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Recently, Yb-based triangular-lattice antiferromagnets have garnered significant interest as possible quantum spin-liquid candidates. One example is YbMgGaO4, which showed many promising spin-liquid features, but also possesses a high degree of disorder owing to site-mixing between the non-magnetic cations. To further elucidate the role of chemical disorder and to explore the phase diagram of these materials in applied field, we present neutron scattering and sensitive magnetometry measurements of the closely related compound, YbZnGaO4. Our results suggest a difference in magnetic anisotropy between the two compounds, and we use key observations of the magnetic phase crossover to motivate an exploration of the field- and exchange parameter-dependent phase diagram, providing an expanded view of the available magnetic states in applied field. This enriched map of the phase space serves as a basis to restrict the values of parameters describing the magnetic Hamiltonian with broad application to recently discovered related materials.

The liquidus temperatures and electrical conductivity of the (CsCl-NaCl-KCl)eut-ReCl4 melts, feasible for Re production, were studied by thermal analysis and impedance spectroscopy. A part of the quasi-binary phase diagram for [CsCl-KCl-NaCl]eut-ReCl4 in the ReCl4 concertation range of 0–7.61 mol % was compiled on the basis of obtained thermal analysis data. ReCl4 is most likely to dissolve in molten eutectic CsCl-KCl-NaCl with the formation of the ReCl62– ions. Compound Cs2ReCl6 was identified in the frozen samples by XRD analysis. The electrical conductivity of molten mixture (CsCl-KCl-NaCl)eut.-ReCl4, measured in the cell with the coaxial glassy carbon electrodes, was found to decrease with increasing ReCl4 content.

Novel effects induced by nonmagnetic impurities in frustrated magnets and quantum spin liquid represent a highly nontrivial and interesting problem. A theoretical proposal of extended modulated spin structures induced by doping of such magnets, distinct from the well-known skyrmions has attracted significant interest. Here, we demonstrate that nonmagnetic impurities can produce such extended spin structures in h-YMnO3, a triangular antiferromagnet with noncollinear magnetic order. Using inelastic neutron scattering (INS), we measured the full dynamical structure factor in Al-doped h-YMnO3 and confirmed the presence of magnon damping with a clear momentum dependence. Our theoretical calculations can reproduce the key features of the INS data, supporting the formation of the proposed spin textures. As such, our study provides the first experimental confirmation of the impurity-induced spin textures. It offers new insights and understanding of the impurity effects in a broad class of noncollinear magnetic systems., Comment: 18 pages, 4 figures and supplementary Information. Accepted for publication in Nature Communications

CeCd$_3$As$_3$ is a rare-earth triangular-lattice antiferromagnet with large inter-layer separation. Our field-dependent heat capacity measurements at dilution fridge temperatures allow us to trace the field-evolution of the spin-excitation gaps throughout the antiferromagnetic and paramagnetic regions. The distinct gap evolution places strong constraints on the microscopic pseudo-spin model, which, in return, yields a close {\it quantitative} description of the gap behavior. This analysis provides crucial insights into the nature of the magnetic state of CeCd$_3$As$_3$, with a certainty regarding its stripe order and low-energy model parameters that sets a compelling paradigm for exploring and understanding the rapidly growing family of the rare-earth-based triangular-lattice systems., Main Text: 6 pages, 3 figures SM: 19 pages, 23 figures Some clarifications are made relative to previous version

We calculate magnon dispersions and damping in the Kitaev-Heisenberg model with an off-diagonal exchange $\mathrm{\ensuremath{\Gamma}}$ and isotropic third-nearest-neighbor interact ion ${J}_{3}$ on a honeycomb lattice. This model is relevant to a description of the magnetic properties of iridium oxides $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Li}}_{2}{\mathrm{IrO}}_{3}$ and ${\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}$, and Ru-based materials such as $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$. We use an unconventional parametrization of the spin-wave expansion, in which each Holstein-Primakoff boson is represented by two conjugate Hermitian operators. This approach gives us an advantage over the conventional one in identifying parameter regimes where calculations can be performed analytically. Focusing on the parameter regime with the zigzag spin pattern in the ground state that is consistent with experiments, we demonstrate that one such region is $\mathrm{\ensuremath{\Gamma}}=Kg0$, where $K$ is the Kitaev coupling. Within our approach, we are able to obtain explicit analytical expressions for magnon energies and eigenstates and go beyond the standard linear spin-wave theory approximation by calculating magnon damping and demonstrating its role in the dynamical structure factor. We show that the magnon damping effects in both Born and self-consistent approximations are very significant, underscoring the importance of nonlinear magnon coupling in interpreting broad features in the neutron-scattering spectra.

