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

Ab Initio Treatments of the Ising Model in a Transverse Field

In this article, new results are presented for the zero-temperature ground-state properties of the spin-half transverse Ising model on various lattices using three different approximate techniques. These are, respectively, the coupled cluster method, the correlated basis function method, and the variational quantum Monte Carlo method. The methods, at different levels of approximation, are used to study the ground-state properties of these systems, and the results are found to be in excellent agreement both with each other and with results of exact calculations for the linear chain and results of exact cumulant series expansions for lattices of higher spatial dimension. The different techniques used are compared and contrasted in the light of these results, and the constructions of the approximate ground-state wave functions are especially discussed.Comment: 28 Pages, 4 Figures, 1 Tabl

A frustrated quantum spin-{\boldmath s} model on the Union Jack lattice with spins {\boldmath s>1/2}

The zero-temperature phase diagrams of a two-dimensional frustrated quantum antiferromagnetic system, namely the Union Jack model, are studied using the coupled cluster method (CCM) for the two cases when the lattice spins have spin quantum number $s=1$ and $s=3/2$. The system is defined on a square lattice and the spins interact via isotropic Heisenberg interactions such that all nearest-neighbour (NN) exchange bonds are present with identical strength $J_{1}>0$, and only half of the next-nearest-neighbour (NNN) exchange bonds are present with identical strength $J_{2} \equiv \kappa J_{1} > 0$. The bonds are arranged such that on the $2 \times 2$ unit cell they form the pattern of the Union Jack flag. Clearly, the NN bonds by themselves (viz., with $J_{2}=0$) produce an antiferromagnetic N\'{e}el-ordered phase, but as the relative strength $\kappa$ of the frustrating NNN bonds is increased a phase transition occurs in the classical case ($s \rightarrow \infty$) at $\kappa^{\rm cl}_{c}=0.5$ to a canted ferrimagnetic phase. In the quantum cases considered here we also find strong evidence for a corresponding phase transition between a N\'{e}el-ordered phase and a quantum canted ferrimagnetic phase at a critical coupling $\kappa_{c_{1}}=0.580 \pm 0.015$ for $s=1$ and $\kappa_{c_{1}}=0.545 \pm 0.015$ for $s=3/2$. In both cases the ground-state energy $E$ and its first derivative $dE/d\kappa$ seem continuous, thus providing a typical scenario of a second-order phase transition at $\kappa=\kappa_{c_{1}}$, although the order parameter for the transition (viz., the average ground-state on-site magnetization) does not go to zero there on either side of the transition.Comment: 1

Magnetic order in a spin-half interpolating square-triangle Heisenberg antiferromagnet

Using the coupled cluster method we study the zero-temperature phase diagram of a spin-half Heisenberg antiferromagnet (HAF), the so-called $J_{1}$--$J_{2}'$ model, defined on an anisotropic 2D lattice. With respect to an underlying square-lattice geometry the model contains antiferromagnetic ($J_{1} > 0$) bonds between nearest neighbors and competing ($J_{2}'>0$) bonds between next-nearest neighbors across only one of the diagonals of each square plaquette, the same diagonal in every square. Considered on an equivalent triangular-lattice geometry the model may be regarded as having two sorts of nearest-neighbor bonds, with $J_{2}' \equiv \kappa J_{1}$ bonds along parallel chains and $J_{1}$ bonds providing an interchain coupling. Hence, the model interpolates between a spin-half HAF on the square lattice at one extreme ($\kappa = 0$) and a set of decoupled spin-half chains at the other ($\kappa \to \infty$), with the spin-half HAF on the triangular lattice in between at $\kappa = 1$. We find strong evidence that quantum fluctuations favor a first-order transition from quasiclassical N\'{e}el order to a quantum helical state at a first critical point at $\kappa_{c_{1}} = 0.80 \pm 0.01$, by contrast with the corresponding second-order transition between the equivalent classical states at $\kappa_{{\rm cl}} = 0.5$. We also find strong evidence for a second critical point at $\kappa_{c_{2}} = 1.8 \pm 0.4$ where another first-order transition occurs, this time from the quantum helical phase to a collinear stripe-ordered phase. This latter result provides quantitative verification of a recent qualitative prediction of Starykh and Balents [Phys.\ Rev. Lett. {\bf 98}, 077205 (2007)] for the $J_{1}$--$J_{2}'$ model that did not, however, evaluate the corresponding critical point.Comment: 28 pages, 8 figure

The influence of irrigant activation, concentration and contact time on sodium hypochlorite penetration into root dentine: an ex vivo experiment

