Compass Model Research Articles

Engaging with distress: Training in the compassionate approach.

WHAT IS KNOWN ON THE SUBJECT?: Mental health nurses provide care within an environment that is often threatening. The environment is often threatening because: (a) patients' needs are complex and highly emotional, (b) nurses often do not have the time and resources they would wish for and (c) caring for patients can be emotionally exhausting and distressing. Compassionate care involves providing a welcoming environment, promoting bidirectional compassion, providing training in compassion and creating supportive organizations. To date, there is no study evaluating compassion interventions for the high-threat profession of mental health nursing and no study qualitatively evaluating compassion training and implementation. WHAT THE PAPER ADDS TO EXISTING KNOWLEDGE?: This study looked at what happens if compassion training delivered by the originator of Gilbert's model of compassion is given to mental health nurses. Nurses were interviewed 1year later to see how relevant and useful the training was, and whether they had been able to use it in their daily work. Consistent with previous studies, the study found a reduction in professionals' self-criticism and an increase in self-compassion, which in this study extended to increased compassion and reduced criticism of colleagues and patients; and professionals applying the training directly to reduce patient self-criticism. WHAT ARE THE IMPLICATIONS FOR PRACTICE?: Nurses felt that more training and supervision was needed to build the confidence to use the training regularly at work. They felt it had been difficult to use the training because of the threatening environment in which they worked. Nurses recommended that the whole organization would need the training to make it part of their everyday work. ABSTRACT: Introduction Compassionate care involves providing a welcoming environment, promoting bidirectional compassion, providing training in compassion and creating supportive organizations. To date, there has not been a study evaluating compassion interventions for the high-threat profession of mental health nursing. Neither has there been a study providing an in-depth qualitative evaluation of training and implementation. The current study aims to address these gaps in the literature. Aim The aims were to evaluate Compassionate Mind Training-CMT for mental health nurses and to assess implementation. Method Focus groups were conducted (N=28) 1year later to evaluate CMT and implementation. Results Content analysis revealed four training themes: (a) Useful framework; (b) Thought-provoking and exciting; (c) Appreciation of person-centred approach; and (d) Need for ongoing training and supervision. Three implementation themes emerged: (a) Applied approach with patients and staff themselves; (b) Environmental challenges to implementation; and (c) Attitudinal challenges to implementation. Discussion Consistent with previous studies, professionals experienced reduced self-criticism and an increased self-compassion, which extended to increased compassion and reduced criticism of colleagues and patients; and professionals applying training directly to reduce patient self-criticism. Implications For successful implementation, formal adoption of compassion approaches is needed with strategic integration at all levels.

Interacting Majorana modes at surfaces of noncentrosymmetric superconductors

Noncentrosymmetric superconductors with line nodes are expected to possess topologically protected flat zero-energy bands of surface states, which can be described as Majorana modes. We here investigate their fate if residual interactions beyond BCS theory are included. For a minimal square-lattice model with a plaquette interaction, we find string-like integrals of motion that form Clifford algebras and lead to exact degeneracies. These degeneracies strongly depend on whether the numbers of sites in the $x$ and $y$ directions are even or odd, and are robust against disorder in the interactions. We show that the mapping of the Majorana model onto two decoupled spin compass models [Kamiya et al., Phys. Rev. B 98, 161409 (2018)] and extra spectator degrees of freedom only works for open boundary conditions. The mapping shows that the three-leg and four-leg Majorana ladders are integrable, while systems of larger width are not. In addition, the mapping maximally reduces the effort for exact diagonalization, which is utilized to obtain the gap above the ground states. We find that this gap remains open if one dimension is kept constant and even, while the other is sent to infinity, at least if that dimension is odd. Moreover, we compare the topological properties of the interacting Majorana model to those of the toric-code model. The Majorana model has long-range entangled ground states that differ by $\mathbb{Z}_2$ fluxes through the system on a torus. The ground states exhibit string condensation similar to the toric code but the topological order is not robust. While the spectrum is gapped - due to spontaneous symmetry breaking inherited from the compass models - states with different values of the $\mathbb{Z}_2$ fluxes end up in the ground-state sector in the thermodynamic limit. Hence, the gap does not protect these fluxes against weak perturbations.

