquid: flux binding and local moment formation.

We study the consequences of disorder in the Kitaev honeycomb model, considering both site dilution and exchange randomness. We show that a single vacancy binds a flux and induces a local moment. This moment is polarized by an applied field h: in the gapless phase, for small h the local susceptibility diverges as χ(h)∼ln(1/h); for a pair of nearby vacancies on the same sublattice, this even increases to χ(h)∼1/(h[ln(1/h)](3/2)). By contrast, weak exchange randomness does not qualitatively alter the susceptibility but has its signature in the heat capacity, which in the gapless phase is power law in temperature with an exponent dependent on disorder strength.

Spin ice under pressure: symmetry enhancement and infinite order multicriticality.

We study the low-temperature behavior of spin ice when uniaxial pressure induces a tetragonal distortion. There is a phase transition between a Coulomb liquid and a fully magnetized phase. Unusually, it combines features of discontinuous and continuous transitions: the order parameter exhibits a jump, but this is accompanied by a divergent susceptibility and vanishing domain wall tension. All these aspects can be understood as a consequence of an emergent SU(2) symmetry at the critical point. We map out a possible experimental realization.

Spin dynamics in pyrochlore Heisenberg antiferromagnets.

We study the low temperature dynamics of the classical Heisenberg antiferromagnet with nearest neighbor interaction on the frustrated pyrochlore lattice. We present extensive results for the wave vector and frequency dependence of the dynamical structure factor, obtained from simulations of the precessional dynamics. We also construct a solvable stochastic model for dynamics with conserved magnetization, which accurately reproduces most features of the precessional results. Spin correlations relax at a rate independent of the wave vector and proportional to the temperature.

Random walks and Anderson localization in a three-dimensional class C network model.

We study the disorder-induced localization transition in a three-dimensional network model that belongs to symmetry class C. The model represents quasiparticle dynamics in a gapless spin-singlet superconductor without time-reversal invariance. It is a special feature of network models with this symmetry that the conductance and density of states can be expressed as averages in a classical system of dense, interacting random walks. Using this mapping, we present a more precise numerical study of critical behavior at an Anderson transition than has been possible previously in any context.

SU(2)-invariant continuum theory for an unconventional phase transition in a three-dimensional classical dimer model.

We derive a continuum theory for the phase transition in a classical dimer model on the cubic lattice, observed in recent Monte Carlo simulations. Our derivation relies on the mapping from a three-dimensional classical problem to a two-dimensional quantum problem, by which the dimer model is related to a model of hard-core bosons on the kagome lattice. The dimer-ordering transition becomes a superfluid-Mott insulator quantum phase transition at fractional filling, described by an SU(2)-invariant continuum theory.