The frustrated Heisenberg antiferromagnet on the honeycomb lattice: J1J_{1}--J2J_{2} model

We study the ground-state (gs) phase diagram of the frustrated spin-1/2 $J_{1}$--$J_{2}$ antiferromagnet with $J_{2}=\kappa J_1>0$ ($J_{1}>0$) on the honeycomb lattice, using the coupled-cluster method. We present results for the ground-state energy, magnetic order parameter and plaquette valence-bond crystal (PVBC) susceptibility. We find a paramagnetic PVBC phase for $\kappa_{c_1}<\kappa<\kappa_{c_2}$, where $\kappa_{c_1} \approx 0.207 \pm 0.003$ and $\kappa_{c_2} \approx 0.385 \pm 0.010$. The transition at $\kappa_{c_1}$ to the N\'{e}el phase seems to be a continuous deconfined transition (although we cannot exclude a very narrow intermediate phase in the range $0.21 \lesssim \kappa \lesssim 0.24$), while that at $\kappa_{c_2}$ is of first-order type to another quasiclassical antiferromagnetic phase that occurs in the classical version of the model only at the isolated and highly degenerate critical point $\kappa = 1/2$. The spiral phases that are present classically for all values $\kappa > 1/6$ are absent for all $\kappa \lesssim 1$.Comment: 6 pages, 5 figure

High-Order Coupled Cluster Method Calculations for the Ground- and Excited-State Properties of the Spin-Half XXZ Model

In this article, we present new results of high-order coupled cluster method (CCM) calculations, based on a N\'eel model state with spins aligned in the $z$-direction, for both the ground- and excited-state properties of the spin-half {\it XXZ} model on the linear chain, the square lattice, and the simple cubic lattice. In particular, the high-order CCM formalism is extended to treat the excited states of lattice quantum spin systems for the first time. Completely new results for the excitation energy gap of the spin-half {\it XXZ} model for these lattices are thus determined. These high-order calculations are based on a localised approximation scheme called the LSUB$m$ scheme in which we retain all $k$-body correlations defined on all possible locales of $m$ adjacent lattice sites ($k \le m$). The ``raw'' CCM LSUB$m$ results are seen to provide very good results for the ground-state energy, sublattice magnetisation, and the value of the lowest-lying excitation energy for each of these systems. However, in order to obtain even better results, two types of extrapolation scheme of the LSUB$m$ results to the limit $m \to \infty$ (i.e., the exact solution in the thermodynamic limit) are presented. The extrapolated results provide extremely accurate results for the ground- and excited-state properties of these systems across a wide range of values of the anisotropy parameter.Comment: 31 Pages, 5 Figure

Phase Transitions in the Spin-Half J_1--J_2 Model

The coupled cluster method (CCM) is a well-known method of quantum many-body theory, and here we present an application of the CCM to the spin-half J_1--J_2 quantum spin model with nearest- and next-nearest-neighbour interactions on the linear chain and the square lattice. We present new results for ground-state expectation values of such quantities as the energy and the sublattice magnetisation. The presence of critical points in the solution of the CCM equations, which are associated with phase transitions in the real system, is investigated. Completely distinct from the investigation of the critical points, we also make a link between the expansion coefficients of the ground-state wave function in terms of an Ising basis and the CCM ket-state correlation coefficients. We are thus able to present evidence of the breakdown, at a given value of J_2/J_1, of the Marshall-Peierls sign rule which is known to be satisfied at the pure Heisenberg point (J_2 = 0) on any bipartite lattice. For the square lattice, our best estimates of the points at which the sign rule breaks down and at which the phase transition from the antiferromagnetic phase to the frustrated phase occurs are, respectively, given (to two decimal places) by J_2/J_1 = 0.26 and J_2/J_1 = 0.61.Comment: 28 pages, Latex, 2 postscript figure

The frustrated Heisenberg antiferromagnet on the honeycomb lattice: A candidate for deconfined quantum criticality