Development of Digital Compass Based on AVR Microcontroller and MEMS Accelerometer- Magnetometer Module LSM303DLHC

In the paper, the digital compass based on AVR microcontroller has been developed using MEMS accelerometer-magnetometer LSM303DLHC. The structure and hardware of the digital compass have been developed. The calibration algorithms of the accelerometer and magnetometer of the LSM303DLHC module have been described. The calculation algorithm of the pitch and roll angles has been described. The heading calculation algorithm of the digital compass without tilt compensation and with tilt compensation has been described. The operation algorithm and embedded software of the digital compass have been developed. The model and prototype of the digital compass have been created. The simulation and operation test of the developed digital compass have been performed.

The Importance of Flexible Relational Boundaries: The Role of Connectedness in Self-Compassion and Compassion for Others

Self-compassion and compassion for others have largely been studied independently. However, when studied as separate but related constructs, clear self-other differences emerge. Although intrapersonal and interpersonal differences are perhaps best explained through personality theory, specifically Blatt’s (2008) 2 polarities model, limited research has specifically examined the impact personality organization has on the capacity to extend compassion to oneself and others. The present study examined how personality organization according to 2-polarities model of personality is related to and impacts self-compassion and compassion for others. Participants (N = 226) completed a series of self-report questionnaires online to assess personality organization and compassion competencies. Results yielded 2 predictive models of compassion. Efficacy (+), self-criticism (−), and connectedness (−-) predicted self-compassion (R2 = .47, p < .001). Efficacy (+), self-criticism (−), and connectedness (+) predicted compassion for others (R2 = .36, p < .001). Model disparities elucidate key differences between the constructs, specifically that healthy and flexible relational boundaries are essential for self-compassion, while feelings of security and stability within personal relationships are more important for showing others compassion. Understanding how differences in personality proclivities relate to the nuances in self-compassion and compassion for others may aid therapeutic intervention targeting compassion capacities.

Exact solution to a class of generalized Kitaev spin-1/2 models in arbitrary dimensions

We construct a class of exactly solvable generalized Kitaev spin-1/2 models in arbitrary dimensions, which is beyond the category of quantum compass models. The Jordan-Wigner transformation is employed to prove the exact solvability. An exactly solvable quantum spin-1/2 model can be mapped to a gas of free Majorana fermions coupled to static Z2 gauge fields. We classify these exactly solvable models according to their parent models. Any model belonging to this class can be generated by one of the parent models. For illustration, a two dimensional (2D) tetragon-octagon model and a three dimensional (3D) xy bond model are studied.

Simulation verification for the robustness of passive compass gait with a joint stiffness adjustment

ABSTRACTA passive walking robot can achieve a smooth gait without any sensory feedback while walking down a slope. This phenomenon is based on the transformation of potential energy into kinetic energy in the legs. Although the entrainment is observed in a passive gait motion, there is a possibility that the passive gait cannot be achieved in the case of variations in physical parameters, initial conditions, and disturbances. To realize a robust passive gait against variations in physical parameters, this paper proposes a passive gait system that possesses a joint stiffness adjustment. Targeting a compass model, this paper investigates the effectiveness of the proposed method for a passive gait against variations in slope angle and hip joint mass through simulation. As a result, the simulation results show that this method especially has strong robustness against the slope angle variation.

Strategies for Maintaining the Coach-Analyst Relationship Within Professional Football Utilizing the COMPASS Model: The Performance Analyst's Perspective.

There is a considerable body of research by that has investigated the coach–athlete relationship in sport. However, given the multi-disciplinary nature of modern elite coaching, there is a scarcity of research focusing on the relationship between coaches and other members of the coaching and support team. This study examined the perceptions of six elite professional football analyst’s relationships with their respective coaches. Semi structured interviews utilizing the COMPASS Framework were conducted focusing on Conflict, Openness, Motivation, Preventative Strategies, Assurance, Support, and Social Networks. The results verified that the COMPASS Model of relationship maintenance was applicable to this dyad. Content analysis indicated that there was 215 raw data units comprising of 16 higher order themes across the model which was further broken down into 29 lower order themes. All aspects of the model were found to contribute toward a positively maintained relationship. Having an open relationship underpinned by honesty and being able to provide an opinion was seen as the highest rated attribute that was closely followed by supporting the coach by understanding their requirements for successful coaching practice. Not meeting the coach’s expectations was found to cause conflict and was further highlighted by an inductive analysis that revealed the existence of a relationship that is fundamentally dictated by the coach. Implications of this investigation are that professionals which support elite performers need to set out clear expectations of working practice and hierarchies in order to minimize the chance of internal conflict that can impact on the service levels received by the performer.