We present an extensive overview of the phase diagram, spin-wave excitations, and finite-temperature transitions of the anisotropic-exchange magnets on an ideal nearest-neighbor triangular lattice. We investigate transitions between five principal classical phases of the corresponding model: ferromagnetic, N\'{e}el, its dual, and the two stripe phases. Transitions are identified by the spin-wave instabilities and by the Luttinger-Tisza approach. Some of the transitions are direct and others occur via intermediate phases with more complicated forms of ordering. In a portion of the N\'{e}el phase, we find spin-wave instabilities to a long-range spiral-like state. In the stripe phases, quantum fluctuations are mostly negligible, leaving the ordered moment nearly saturated even for the $S=1/2$ case. However, for a two-dimensional surface of the full 3D parameter space, the spin-wave spectrum in one of the stripe phases exhibits an enigmatic accidental degeneracy manifested by pseudo-Goldstone modes. As a result, despite the nearly classical ground state, the ordering transition temperature in a wide region of the phase diagram is significantly suppressed from the mean-field expectation. We identify this accidental degeneracy as due to an exact correspondence to an extended Kitaev-Heisenberg model with emergent symmetries that naturally lead to the pseudo-Goldstone modes. There are previously studied dualities within the Kitaev-Heisenberg model on the triangular lattice that are exposed here in a wider parameter space. One important implication of this correspondence for the $S=1/2$ case is the existence of a region of the spin-liquid phase that is dual to the spin-liquid phase discovered recently by us. We complement our studies by the density-matrix renormalization group of the $S=1/2$ model to confirm some of the duality relations and to verify the existence of the dual spin-liquid phase., Comment: 26 pages, 23 figures. Text of immense pedagogical power. Version asymptotically close to PRX + corrections from Erratum

Spin systems with frustrated anisotropic interactions are of significant interest due to possible exotic ground states. We have explored their phase diagram on a nearest-neighbor triangular lattice using the density-matrix renormalization group and mapped out the topography of the region that can harbor a spin liquid. We find that this spin-liquid phase is continuously connected to a previously discovered spin-liquid phase of the isotropic $J_1\!-\!J_2$ model. The two limits show nearly identical spin correlations, making the case that their respective spin liquids are isomorphic to each other., Comment: Accepted to PRL; 5 p., 11+ p. supplemental; main text is longer than the accepted version

The description of quantized collective excitations stands as a landmark in the quantum theory of condensed matter. A prominent example occurs in conventional magnets, which support bosonic magnons - quantized harmonic fluctuations of the ordered spins. In striking contrast is the recent discovery that strongly spin-orbital coupled magnets, such as $\alpha$-RuCl$_3$, may display a broad excitation continuum inconsistent with conventional magnons. Due to incomplete knowledge of the underlying interactions unraveling the nature of this continuum remains challenging. The most discussed explanation refers to a coherent continuum of fractional excitations analogous to the celebrated Kitaev spin liquid. Here we present a more general scenario. We propose that the observed continuum represents incoherent excitations originating from strong magnetic anharmoniticity that naturally occurs in such materials. This scenario fully explains the observed inelastic magnetic response of $\alpha$-RuCl$_3$ and reveals the presence of nontrivial excitations in such materials extending well beyond the Kitaev state., Comment: Final version; supplemental information included

The notion of a quasiparticle, such as a phonon, a roton, or a magnon, is used in modern condensed matter physics to describe an elementary collective excitation. The intrinsic zero-temperature magnon damping in quantum spin systems can be driven by the interaction of the one-magnon states and multi-magnon continuum. However, detailed experimental studies on this quantum many-body effect induced by an applied magnetic field are rare. Here we present a high-resolution neutron scattering study in high fields on an S=1/2 antiferromagnet C9H18N2CuBr4. Compared with the non-interacting linear spin-wave theory, our results demonstrate a variety of phenomena including field-induced renormalization of one-magnon dispersion, spontaneous magnon decay observed via intrinsic linewidth broadening, unusual non-Lorentzian two-peak structure in the excitation spectra, and a dramatic shift of spectral weight from one-magnon state to the two-magnon continuum., 8 pages, 6 figures, some typos were corrected in the revised version

