Compass Model Research Articles

Causes and cures XIII: Global medicine approaches

Abstract The past several years have been a landmark moment for violence prevention, with renewed attention on the part of many international agencies, but especially the United Nations, with its adoption of the 2030 Agenda for Sustainable Development . The latter invites the world community to collaborate in an inclusive, long-ranging vision for the future, highlighting our interdependence and collective responsibility for humanity's future. A growing awareness that preventing violence does not just reduce death and disability but promotes creativity, economic growth, and general well-being is at the heart of this “movement”. An integration not only of the major disciplines but of various practical approaches is timely, and for this to occur, we require a broader overview of our existing societal structures. In this context, this fifteen article series modeled after a Global Health Studies course entitled, “Violence: Causes and Cures,” reviews the mechanisms that society has used in an attempt to stem violence. Following the article on public health, which has established that violence is preventable, this paper examines the approaches of global medicine, which begins with the local and human aspects of medical care. A model of compassion, altruism, respect, and encouragement is proposed for a person-centered, humanistic approach. Taking into account human suffering, principles of caregiving, cultural and religious sensitivity, and fostering of resilience and creativity is urgently needed in an increasingly globalizing world.

Detecting topological order with ribbon operators

We introduce a numerical method for identifying topological order in two-dimensional models based on one-dimensional bulk operators. The idea is to identify approximate symmetries supported on thin strips through the bulk that behave as string operators associated to an anyon model. We can express these ribbon operators in matrix product form and define a cost function that allows us to efficiently optimize over this ansatz class. We test this method on spin models with abelian topological order by finding ribbon operators for $\mathbb{Z}_d$ quantum double models with local fields and Ising-like terms. In addition, we identify ribbons in the abelian phase of Kitaev's honeycomb model which serve as the logical operators of the encoded qubit for the quantum error-correcting code. We further identify the topologically encoded qubit in the quantum compass model, and show that despite this qubit, the model does not support topological order. Finally, we discuss how the method supports generalizations for detecting nonabelian topological order.

An Alternative Narrative.

An Alternative Narrative.

Compass impurity model of Tb substitution inSr2IrO4

We show that upon Tb substitution the interaction between the magnetic moments on the impurity ${\mathrm{Tb}}^{4+}$ ion and its surrounding ${\mathrm{Ir}}^{4+}$ ions is described by a ``compass'' model, i.e., an Ising-like interaction favoring the magnetic moments across each bond to align along the bond direction. Such an interaction nucleates quenched magnetic vortices near the impurities and drives a reentrant transition out of the antiferromagnetic ordered phase at low temperatures, hence quickly suppressing the N\'eel temperature, consistent with the experiment [J. C. Wang et al., Phys. Rev. B 92, 214411 (2015)]. As a by-product, we propose that the compass model can be realized in ordered double perovskites composed of spin-orbital-coupled ${d}^{5}$ ions and half-closed-shell ${f}^{7}$ ions.

Energy dynamics in a generalized compass chain

We investigate the energy dynamics in a generalized compass chain under an external magnetic field. We show that the energy current operators act on three contiguous sites in the absence of the magnetic field, and they are incorporated with inhomogenous Dzyaloshinskii-Moriya interactions in the presence of the magnetic field. Under these complex interactions the Hamiltonian remains an exactly solvable spin model. We study the effects of the three-site interactions and the Dzyaloshinskii–Moriya interactions on the energy spectra and phase diagram. The results have revealed that the energy current of the pristine quantum compass model is conserved due to the associated intermediate symmetries, and for other general cases such a characteristic does not exist.

Fermionic Symmetry-Protected Topological Phase in a Two-Dimensional Hubbard Model.