We study the ground-state (gs) phase diagram of the frustrated spin-1/2 $J_{1}$-$J_{2}$-$J_{3}$ antiferromagnet with $J_{2} = J_{3} =\kappa J_1$ on the honeycomb lattice, using coupled-cluster theory and exact diagonalization methods. We present results for the gs energy, magnetic order parameter, spin-spin correlation function, and plaquette valence-bond crystal (PVBC) susceptibility. We find a N\'eel antiferromagnetic (AFM) phase for $\kappa < \kappa_{c_{1}} \approx 0.47$, a collinear striped AFM phase for $\kappa > \kappa_{c_{2}} \approx 0.60$, and a paramagnetic PVBC phase for $\kappa_{c_{1}} \lesssim \kappa \lesssim \kappa_{c_{2}}$. The transition at $\kappa_{c_{2}}$ appears to be of first-order type, while that at $\kappa_{c_{1}}$ is continuous. Since the N\'eel and PVBC phases break different symmetries our results favor the deconfinement scenario for the transition at $\kappa_{c_{1}}$

Factors influencing utilisation of ‘free-standing’ and ‘alongside’ midwifery units for low-risk births in England: a mixed-methods study

Background Midwifery-led units (MUs) are recommended for ‘low-risk’ births by the National Institute for Health and Care Excellence but according to the National Audit Office were not available in one-quarter of trusts in England in 2013 and, when available, were used by only a minority of the low-risk women for whom they should be suitable. This study explores why. Objectives To map the provision of MUs in England and explore barriers to and facilitators of their development and use; and to ascertain stakeholder views of interventions to address these barriers and facilitators. Design Mixed methods – first, MU access and utilisation across England was mapped; second, local media coverage of the closure of free-standing midwifery units (FMUs) were analysed; third, case studies were undertaken in six sites to explore the barriers and facilitators that have an impact on the development of MUs; and, fourth, by convening a stakeholder workshop, interventions to address the barriers and facilitators were discussed. Setting English NHS maternity services. Participants All trusts with maternity services. Interventions Establishing MUs. Main outcome measures Numbers and types of MUs and utilisation of MUs. Results Births in MUs across England have nearly tripled since 2011, to 15% of all births. However, this increase has occurred almost exclusively in alongside units, numbers of which have doubled. Births in FMUs have stayed the same and these units are more susceptible to closure. One-quarter of trusts in England have no MUs; in those that do, nearly all MUs are underutilised. The study findings indicate that most trust managers, senior midwifery managers and obstetricians do not regard their MU provision as being as important as their obstetric-led unit provision and therefore it does not get embedded as an equal and parallel component in the trust’s overall maternity package of care. The analysis illuminates how provision and utilisation are influenced by a complex range of factors, including the medicalisation of childbirth, financial constraints and institutional norms protecting the status quo. Limitations When undertaking the case studies, we were unable to achieve representativeness across social class in the women’s focus groups and struggled to recruit finance directors for individual interviews. This may affect the transferability of our findings. Conclusions Although there has been an increase in the numbers and utilisation of MUs since 2011, significant obstacles remain to MUs reaching their full potential, especially FMUs. This includes the capacity and willingness of providers to address women’s information needs. If these remain unaddressed at commissioner and provider level, childbearing women’s access to MUs will continue to be restricted. Future work Work is needed on optimum approaches to improve decision-makers’ understanding and use of clinical and economic evidence in service design. Increasing women’s access to information about MUs requires further studies of professionals’ understanding and communication of evidence. The role of FMUs in the context of rural populations needs further evaluation to take into account user and community impact. Funding This project was funded by the National Institute for Health Research (NIHR) Health Services and Delivery Research programme and will be published in full in Health Services and Delivery Research; Vol. 8, No. 12. See the NIHR Journals Library website for further project information

General relativistic null-cone evolutions with a high-order scheme

We present a high-order scheme for solving the full non-linear Einstein equations on characteristic null hypersurfaces using the framework established by Bondi and Sachs. This formalism allows asymptotically flat spaces to be represented on a finite, compactified grid, and is thus ideal for far-field studies of gravitational radiation. We have designed an algorithm based on 4th-order radial integration and finite differencing, and a spectral representation of angular components. The scheme can offer significantly more accuracy with relatively low computational cost compared to previous methods as a result of the higher-order discretization. Based on a newly implemented code, we show that the new numerical scheme remains stable and is convergent at the expected order of accuracy.Comment: 24 pages, 3 figure

Magnetic order in a spin-1/2 interpolating kagome-square Heisenberg antiferromagnet