Aim To establish if irrigant activation techniques, namely manual‐dynamic‐activation (MDA), passive‐ultrasonic‐irrigation (PUI) and sonic‐irrigation (SI), improve the tubular penetration of sodium hypochlorite (NaOCl) into root dentine when compared with conventional‐needle‐irrigation (CNI). Secondly, investigate if increasing NaOCl concentration and/or contact‐time improves the performance of these techniques. Methodology A total of 83 extracted human maxillary permanent canines were decoronated to 15 mm and root canals prepared to a size 40,.10 taper. Root dentine was stained with crystal violet for 72 h and embedded in silicone. Eighty specimens were randomly distributed into 16 groups (n = 5) according to the irrigant activation technique, NaOCl concentration (2%; 5.25%) and irrigant contact‐time (10 min; 20 min). All activation techniques were used for 60 s in the last minute of irrigation. Additionally, 3 teeth were not exposed to NaOCl to confirm adequate dentine staining had occurred (i.e. negative control). All specimens were subsequently dissected, observed under a light microscope and NaOCl penetration depth (µm) determined by measuring the average width of bleached dentine using ImageJ software. Statistical comparisons were made with paired and unpaired t‐tests, ANOVAs followed by post‐hoc Tukey and Dunnett’s tests, and a general linear model (α < 0.05). Results Overall, NaOCl penetration ranged from 38.8 µm – 411.0 µm with MDA, PUI and SI consistently resulting in significantly greater tubular infiltration than CNI (P < 0.05). The deepest measurements in the coronal, middle and apical segments were all recorded in the MDA; 5.25%; 20 min group and the least in the CNI; 2%; 10 min group. Increasing either irrigant concentration or contact‐time resulted in significantly greater NaOCl penetration depths for all techniques and segments of the canal (P < 0.05). However, when irrigant concentration and contact‐time were increased together, a significant interaction effect between these two independent variables was observed on overall NaOCl penetration (P < 0.05). Conclusions Agitating irrigants with MDA, PUI or SI, as well as using greater irrigant concentrations or contact‐times, potentiated NaOCl penetration into root dentine. However, longer durations of NaOCl exposure at lower concentrations resulted in similar depths of tubular penetration as those achieved at higher concentrations

The three-item ALERT-B questionnaire provides a validated screening tool to detect chronic gastrointestinal symptoms after pelvic radiotherapy in cancer survivors

Aims: Although pelvic radiotherapy is an effective treatment for various malignancies, around half of patients develop significant gastrointestinal problems. These symptoms often remain undetected, despite the existence of effective treatments. This study developed and refined a simple screening tool to detect common gastrointestinal symptoms in outpatient clinics. These symptoms have a significant effect on quality of life. This tool will increase detection rates and so enable access to specialist gastroenterologists, which will in turn lead to improved symptom control and quality of life after treatment. Materials and methods: A literature review and expert consensus meeting identified four items for the ALERT-B (Assessment of Late Effects of RadioTherapy - Bowel) screening tool. ALERT-B was face tested for its usability and acceptability using cognitive interviews with 12 patients experiencing late gastrointestinal symptoms after pelvic radiotherapy. Thematic analysis and probe category were used to analyse interview transcripts. Interview data were presented to a group of experts to agree on the final content and format of the tool. ALERT-B was assessed for reliability and tested for validity against the Gastrointestinal Symptom Rating Scale in a clinical study (EAGLE). Results: Overall, the tool was found to be acceptable in terms of wording, response format and completion time. Participant-reported experiences, including lifestyle modifications and the psychological effect of the symptoms, led to further modifications of the tool. The refined tool includes three questions covering rectal bleeding, incontinence, nocturnal bowel movements and impact on quality of life, including mood, relationships and socialising. ALERT-B was successfully validated against the Gastrointestinal Symptom Rating Scale in the EAGLE study with the tool shown broadly to be internally consistent (Cronbach’s alpha=0.61 and all item-subscale correlation [Spearman] coefficients are > 0.6). Conclusion: The ALERT-B screening tool can be used in clinical practice to improve post-treatment supportive care by triggering the clinical assessment of patients suitable for referral to a gastroenterologist

Investigating the potential clinical benefit of Selumetinib in resensitising advanced iodine refractory differentiated thyroid cancer to radioiodine therapy (SEL-I-METRY): protocol for a multicentre UK single arm phase II trial