We study the two-dimensional (2D) Hubbard model using exact diagonalization for spin-1/2 fermions on the triangular and honeycomb lattices decorated with a single hexagon per site. In certain parameter ranges, the Hubbard model maps to a quantum compass model on those lattices. On the triangular lattice, the compass model exhibits collinear stripe antiferromagnetism, implying d-density wave charge order in the original Hubbard model. On the honeycomb lattice, the compass model has a unique, quantum disordered ground state that transforms nontrivially under lattice reflection. The ground state of the Hubbard model on the decorated honeycomb lattice is thus a 2D fermionic symmetry-protected topological phase. This state-protected by time-reversal and reflection symmetries-cannot be connected adiabatically to a free-fermion topological phase.

Kondo Impurities in the Kitaev Spin Liquid: Numerical Renormalization Group Solution and Gauge-Flux-Driven Screening.

Kitaev's honeycomb-lattice compass model describes a spin liquid with emergent fractionalized excitations. Here, we study the physics of isolated magnetic impurities coupled to the Kitaev spin-liquid host. We reformulate this Kondo-type problem in terms of a many-state quantum impurity coupled to a multichannel bath of Majorana fermions and present the numerically exact solution using Wilson's numerical renormalization group technique. Quantum phase transitions occur as a function of Kondo coupling and locally applied field. At zero field, the impurity moment is partially screened only when it binds an emergent gauge flux, while otherwise it becomes free at low temperatures. We show how Majorana degrees of freedom determine the fixed-point properties, make contact with Kondo screening in pseudogap Fermi systems, and discuss effects away from the dilute limit.

Quantum phase transitions in a generalized compass chain with three-site interactions

We consider a class of one-dimensional compass models with XYZ$-$YZX-type of three-site exchange interaction in an external magnetic field. We present the exact solution derived by means of Jordan-Wigner transformation, and study the excitation gap, spin correlations, and establish the phase diagram. Besides the canted antiferromagnetic and polarized phases, the three-site interactions induce two distinct chiral phases, corresponding to gapless spinless-fermion systems having two or four Fermi points. We find that the $z$ component of scalar chirality operator can act as an order parameter for these chiral phases. We also find that the thermodynamic quantities including the Wilson ratio can characterize the liquid phases. Finally, a nontrivial magnetoelectric effect is explored, and we show that the polarization can be manipulated by the magnetic field in the absence of electric field.

One-dimensional frustrated plaquette compass model: Nematic phase and spontaneous multimerization

We introduce a one-dimensional (1D) pseudospin model on a ladder where the Ising interactions along the legs and along the rungs alternate between $X_{i}X_{i+1}$ and $Z_{i}Z_{i+1}$ for even/odd bond (rung). We include also the next nearest neighbor Ising interactions on plaquettes' diagonals that alternate in such a way that a model where only leg interactions are switched on is equivalent to the one when only the diagonal ones are present. Thus in the absence of rung interactions the model can interpolate between two 1D compass models. The model posses local symmetries which are the parities within each $2\times 2$ cell (plaquette) of the ladder. We find that for different values of the interaction it can realize ground states that differ by the patterns formed by these local parities. By exact diagonalization we derive detailed phase diagrams for small systems of $L=4$, 6 and 8 plaquettes, and use next $L=12$ to identify generic phases that appear in larger systems as well. Among them we find a nematic phase with macroscopic degeneracy when the leg and diagonal interactions are equal and the rung interactions are larger than a critical value. The nematic phase is similar to the one found in the two-dimensional compass model. For particular parameters the low-energy sector of the present plaquette model reduces to a 1D compass model with spins $S=1$ which suggests that it realizes peculiar crossovers within the class of compass models. Finally, we show that the model can realize phases with broken translation invariance which can be either dimerized, trimerized, \textit{etcetera}, or completely disordered and highly entangled in a~well identified window of the phase diagram.