The coupled cluster method is applied to a spin-half model at zero temperature ($T=0$), which interpolates between Heisenberg antiferromagnets (HAF's) on a kagome and a square lattice. With respect to an underlying triangular lattice the strengths of the Heisenberg bonds joining the nearest-neighbor (NN) kagome sites are $J_{1} \geq 0$ along two of the equivalent directions and $J_{2} \geq 0$ along the third. Sites connected by $J_{2}$ bonds are themselves connected to the missing NN non-kagome sites of the triangular lattice by bonds of strength $J_{1}' \geq 0$. When $J_{1}'=J_{1}$ and $J_{2}=0$ the model reduces to the square-lattice HAF. The magnetic ordering of the system is investigated and its $T=0$ phase diagram discussed. Results for the kagome HAF limit are among the best available.Comment: 21 pages, 8 figure

Factors influencing the utilisation of free-standing and alongside midwifery units in England: a qualitative research study

OBJECTIVE: To identify factors influencing the provision, utilisation and sustainability of midwifery units (MUs) in England. DESIGN: Case studies, using individual interviews and focus groups, in six National Health Service (NHS) Trust maternity services in England. SETTING AND PARTICIPANTS: NHS maternity services in different geographical areas of England Maternity care staff and service users from six NHS Trusts: two Trusts where more than 20% of all women gave birth in MUs, two Trusts where less than 10% of all women gave birth in MUs and two Trusts without MUs. Obstetric, midwifery and neonatal clinical leaders, managers, service user representatives and commissioners were individually interviewed (n=57). Twenty-six focus groups were undertaken with midwives (n=60) and service users (n=52). MAIN OUTCOME MEASURES: Factors influencing MU use. FINDINGS: The study findings identify several barriers to the uptake of MUs. Within a context of a history of obstetric-led provision and lack of decision-maker awareness of the clinical and economic evidence, most Trust managers and clinicians do not regard their MU provision as being as important as their obstetric unit (OU) provision. Therefore, it does not get embedded as an equal and parallel component in the Trust's overall maternity package of care. The analysis illuminates how implementation of complex interventions in health services is influenced by a range of factors including the medicalisation of childbirth, perceived financial constraints, adequate leadership and institutional norms protecting the status quo. CONCLUSIONS: There are significant obstacles to MUs reaching their full potential, especially free-standing midwifery units. These include the lack of commitment by providers to embed MUs as an essential service provision alongside their OUs, an absence of leadership to drive through these changes and the capacity and willingness of providers to address women's information needs. If these remain unaddressed, childbearing women's access to MUs will continue to be restricted

Spin-1/2 Heisenberg antiferromagnet on an anisotropic kagome lattice

We use the coupled cluster method to study the zero-temperature properties of an extended two-dimensional Heisenberg antiferromagnet formed from spin-1/2 moments on an infinite spatially anisotropic kagome lattice of corner-sharing isosceles triangles, with nearest-neighbor bonds only. The bonds have exchange constants $J_{1}>0$ along two of the three lattice directions and $J_{2} \equiv \kappa J_{1} > 0$ along the third. In the classical limit the ground-state (GS) phase for $\kappa < 1/2$ has collinear ferrimagnetic (N\'{e}el$'$) order where the $J_2$-coupled chain spins are ferromagnetically ordered in one direction with the remaining spins aligned in the opposite direction, while for $\kappa > 1/2$ there exists an infinite GS family of canted ferrimagnetic spin states, which are energetically degenerate. For the spin-1/2 case we find that quantum analogs of both these classical states continue to exist as stable GS phases in some regions of the anisotropy parameter $\kappa$, namely for $0<\kappa<\kappa_{c_1}$ for the N\'{e}el$'$ state and for (at least part of) the region $\kappa>\kappa_{c_2}$ for the canted phase. However, they are now separated by a paramagnetic phase without either sort of magnetic order in the region $\kappa_{c_1} < \kappa < \kappa_{c_2}$, which includes the isotropic kagome point $\kappa = 1$ where the stable GS phase is now believed to be a topological ($\mathbb{Z}_2$) spin liquid. Our best numerical estimates are $\kappa_{c_1} = 0.515 \pm 0.015$ and $\kappa_{c_2} = 1.82 \pm 0.03$