We suggest that a randomization of the pseudo-dipolar interaction in the spin-orbit-generated low-energy Hamiltonian of YbMgGaO$_4$ due to an inhomogeneous charge environment from a natural mixing of Mg$^{2+}$ and Ga$^{3+}$ can give rise to orientational spin disorder and mimic a spin-liquid-like state. In the absence of such quenched disorder, $1/S$ and density matrix renormalization group calculations both show robust ordered states for the physically relevant phases of the model. Our scenario is consistent with the available experimental data and further experiments are proposed to support it., Comment: 5+ main text, 7+ supplemental, text asymptotically close to PRL

We demonstrate that interactions can substantially undermine the free-particle description of magnons in ferromagnets on geometrically frustrated lattices. The anharmonic coupling, facilitated by the Dzyaloshinskii-Moriya interaction, and a highly-degenerate two-magnon continuum yield a strong, non-perturbative damping of the high-energy magnon modes. We provide a detailed account of the effect for the $S=1/2$ ferromagnet on the kagom\'e lattice and propose further experiments., Comment: 4.5 p + 4 figs main, 8 p + 16 figs supplemental, typos corrected

Magnons and phonons are fundamental quasiparticles in a solid and can be coupled together to form a hybrid quasi-particle. However, detailed experimental studies on the underlying Hamiltonian of this particle are rare for actual materials. Moreover, the anharmonicity of such magnetoelastic excitations remains largely unexplored, although it is essential for a proper understanding of their diverse thermodynamic behaviour and intrinsic zero-temperature decay. Here we show that in non-collinear antiferromagnets, a strong magnon–phonon coupling can significantly enhance the anharmonicity, resulting in the creation of magnetoelastic excitations and their spontaneous decay. By measuring the spin waves over the full Brillouin zone and carrying out anharmonic spin wave calculations using a Hamiltonian with an explicit magnon–phonon coupling, we have identified a hybrid magnetoelastic mode in (Y,Lu)MnO3 and quantified its decay rate and the exchange-striction coupling term required to produce it., The properties of magnetic, crystalline solids can be described in terms of quantum particles of spin-wave and lattice-vibration energy, known as magnons and phonons respectively. Here, the authors show that strong magnon-phonon coupling in a noncollinear antiferromagnet can create magnetoelastic excitations.

We investigate field-induced transformations in the dynamical response of the $XXZ$ model on the triangular lattice that are associated with the anharmonic magnon coupling and decay phenomena. A set of concrete theoretical predictions is made for a close physical realization of the spin-1/2 $XXZ$ model, Ba$_3$CoSb$_2$O$_9$. We demonstrate that dramatic modifications in magnon spectrum must occur in low out-of-plane fields that are easily achievable for this material. The hallmark of the effect is a coexistence of the clearly distinct well-defined magnon excitations with significantly broadened ones in different regions of the ${\bf k}-\omega$ space. The field-induced decays are generic for this class of models and become more prominent at larger anisotropies and in higher fields., Comment: 5 p. + 4 figs main, 6+ p. + 8 figs Supp, typos corrected, Sqw replotted, few changes

Two ubiquitous features of frustrated spin systems stand out: massive degeneracy of their ground states and flat, or dispersionless, excitation branches. In real materials, the former is frequently lifted by secondary interactions or quantum fluctuations, in favor of an ordered or spin-liquid state, but the latter often survive. We demonstrate that flat modes may precipitate remarkably strong quantum effects even in the systems that are otherwise written off as almost entirely classical. The resultant spectral features should be reminiscent of the quasiparticle breakdown in quantum systems, only here the effect is strongly amplified by the flatness of spin-excitation branches, leading to the damping that is not vanishingly small even at $S\!\gg\!1$. We provide a theoretical analysis of excitation spectrum of the $S=5/2$ iron-jarosite to illustrate our findings and to suggest further studies of this and other frustrated spin systems., Comment: 7 pages, accepted to PRB