Exact zero modes in a quantum compass chain under inhomogeneous transverse fields

We study the emergence of exact Majorana zero modes (EMZMs) in a one-dimensional quantum transverse compass model with both the nearest-neighbor interactions and transverse fields varying over space. By transforming the spin system into a quadratic Majorana-fermion model, we derive an exact formula for the number of the emergent EMZMs, which is found to depend on the partition nature of the lattice sites on which the magnetic fields vanish. We also derive explicit expressions for the wavefunctions of these EMZMs and show that they indeed depend on fine features of the foregoing partition of site indices. Based on the above rigorous results about the EMZMs, we provide an interpretation for the interesting dependence of the eigenstate-degeneracy on the transverse fields observed in prior literatures. As a special case, we employ a plane-wave ansatz to exactly solve an open compass chain with alternating nearest-neighbor interactions and staggered magnetic fields. Explicit forms of the canonical Majorana modes diagonalizing the model are given even for finite chains. We show that besides the possibly existing EMZMs, no almost Majorana zero modes exist unless the fields on both the two sublattices are turned off. Our results might shed light on the control of ground-state degeneracies by solely tuning the external fields in related systems.

The Role of Compassion and Mindfulness in Building Parental Resilience When Caring for Children With Chronic Conditions: A Conceptual Model.

Compassion- and mindfulness-based interventions (CMBIs) and therapies hold promise to support parent resilience by enabling adaptive stress appraisal and coping, mindful parenting, and perhaps crucially, self-compassion. These contemplative modalities have recently been expanded to parents of children with chronic illness, building on successful applications for adults facing stress, chronic pain, or mental illness, and for healthcare professionals in response to caregiver burnout resulting from their work. The design and adaptation of interventions and therapies require a conceptual model of parent resilience in the context of childhood chronic illness that integrates mindfulness and compassion. The objective of this paper is to propose and describe such a model. First, we review the need for parent support interventions for this population. Second, we introduce a Model of Compassion, Mindfulness, and Resilience in Parental Caregiving. We highlight the mindful parenting approaches, guiding theories for adaptive coping, and family resilience frameworks that informed our model. Third, we describe a case of a parent to illustrate a practical application model. Finally, we outline future directions for intervention development and research to examine the impact of CMBIs on parent resilience.

Cultivating organizational compassion in healthcare

AbstractThe compassion of healthcare workers towards patients is widely recognized, but research suggests a dearth of compassion among co-workers. Indeed, workplace bullying and negative employee outcomes are over-represented in the healthcare sector (including burnout and substantial staff turnover). In this paper, we discuss the cultivation of compassion for healthcare workers, using the lens of positive organizational scholarship. Our concern is not only with the individual level compassion (i.e. between employees), we also consider how compassion can be cultivated systemically across healthcare institutions at the organizational level. More specifically, we present a proposed Noticing, Empathising, Assessing and Responding Mechanisms Model of Organizational Compassion as a tool for consciously cultivating workplace compassion in healthcare organizations.

2D Compass Codes

The compass model on a square lattice provides a natural template for building subsystem stabilizer codes. The surface code and the Bacon-Shor code represent two extremes of possible codes depending on how many gauge qubits are fixed. We explore threshold behavior in this broad class of local codes by trading locality for asymmetry and gauge degrees of freedom for stabilizer syndrome information. We analyze these codes with asymmetric and spatially inhomogeneous Pauli noise in the code capacity and phenomenological models. In these idealized settings, we observe considerably higher thresholds against asymmetric noise. At the circuit level, these codes inherit the bare-ancilla fault-tolerance of the Bacon-Shor code.

Dissipative spin chain as a non-Hermitian Kitaev ladder

We derive exact results for the Lindblad equation for a quantum spin chain (one-dimensional quantum compass model) with dephasing noise. The system possesses doubly degenerate nonequilibrium steady states due to the presence of a conserved charge commuting with the Hamiltonian and Lindblad operators. We show that the system can be mapped to a non-Hermitian Kitaev model on a two-leg ladder, which is solvable by representing the spins in terms of Majorana fermions. This allows us to study the Liouvillian gap, the inverse of relaxation time, in detail. We find that the Liouvillian gap increases monotonically when the dissipation strength $ \gamma $ is small, while it decreases monotonically for large $ \gamma $, implying a kind of phase transition in the first decay mode. The Liouvillian gap and the transition point are obtained in closed form in the case where the spin chain is critical. We also obtain the explicit expression for the autocorrelator of the edge spin. The result implies the suppression of decoherence when the spin chain is in the topological regime.