Model for Parents Education to assist forming a Faith Identity of youth: Compassion Model

Model for Parents Education to assist forming a Faith Identity of youth: Compassion Model

Variational tensor network renormalization in imaginary time: Two-dimensional quantum compass model at finite temperature

Progress in describing thermodynamic phase transitions in quantum systems is obtained by noticing that the Gibbs operator $e^{-\beta H}$ for a two-dimensional (2D) lattice system with a Hamiltonian $H$ can be represented by a three-dimensional tensor network, the third dimension being the imaginary time (inverse temperature) $\beta$. Coarse-graining the network along $\beta$ results in a 2D projected entangled-pair operator (PEPO) with a finite bond dimension $D$. The coarse-graining is performed by a tree tensor network of isometries. The isometries are optimized variationally --- taking into account full tensor environment --- to maximize the accuracy of the PEPO. The algorithm is applied to the isotropic quantum compass model on an infinite square lattice near a symmetry-breaking phase transition at finite temperature. From the linear susceptibility in the symmetric phase and the order parameter in the symmetry-broken phase the critical temperature is estimated at ${\cal T}_c=0.0606(4)J$, where $J$ is the isotropic coupling constant between $S=1/2$ pseudospins.

A continuum of compass spin models on the honeycomb lattice

Quantum spin models with spatially dependent interactions, known as compass models, play an important role in the study of frustrated quantum magnetism. One example is the Kitaev model on the honeycomb lattice with spin-liquid (SL) ground states and anyonic excitations. Another example is the geometrically frustrated quantum 120° model on the same lattice whose ground state has not been unambiguously established. To generalize the Kitaev model beyond the exactly solvable limit and connect it with other compass models, we propose a new model, dubbed ‘the tripod model’, which contains a continuum of compass-type models. It smoothly interpolates the Ising model, the Kitaev model, and the quantum 120° model by tuning a single parameter , the angle between the three legs of a tripod in the spin space. Hence it not only unifies three paradigmatic spin models, but also enables the study of their quantum phase transitions. We obtain the phase diagram of the tripod model numerically by tensor networks in the thermodynamic limit. We show that the ground state of the quantum 120° model has long-range dimer order. Moreover, we find an extended spin-disordered (SL) phase between the dimer phase and an antiferromagnetic phase. The unification and solution of a continuum of frustrated spin models as outline here may be useful to exploring new domains of other quantum spin or orbital models.

Quench dynamics and ground state fidelity of the one-dimensional extended quantum compass model in a transverse field

We study the ground state fidelity, fidelity susceptibility, and quench dynamics of the extended quantum compass model in a transverse field. This model reveals a rich phase diagram which includes several critical surfaces depending on exchange couplings. We present a characterization of quantum phase transitions in terms of the ground state fidelity between two ground states obtained for two different values of external parameters. We also derive scaling relations describing the singular behavior of the fidelity susceptibility in the quantum critical surfaces. Moreover, we study the time evolution of the system after a critical quantum quench using the Loschmidt echo (LE). We find that the revival times of LE are given by , where N is the size of the system and vmax is the maximum of the lower bound group velocity of quasi-particles. Although the fidelity susceptibility shows the same exponent in all critical surfaces, the structure of the revivals after critical quantum quenches displays two different regimes reflecting different equilibration dynamics.

Topological phases of shaken quantum Ising lattices

The quantum compass model consists of a two-dimensional square spin lattice where the orientation of the spin–spin interactions depends on the spatial direction of the bonds. It has remarkable symmetry properties and the ground state shows topological degeneracy. The implementation of the quantum compass model in quantum simulation setups like ultracold atoms and trapped ions is far from trivial, since spin interactions in those systems typically are independent of the spatial direction. Ising spin interactions, on the contrary, can be induced and controlled in atomic setups with state-of-the art experimental techniques. In this work, we show how the quantum compass model on a rectangular lattice can be simulated by the use of the photon-assisted tunneling induced by periodic drivings on a quantum Ising spin model. We describe a procedure to adiabatically prepare one of the doubly degenerate ground states of this model by adiabatically ramping down a transverse magnetic field, with surprising differences depending on the parity of the lattice size. Exact diagonalizations confirm the validity of this approach for small lattices. Specific implementations of this scheme are presented with ultracold atoms in optical lattices in the Mott insulator regime, as well as with Rydberg atoms.