We systematically investigate the ground-state and the spectral properties of antiferromagnets on a kagom\'{e} lattice with several common types of the planar anisotropy: $XXZ$, single-ion, and out-of-plane Dzyaloshinskii-Moriya. Our main focus is on the role of nonlinear, anharmonic terms, which are responsible for the quantum order-by-disorder effect and for the corresponding selection of the ground-state spin structure in many of these models. The $XXZ$ and the single-ion anisotropy models exhibit a quantum phase transition between the ${\bf q}\!=\!0$ and the $\sqrt{3}\times\!\sqrt{3}$ states as a function of the anisotropy parameter, offering a rare example of the quantum order-by-disorder fluctuations favoring a ground state which is different from the one selected by thermal fluctuations. The nonlinear terms are also shown to be crucial for a very strong near-resonant decay phenomenon leading to the quasiparticle breakdown in the kagom\'{e}-lattice antiferromagnets whose spectra are featuring flat or weakly dispersive modes. The effect is shown to persist even in the limit of large spin values and should be common to other frustrated magnets with flat branches of excitations. Model calculations of the spectrum of the $S=5/2$ Fe-jarosite with Dzyaloshinskii-Moriya anisotropy provide a convincing and detailed characterization of the proposed scenario., Comment: 17 pages, 13 figures, published version. Recipient of the PRB beauty award (Editors' Suggestion)

Motivated by the recent heat transport experiments in 2D antiferromagnets, such as La$_2$CuO$_4$, where the exchange coupling $J$ is larger than the Debye energy $\Theta_{\rm D}$, we discuss different types of relaxation processes for magnon heat current with a particular focus on coupling to 3D phonons. We study thermal conductivity by these in-plane magnetic excitations using two distinct techniques, Boltzmann formalism within the relaxation-time approximation and memory-function approach. Within these approaches, a close consideration is given to the scattering of magnons by both acoustic and optical branches of phonons. A remarkable accord between the two methods with regards to the asymptotic behavior of the effective relaxation rates is demonstrated. Additional scattering mechanisms, due to grain boundaries, impurities, and finite correlation length in the paramagnetic phase, are discussed and included in the calculations of the thermal conductivity $\kappa(T)$. Again, we demonstrate a close similarity of the results from the two techniques of calculating $\kappa(T)$. Our complementary approach strongly suggests that scattering from optical or zone-boundary phonons is important for magnon heat current relaxation in a high temperature window of $\Theta_D\lesssim T \ll J$., Comment: 21+ pages, 16 figures

The heat transport in a system of $S=1/2$ large-$J$ Heisenberg spin chains, describing closely Sr$_2$CuO$_3$ and SrCuO$_2$ cuprates, is studied theoretically at $T\ll J$ by considering interactions of the bosonized spin excitations with optical phonons and defects. Treating rigorously the multi-boson processes, we derive a microscopic spin-phonon scattering rate that adheres to an intuitive picture of phonons acting as thermally populated defects for the fast spin excitations. The mean-free path of the latter exhibits a distinctive $T$-dependence reflecting a critical nature of spin chains and gives a close description of experiments. By the naturalness criterion of realistically small spin-phonon interaction, our approach stands out from previous considerations that require large coupling constants to explain the data and thus imply a spin-Peierls transition, absent in real materials., Comment: 5+ pages main text, 4+ pages supplemental, 4+2 figures, adiabatic approximation to the published version

We present a comprehensive $1/S$ study of the field-induced dynamical properties of the nearest-neighbor $XXZ$ antiferromagnet on a honeycomb lattice using the formalism of the nonlinear spin-wave theory developed for this model. The external magnetic field controls spin frustration in the system and induces non-collinearity of the spin structure, which is essential for the two-magnon decay processes. Our results include an intriguing field-evolution of the regions of the Brillouin zone wherein decays of spin excitations are prominent, a detailed classification of the decay channels involving magnons from both excitation branches, and a thorough analysis of the singularities in the magnon spectra due to coupling to the two magnon continuum, all of which are illustrated for several field and anisotropy values. We highlight a number of features related to either the non-Bravais nature of the lattice, or the existence of the Dirac-like points in the spectrum. In addition, the asymptotic behavior of the decay rates near high-symmetry points is analyzed in detail. The inelastic neutron-scattering spin-spin structure factor is obtained in the leading $1/S$ order and is shown to exhibit qualitatively distinct fingerprints of the decay-induced magnon dynamics such as quasiparticle peaks broadened by decays and strong spectral weight redistribution., Comment: 19 pages, 17 figures