Microscopic theory of electric polarization induced by skyrmionic order in GaV4S8

The lacunar spinel GaV$_{4}$S$_{8}$ was recently suggested to be a prototype multiferroic material hosting skyrmion lattice states with a sizeable polarization $\boldsymbol{P}$ coupled to magnetic order. We explain this phenomenon on the microscopic level. On the basis of density functional theory, we construct an effective model describing the behavior of magnetically active electrons in a weakly coupled lattice formed by molecular orbitals of the (V$_{4}$S$_{4}$)$^{5+}$ clusters. By applying superexchange theory combined with the Berry-phase theory for $\boldsymbol{P}$, we derive a compass model relating the energy and polarization change with the directions of spins $\boldsymbol{e}_{i}$ in magnetic bonds. We argue that, although each skyrmion layer is mainly formed by superexchange interactions in the same plane, the spin-dependence of $\boldsymbol{P}$ arises from the stacking misalignment of such planes in the perpendicular direction, which is inherent to the lacunar spinel structure. We predict a strong competition of isotropic, $\sim \boldsymbol{e}_{i}\boldsymbol{e}_{j}$, and antisymmetric, $\sim \boldsymbol{e}_{i} \times \boldsymbol{e}_{j}$, contributions to $\boldsymbol{P}$ that explains the experimentally observed effect.

Dynamical Quantum Phase Transition and Quasi Particle Excitation

Dynamical phase transitions (DPTs) are signaled by the non-analytical time evolution of the dynamical free energy after quenching some global parameters in quantum systems. The dynamical free energy is calculated from the overlap between the initial and the time evolved states (Loschmidt amplitude). In a recent study it was suggested that DPTs are related to the equilibrium phase transitions (EPTs) (Heyl, M. et al. Phys. Rev. Lett. 110, 135704 (2013)). We here study an exactly solvable model, the extended XY model, the Loschmidt amplitude of which provides a counterexample. We show analytically that the connection between the DPTs and the EPTs does not hold generally. Analysing also the general compass model as a second example, assists us to propound the physical condition under which the DPT occurs without crossing the equilibrium critical point, and also no DPT by crossing the equilibrium critical point.

Kitaev-like honeycomb magnets: Global phase behavior and emergent effective models

Compounds of transition metal ions with strong spin-orbit coupling recently attracted attention due to the possibility to host frustrated bond-dependent anisotropic magnetic interactions. In general, such interactions lead to complex phase diagrams that may include exotic phases, e.g. the Kitaev spin liquid. Here we report on our comprehensive analysis of the global phase diagram of the extended Kitaev-Heisenberg model relevant to honeycomb lattice compounds Na2IrO3 and alpha-RuCl3. We have utilized recently developed method based on spin coherent states that enabled us to resolve arbitrary spin patterns in the cluster ground states obtained by exact diagonalization. Global trends in the phase diagram are understood in combination with the analytical mappings of the Hamiltonian that uncover peculiar links to known models - Heisenberg, Ising, Kitaev, or compass models on the honeycomb lattice - or reveal entire manifolds of exact fluctuation-free ground states. Finally, our study can serve as a methodological example that can be applied to other spin models with complex bond-dependent non-Heisenberg interactions.

Local broken symmetry and spin conductivity in the two-dimensional model in the compass lattice

The spin transport in the neighborhood of a quantum phase transition in the two-dimensional compass model is studied. The model presents Heisenberg compass interactions of amplitudes Jx and Jz and next and next-nearest neighbor Heisenberg interactions J1 and J2. Where the Heisenberg interactions are isotropic in spin space, but the compass interactions depending on the bond direction. Our results show a conductivity varying a little with the behavior of critical parameters η = J2∕J1, Jz and Jx. Hence, we obtain a little variation of the phase transition to magnetically ordered phase on conductivity. Besides, we obtain a conventional conductor behavior for the AC spin transport in the limit ω → 0 or DC limit.