Background Thyroid cancer is the most common endocrine malignancy. Some advanced disease is, or becomes, resistant to radioactive iodine therapy (refractory disease); this holds poor prognosis of 10% 10-year overall survival. Whilst Sorafenib and Lenvatinib are now licenced for the treatment of progressive iodine refractory thyroid cancer, these treatments require continuing treatment and can be associated with significant toxicity. Evidence from a pilot study has demonstrated feasibility of Selumetinib to allow the reintroduction of I-131 therapy; this larger, multicentre study is required to demonstrate the broader clinical impact of this approach before progression to a confirmatory trial. Methods SEL-I-METRY is a UK, single-arm, multi-centre, two-stage phase II trial. Participants with locally advanced or metastatic differentiated thyroid cancer with at least one measureable lesion and iodine refractory disease will be recruited from 8 NHS Hospitals and treated with 4-weeks of oral Selumetinib and assessed for sufficient I-123 uptake (defined as any uptake in a lesion with no previous uptake or 30% or greater increase in uptake). Those with sufficient uptake will be treated with I-131 and followed for clinical outcomes. Radiation absorbed doses will be predicted from I-123 SPECT/CT and verified from scans following the therapy. 60 patients will be recruited to assess the primary objective of whether the treatment schedule leads to increased progression-free survival compared to historical control data. Discussion The SEL-I-METRY trial will investigate the effect of Selumetinib followed by I-131 therapy on progression-free survival in radioiodine refractory patients with differentiated thyroid cancer showing increased radioiodine uptake following initial treatment with Selumetinib. In addition, information on toxicity and dosimetry will be collected. This study presents an unprecedented opportunity to investigate the role of lesional dosimetry in molecular radiotherapy, leading to greater personalisation of therapy. To date this has been a neglected area of research. The findings of this trial will be useful to healthcare professionals and patients alike to determine whether further study of this agent is warranted. It is hoped that the development of the infrastructure to deliver a multicentre trial involving molecular radiotherapy dosimetry will lead to further trials in this field. Trial registration SEL-I-METRY is registered under ISRCTN17468602, 02/12/2015

Surface acoustic wave attenuation by a two-dimensional electron gas in a strong magnetic field

The propagation of a surface acoustic wave (SAW) on GaAs/AlGaAs heterostructures is studied in the case where the two-dimensional electron gas (2DEG) is subject to a strong magnetic field and a smooth random potential with correlation length Lambda and amplitude Delta. The electron wave functions are described in a quasiclassical picture using results of percolation theory for two-dimensional systems. In accordance with the experimental situation, Lambda is assumed to be much smaller than the sound wavelength 2*pi/q. This restricts the absorption of surface phonons at a filling factor \bar{\nu} approx 1/2 to electrons occupying extended trajectories of fractal structure. Both piezoelectric and deformation potential interactions of surface acoustic phonons with electrons are considered and the corresponding interaction vertices are derived. These vertices are found to differ from those valid for three-dimensional bulk phonon systems with respect to the phonon wave vector dependence. We derive the appropriate dielectric function varepsilon(omega,q) to describe the effect of screening on the electron-phonon coupling. In the low temperature, high frequency regime T << Delta (omega_q*Lambda /v_D)^{alpha/2/nu}, where omega_q is the SAW frequency and v_D is the electron drift velocity, both the attenuation coefficient Gamma and varepsilon(omega,q) are independent of temperature. The classical percolation indices give alpha/2/nu=3/7. The width of the region where a strong absorption of the SAW occurs is found to be given by the scaling law |Delta \bar{\nu}| approx (omega_q*Lambda/v_D)^{alpha/2/nu}. The dependence of the electron-phonon coupling and the screening due to the 2DEG on the filling factor leads to a double-peak structure for Gamma(\bar{\nu}).Comment: 17 pages, 3 Postscript figures, minor changes mad

Influence of quantum fluctuations on zero-temperature phase transitions between collinear and noncollinear states in frustrated spin systems

We study a square-lattice spin-half Heisenberg model where frustration is introduced by competing nearest-neighbor bonds of different signs. We discuss the influence of quantum fluctuations on the nature of the zero-temperature phase transitions from phases with collinear magnetic order at small frustration to phases with noncollinear spiral order at large frustration. We use the coupled cluster method (CCM) for high orders of approximation (up to LSUB6) and the exact diagonalization of finite systems (up to 32 sites) to calculate ground-state properties. The role of quantum fluctuations is examined by comparing the ferromagnetic-spiral and the antiferromagnetic-spiral transition within the same model. We find clear evidence that quantum fluctuations prefer collinear order and that they may favour a first order transition instead of a second order transition in case of no quantum fluctuations.Comment: 6 pages, 6 Postscipt figures; Accepted for publication in Phys. Rev.

The Extended Coupled Cluster Treatment of Correlations in Quantum Magnets

The spin-half XXZ model on the linear chain and the square lattice are examined with the extended coupled cluster method (ECCM) of quantum many-body theory. We are able to describe both the Ising-Heisenberg phase and the XY-Heisenberg phase, starting from known wave functions in the Ising limit and at the phase transition point between the XY-Heisenberg and ferromagnetic phases, respectively, and by systematically incorporating correlations on top of them. The ECCM yields good numerical results via a diagrammatic approach, which makes the numerical implementation of higher-order truncation schemes feasible. In particular, the best non-extrapolated coupled cluster result for the sublattice magnetization is obtained, which indicates the employment of an improved wave function. Furthermore, the ECCM finds the expected qualitatively different behaviours of the linear chain and the square lattice cases.Comment: 22 pages, 3 tables, and 15 figure