Moloka‘i Kannon

Moloka‘i Kannon John Clark (bio) In 2004, while researching a book I wrote called Guardian of the Sea: Jizo in Hawai‘i, I interviewed Rev. Shugen Komagata several times at the Wahiawa Rusenji Soto Mission. During one of our talks he told me his grandfather, Bishop Zenkyo Komagata, then the head of the Soto Mission of Hawai‘i, had established Guzeiji Soto Mission of Moloka‘i in 1928. Rev. Komagata also mentioned that the Guzeiji temple had opened a satellite chapel at the leprosy settlement in Kalaupapa with a special statue called the Moloka‘i Kannon. In 2015, while I was researching a book on Kalaupapa, I visited Rev. Komagata, now Bishop Komagata, at his office in the Soto Mission of Hawai‘i headquarters on Nu‘uanu Avenue. When I asked him to tell me about the Moloka‘i Kannon, he provided the information that follows. When the first Pan-Pacific Congress of the Young Men’s Buddhist Association was held in Honolulu during the summer of 1930, one of the delegates from Japan was Rev. Chiyu Misawa. A representative of Tsurumi Girls High School in Yokohama, he boarded for three weeks at the Soto Mission of Hawai‘i in Honolulu. During his stay in Hawai‘i Rev. Misawa visited the leprosy settlement at Kalaupapa to pay [End Page 141] his respects to the memory of Father Damien, who was well known in Japan. While he was there, he met Japanese patients who asked him to send them a statue of Kannon from Japan to help fulfill their religious needs. Kannon is a Buddhist deity, a bosatsu, or bodhisattva, who, as a model of love and compassion, is special to those who are suffering. Click for larger view View full resolution On November 9, 2010, Bishop Shugen Komagata and his wife Faye visited Tsurumi High School in Yokohama, Japan, the home of the Moloka‘i Kannon. Courtesy of Bishop Shugen Komagata. When Rev. Misawa returned to Japan, he conducted a successful fund raising campaign at Tsurumi Girls High School and used the donations to commission a statue of Kannon from Zuiun Yamamoto, a prominent Buddhist sculptor. When Yamamoto finished the statue, Dr. Daijo Ohinata delivered it to Hawai‘i. Earlier on April 25, 1928, the Soto Mission of Hawai‘i had opened a temple in Kaunakakai, the Guzeiji Soto Mission of Moloka‘i, with a full-time minister. The minister and members of his congregation delivered the statue of Kannon to Kalaupapa and installed it in a building that served as a satellite [End Page 142] chapel. It is now known as Buddhist Hall. During the years that followed the enshrinement of the statue, successive Buddhist ministers and visiting ministers continued to provide services to the patients. In the absence of a permanent minister Kalaupapa staff member Sachihito Kamemoto and his wife took care of the chapel and the statue, while the Guzeiji temple in Kaunakakai continued an annual tradition of presenting New Year’s mochi to the Japanese patients. When the need for Buddhist services at Kalaupapa finally ended, the statue was returned to Guzeiji Soto Mission of Moloka‘i, where it remained for 15 years. In October 1996, it was moved to the Soto Mission of Hawai‘i in Honolulu. Due to the statue’s extraordinary value, which was estimated then to be $100,000, the headquarters decided to return it to the original donor, which is Tsurumi High School today. It was sent back to the school in March 1997, where it was enshrined in their auditorium. It is still known as the Moloka‘i Kannon. [End Page 143] John Clark John Clark is co-editor of The Hawaiian Journal of History. He is also the author of a series of books on Hawai‘i’s beaches and shoreline place names published by the University of Hawaii Press. Copyright © 2016 The Hawaiian Journal of History