Selection of the ground state of the kagom\'e-lattice $XXZ$ antiferromagnet by quantum fluctuations is investigated by combining non-linear spin-wave and real-space perturbation theories. The two methods unanimously favor ${\bf q}=0$ over $\sqrt{3}\times\sqrt{3}$ magnetic order in a wide range of the anisotropy parameter $0\leq \Delta\leq 0.72$. Both approaches are also in an accord on the magnitude of the quantum order-by-disorder effect generated by topologically non-trivial, loop-like spin-flip processes. A tentative $S-\Delta$ phase diagram of the model is proposed., Comment: 5 pages, 4 figures + 6.2 pages, 4 figures supplemental, minor changes, accepted version

The t-J{sub z} model is the strongly anisotropic limit of the t-J model which captures some general properties of doped antiferromagnets (AF{close_quote}s). The absence of spin fluctuations simplifies the analytical treatment of hole motion in an AF background, and allows us to calculate single- and two-hole spectra with a high accuracy using a regular diagram technique combined with a real-space approach. At the same time, numerical studies of this model via exact diagonalization on small clusters show negligible finite-size effects for a number of quantities, thus allowing a direct comparison between analytical and numerical results. Both approaches demonstrate that the holes have a tendency to pair in {ital p}- and {ital d}-wave channels at realistic values of t/J. Interactions leading to pairing and effects selecting {ital p} and {ital d} waves are thoroughly investigated. The role of transverse spin fluctuations is considered using perturbation theory. Based on the results of the present study, we discuss the pairing problem in the realistic t-J-like model. Possible implications for preformed pairs formation and phase separation are drawn. {copyright} {ital 1999} {ital The American Physical Society}

We predict that spin-waves in an ordered quantum antiferromagnet (AFM) in a strong magnetic field become unstable with respect to spontaneous two-magnon decays. At zero temperature, the instability occurs between the threshold field $H^*$ and the saturation field $H_c$. As an example, we investigate the high-field dynamics of a Heisenberg antiferromagnet on a square lattice and show that the single-magnon branch of the spectrum disappears in the most part of the Brillouin zone., RevTeX, 4 pages, 3 figures, accepted to PRL

We report on a detailed examination of numerical results and analytical calculations devoted to a study of two holes doped into a two-dimensional, square lattice described by the t-J model. Our exact diagonalization numerical results represent the first solution of the exact ground state of 2 holes in a 32-site lattice. Using this wave function, we have calculated several important correlation functions, notably the electron momentum distribution function and the hole-hole spatial correlation function. Further, by studying similar quantities on smaller lattices, we have managed to perform a finite-size scaling analysis. We have augmented this work by endeavouring to compare these results to the predictions of analytical work for two holes moving in an infinite lattice. This analysis relies on the canonical transformation approach formulated recently for the t-J model. From this comparison we find excellent correspondence between our numerical data and our analytical calculations. We believe that this agreement is an important step helping to justify the quasiparticle Hamiltonian, and in particular, the quasiparticle interactions, that result from the canonical transformation approach. Also, the analytical work allows us to critique the finite-size scaling ansatzes used in our analysis of the numerical data. One important feature that we can infer from this successful comparison involves the role of higher harmonics in the two-particle, d-wave symmetry bound state -- the conventional (\cos(k_x) - \cos(k_y)) term is only one of many important contributions to the d-wave symmetry pair wave function.

The S=1/2 spin chain material SrCuO2 doped with 1% S=1 Ni-impurities is studied by inelastic neutron scattering. At low temperatures, the spectrum shows a pseudogap \Delta ~ 8 meV, absent in the parent compound, and not related to any structural phase transition. The pseudogap is shown to be a generic feature of quantum spin chains with dilute defects. A simple model based on this idea quantitatively accounts for the exprimental data measured in the temperature range 2-300 K, and allows to represent the momentum-integrated dynamic structure factor in a universal scaling form., Comment: 5 pages, 3 figures

