Reduced fidelity in Kitaev honeycomb model

We study the reduced fidelity and reduced fidelity susceptibility in the Kitaev honeycomb model. It is shown that the reduced fidelity susceptibility of two nearest site manifest itself a peak at the quantum phase transition point, although the one-site reduced fidelity susceptibility vanishes. Our results directly reveal that the reduced fidelity susceptibility can be used to characterize the quantum phase transition in the Kitaev honeycomb model, and thus suggest that the reduced fidelity susceptibility is an accurate marker of the topological phase transition when it is properly chosen, despite of its local nature.Comment: 5 pages, 9 figure

Critical Fidelity

Using a Wigner Lorentzian Random Matrix ensemble, we study the fidelity, $F(t)$, of systems at the Anderson metal-insulator transition, subject to small perturbations that preserve the criticality. We find that there are three decay regimes as perturbation strength increases: the first two are associated with a gaussian and an exponential decay respectively and can be described using Linear Response Theory. For stronger perturbations $F(t)$ decays algebraically as $F(t)\sim t^{-D_2}$, where $D_2$ is the correlation dimension of the critical eigenstates.Comment: 4 pages, 3 figures. Revised and published in Phys. Rev. Let

Fidelity susceptibility in the two-dimensional spin-orbit models

We study the quantum phase transitions in the two-dimensional spin-orbit models in terms of fidelity susceptibility and reduced fidelity susceptibility. An order-to-order phase transition is identified by fidelity susceptibility in the two-dimensional Heisenberg XXZ model with Dzyaloshinsky-Moriya interaction on a square lattice. The finite size scaling of fidelity susceptibility shows a power-law divergence at criticality, which indicates the quantum phase transition is of second order. Two distinct types of quantum phase transitions are witnessed by fidelity susceptibility in Kitaev-Heisenberg model on a hexagonal lattice. We exploit the symmetry of two-dimensional quantum compass model, and obtain a simple analytic expression of reduced fidelity susceptibility. Compared with the derivative of ground-state energy, the fidelity susceptibility is a bit more sensitive to phase transition. The violation of power-law behavior for the scaling of reduced fidelity susceptibility at criticality suggests that the quantum phase transition belongs to a first-order transition. We conclude that fidelity susceptibility and reduced fidelity susceptibility show great advantage to characterize diverse quantum phase transitions in spin-orbit models.Comment: 11 pages. 11 figure

Entanglement, fidelity, and quantum phase transition in antiferromagnetic-ferromagnetic alternating Heisenberg chain

The fidelity and entanglement entropy in an antiferromagnetic-ferromagnetic alternating Heisenberg chain are investigated by using the method of density-matrix renormalization-group. The effect of anisotropy on fidelity and entanglement entropy are investigated. The relations between fidelity, entanglement entropy and quantum phase transition are analyzed. It is found that the quantum phase transition point can be well characterized by both the ground-state entropy and fidelity for large system.Comment: 10 pages, 4 figure

Fidelity protocol for the Action Success Knowledge (ASK) trial: A psychosocial intervention administered by speech and language therapists to prevent depression in people with post-stroke aphasia

Introduction: Treatment fidelity is a complex, multifaceted evaluative process which refers to whether a studied intervention was delivered as intended. Monitoring and enhancing fidelity is one recommendation of the TiDIER (Template for Intervention Description and Replication) checklist, as fidelity can inform interpretation and conclusions drawn about treatment effects. Despite the methodological and translational benefits, fidelity strategies have been used inconsistently within health behaviour intervention studies; in particular, within aphasia intervention studies, reporting of fidelity remains relatively rare. This paper describes the development of a fidelity protocol for the Action Success Knowledge (ASK) study, a current cluster randomised trial investigating an early mood intervention for people with aphasia (a language disability caused by stroke). Methods and analysis: A novel fidelity protocol and tool was developed to monitor and enhance fidelity within the two arms (experimental treatment and attention control) of the ASK study. The ASK fidelity protocol was developed based on the National Institutes of Health Behaviour Change Consortium fidelity framework. Ethics and dissemination: The study protocol was approved by the Darling Downs Hospital and Health Service Human Research Ethics Committee in Queensland, Australia under the National Mutual Acceptance scheme of multicentre human research projects. Specific ethics approval was obtained for those participating sites who were not under the National Mutual Agreement at the time of application. The monitoring and ongoing conduct of the research project is in line with requirements under the National Mutual Acceptance. On completion of the trial, findings from the fidelity reviews will be disseminated via publications and conference presentations. Trial registration number ACTRN12614000979651

Maximum Fidelity

The most fundamental problem in statistics is the inference of an unknown probability distribution from a finite number of samples. For a specific observed data set, answers to the following questions would be desirable: (1) Estimation: Which candidate distribution provides the best fit to the observed data?, (2) Goodness-of-fit: How concordant is this distribution with the observed data?, and (3) Uncertainty: How concordant are other candidate distributions with the observed data? A simple unified approach for univariate data that addresses these traditionally distinct statistical notions is presented called "maximum fidelity". Maximum fidelity is a strict frequentist approach that is fundamentally based on model concordance with the observed data. The fidelity statistic is a general information measure based on the coordinate-independent cumulative distribution and critical yet previously neglected symmetry considerations. An approximation for the null distribution of the fidelity allows its direct conversion to absolute model concordance (p value). Fidelity maximization allows identification of the most concordant model distribution, generating a method for parameter estimation, with neighboring, less concordant distributions providing the "uncertainty" in this estimate. Maximum fidelity provides an optimal approach for parameter estimation (superior to maximum likelihood) and a generally optimal approach for goodness-of-fit assessment of arbitrary models applied to univariate data. Extensions to binary data, binned data, multidimensional data, and classical parametric and nonparametric statistical tests are described. Maximum fidelity provides a philosophically consistent, robust, and seemingly optimal foundation for statistical inference. All findings are presented in an elementary way to be immediately accessible to all researchers utilizing statistical analysis.Comment: 66 pages, 32 figures, 7 tables, submitte

Fidelity susceptibility and geometric phase in critical phenomenon

Motivated by recent development in quantum fidelity and fidelity susceptibility, we study relations among Lie algebra, fidelity susceptibility and quantum phase transition for a two-state system and the Lipkin-Meshkov-Glick model. We get the fidelity susceptibility for SU(2) and SU(1,1) algebraic structure models. From this relation, the validity of the fidelity susceptibility to signal for the quantum phase transition is also verified in these two systems. At the same time, we obtain the geometric phase in these two systems in the process of calculating the fidelity susceptibility. In addition, the new method of calculating fidelity susceptibility has been applied to explore the two-dimensional XXZ model and the Bose-Einstein condensate(BEC).Comment: 12 pages, 4 figure