Coarse-grained molecular dynamics simulation of deformation and fracture in polycarbonate: Effect of loading mode, strain rate, temperature and molar mass

Polycarbonate is one of the most promising polymers having potential application as structural materials owing to its prominent properties including lightness, strength and toughness. While computer-aided design of polymer-based engineering products is demanded, obtaining reliable constitutive relations of deformation and fracture has been a challenge. In this study we performed coarse-grained molecular dynamics (CGMD) simulations of polycarbonate to acquire understanding of deformation and fracture mechanism at the molecular level and estimate yield stress under various loading modes. Inter-particle interactions for the CGMD was constructed based on all-atom MD using the COMPASS model, where molecular structures under strain were included. By tensile simulations of four types of loading, namely uniaxial stress, biaxial stress, uniaxial strain and isotropic stress, we calculated yield stress as a function of strain rate. We obtained two master curves of yield stress-strain rate relation; one for the former two loading types and the other for the latter two. The curves can be used for various temperatures by proper shift factors. We also found the effect of molar mass on stress-strain curves; i.e. the larger the molar mass is the larger stress can be attained after yielding, suggesting brittle-ductile transition with increasing molar mass.

Properties and application of SO(3) Majorana representation of spin: Equivalence with Jordan-Wigner transformation and exact Z2 gauge theories for spin models

We explore the properties of the SO(3) Majorana representation of spin. Based on its nonlocal nature, it is shown that there is an equivalence between the SO(3) Majorana representation and the Jordan-Wigner transformation in one and two dimensions. From the relation between the SO(3) Majorana representation and one-dimensional Jordan-Wigner transformation, we show that application of the SO(3) Majorana representation usually results in ${Z}_{2}$ gauge structure. Based on lattice Chern-Simons gauge theory, it is shown that the anticommuting link variables in the SO(3) Majorana representation make it equivalent to an operator form of compact ${\text{U(1)}}_{1}$ Chern-Simons Jordan-Wigner transformation in 2D. As examples of its application, we discuss two spin models, namely the quantum XY model on a honeycomb lattice and the ${90}^{\ensuremath{\circ}}$ compass model on a square lattice. It is shown that under the SO(3) Majorana representation both spin models can be exactly mapped into ${Z}_{2}$ gauge theory of spinons, with the standard form of ${Z}_{2}$ Gauss law constraint.

Signatures of low-energy fractionalized excitations in α−RuCl3 from field-dependent microwave absorption

Topologically ordered states of matter are generically characterized by excitations with quantum number fractionalization. A prime example is the spin liquid realized in Kitaev's honeycomb-lattice compass model where spin-flip excitations fractionalize into Majorana fermions and Ising gauge fluxes. While numerous compounds have been proposed to be proximate to such a spin-liquid phase, clear-cut evidence for fractionalized excitations is lacking. Here we employ microwave absorption measurements to study the low-energy excitations in $\alpha$-RuCl$_3$ over a wide range of frequencies, magnetic fields, and temperatures, covering in particular the vicinity of the field-driven quantum phase transition where long-range magnetic order disappears. In addition to conventional gapped magnon modes we find a highly unusual broad continuum characteristic of fractionalization which -- most remarkably -- extends to energies below the lowest sharp mode and to temperatures significantly higher than the ordering temperature, and develops a gap of a nontrivial origin in strong magnetic fields. Our results unravel the signatures of fractionalized excitations in $\alpha$-RuCl$_3$ and pave the way to a more complete understanding of the Kitaev spin liquid and its instabilities.

Exact Solutions and Degenerate Properties of Spin Chains with Reducible Hamiltonians

The Jordan–Wigner transformation plays an important role in spin models. However, the non-locality of the transformation implies that a periodic chain of N spins is not mapped to a periodic or an anti-periodic chain of lattice fermions. Since only the N − 1 bond is different, the effect is negligible for large systems, while it is significant for small systems. In this paper, it is interesting to find that a class of periodic spin chains can be exactly mapped to a periodic chain and an anti-periodic chain of lattice fermions without redundancy when the Jordan–Wigner transformation is implemented. For these systems, possible high degeneracy is found to appear in not only the ground state, but also the excitation states. Further, we take the one-dimensional compass model and a new XY-XY model ( σ x σ y − σ x σ y ) as examples to demonstrate our proposition. Except for the well-known one-dimensional compass model, we will see that in the XY-XY model, the degeneracy also grows exponentially with the number of sites.