Compassion in Health Care: An Empirical Model

ContextCompassion is frequently referenced as a hallmark of quality care by patients, health care providers, health care administrators, and policy makers. Despite its putative centrality, including its institution in recent health care reform, an empirical understanding based on the perspectives of patients, the recipients of compassion, is lacking—making compassion one of the most referenced yet poorly understood elements of quality care. ObjectivesThe objective of this study was to investigate palliative cancer patients' understanding and experiences of compassion to provide a critical perspective on the nature and importance of compassion. MethodsThis grounded theory study used semi-structured interviews to investigate how patients understand and experience compassion in clinical care. Using convenience and theoretical sampling, 53 advanced cancer inpatients were recruited over a seven-month period from a specialized palliative care unit and hospital-wide palliative care service within a Canadian urban setting. Data were analyzed by four members of the research team through the three stages of Straussian grounded theory. ResultsQualitative analysis yielded seven categories, each containing distinct themes and subthemes. Together, they constitute components of the compassion model—the first empirically based clinical model of compassion. The model defines compassion as a virtuous response that seeks to address the suffering and needs of a person through relational understanding and action. ConclusionThe components of the compassion model provide insight into how patients understand and experience compassion, providing the necessary empirical foundation to develop future research, measures, training, and clinical care based on this vital feature of quality care.

Dances of connection: Neuroaffective development in clinical work with attachment

This article offers a brief outline of key principles of developmental attachment theory, followed by an overview of infant interaction development and the neuroaffective compass model. This model is then used to consider two cases. It is proposed that assessing the client's developmental level of neuroaffective maturity is useful in choosing the intervention level for inviting now-moments and cycles of attunement central to building the interpersonal trust and autonomy inherent in secure attachment.

Geometric phase and the influence of the Dzyaloshinski–Moriya interaction in the one-dimensional quantum compass model

Geometric phase and quantum phase transition (QPT) of the one-dimensional (1D) quantum compass model with the Dzyaloshinski–Moriya (DM) interaction are investigated, and the effect of the DM interaction to the properties of geometric phase and QPTs of the model are discussed in this paper. Our study is an extension of the relation between the geometric phase and QPTs in the 1D spin systems.

Physical states and finite-size effects in Kitaev's honeycomb model: Bond disorder, spin excitations, and NMR line shape

Kitaev's compass model on the honeycomb lattice realizes a spin liquid whose emergent excitations are dispersive Majorana fermions and static ${\mathrm{Z}}_{2}$ gauge fluxes. We discuss the proper selection of physical states for finite-size simulations in the Majorana representation, based on a recent paper by F. L. Pedrocchi, S. Chesi, and D. Loss [Phys. Rev. B 84, 165414 (2011)]. Certain physical observables acquire large finite-size effects, in particular if the ground state is not fermion-free, which we prove to generally apply to the system in the gapless phase and with periodic boundary conditions. To illustrate our findings, we compute the static and dynamic spin susceptibilities for finite-size systems. Specifically, we consider random-bond disorder (which preserves the solubility of the model), calculate the distribution of local flux gaps, and extract the NMR line shape. We also predict a transition to a random-flux state with increasing disorder.

Designing frustrated quantum magnets with laser-dressed Rydberg atoms.

We show how a broad class of lattice spin-1/2 models with angular- and distance-dependent couplings can be realized with cold alkali atoms stored in optical or magnetic trap arrays. The effective spin-1/2 is represented by a pair of atomic ground states, and spin-spin interactions are obtained by admixing van der Waals interactions between fine-structure split Rydberg states with laser light. The strengths of the diagonal spin interactions as well as the "flip-flop," and "flip-flip" and "flop-flop" interactions can be tuned by exploiting quantum interference, thus realizing different spin symmetries. The resulting energy scales of interactions compare well with typical temperatures and decoherence time scales, making the exploration of exotic forms of quantum magnetism, including emergent gauge theories and compass models, accessible within state-of-the-art experiments.