We demonstrate that point-like defects in non-collinear magnets give rise to a highly dispersive structure in the magnon scattering, violating a standard paradigm of its momentum independence. For a single impurity spin coupled to a prototypical non-collinear antiferromagnet we find that the resolvent is dominated by a distinct dispersive structure with its momentum-dependence set by the magnon dispersion and shifted by the ordering vector. This feature is a consequence of umklapp scattering off the impurity-induced spin texture, which arises due to the non-collinear ground state of the host system. Detailed results for the staggered and uniform magnetization of this texture as well as the T-matrix from numerical linear spin-wave theory are presented., 5+5 pages, 4+5 figs

High-resolution neutron resonance spin-echo measurements of superfluid 4He show that the roton energy does not have the same temperature dependence as the inverse lifetime. Diagrammatic analysis attributes this to the interaction of rotons with thermally excited phonons via both four- and three-particle processes, the latter being allowed by the broken gauge symmetry of the Bose condensate. The distinct temperature dependence of the roton energy at low temperatures suggests that the net roton-phonon interaction is repulsive., 5 pages, accepted version

Using the example of Zn-doped La2CuO4, we demonstrate that a spinless impurity doped into a non-frustrated antiferromagnet can induce substantial frustrating interactions among the spins surrounding it. This counterintuitive result is the key to resolving discrepancies between experimental data and earlier theories. Analytic and quantum Monte Carlo studies of the impurity-induced frustration are in a close accord with each other and experiments. The mechanism proposed here should be common to other correlated oxides as well., Comment: 4 pages, updated figures, accepted version

We study the binding of a holon and a spinon in the one-dimensional anisotropic t-J model using a Bethe-Salpeter equation approach, exact diagonalization, and density matrix renormalization group methods on chains of up to 128 sites. We find that holon-spinon binding changes dramatically as a function of anisotropy parameter \alpha=J_\perp/J_z: it evolves from an exactly deducible impurity-like result in the Ising limit to an exponentially shallow bound state near the isotropic case. A remarkable agreement between the theory and numerical results suggests that such a change is controlled by the corresponding evolution of the spinon energy spectrum., Comment: 4 pages, 5 figures, published version

Using examples of the square- and triangular-lattice Heisenberg models we demonstrate that the density matrix renormalization group method (DMRG) can be effectively used to study magnetic ordering in two-dimensional lattice spin models. We show that local quantities in DMRG calculations, such as the on-site magnetization M, should be extrapolated with the truncation error, not with its square root, as previously assumed. We also introduce convenient sequences of clusters, using cylindrical boundary conditions and pinning magnetic fields, which provide for rapidly converging finite-size scaling. This scaling behavior on our clusters is clarified using finite-size analysis of the effective sigma-model and finite-size spin-wave theory. The resulting greatly improved extrapolations allow us to determine the thermodynamic limit of M for the square lattice with an error comparable to quantum Monte Carlo. For the triangular lattice, we verify the existence of three-sublattice magnetic order, and estimate the order parameter to be M = 0.205(15)., 4 pages, 5 figures, typo fixed, reference added

We consider a generalization of the one-dimensional t-J model with anisotropic spin-spin interactions. We show that the anisotropy leads to an effective attractive interaction between the spinon and holon excitations, resulting in a localized bound state. Detailed quantitative analytic predictions for the dependence of the binding energy on the anisotropy are presented, and verified by precise numerical simulations. The binding energy is found to interpolate smoothly between a finite value in the t-Jz limit and zero in the isotropic limit, going to zero exponentially in the vicinity of the latter. We identify changes in spinon dispersion as the primary factor for this non-trivial behavior., Comment: 12 pages, 13 figures, long story. The short story is cond-mat/0702213. Published version

Exact diagonalization numerical results are presented for a 32-site square cluster, with two holes propagating in an antiferromagnetic background described by the t-J model. We characterize the wave function of the lowest energy bound state found in this calculation, which has d_{x^2-y^2} symmetry. Analytical work is presented, based on a Lang-Firsov-type canonical transformation derived quasiparticle Hamiltonian, that accurately agrees with numerically determined values for the electron momentum distribution function and the pair correlation function. We interpret this agreement as strong support for the validity of this description of the hole quasiparticles., Comment: 3 pages, REVTeX, to appear in the proceedings of the Fifth International Conference on Spectroscopies in Novel Superconductors, September 14-18, 1997, Cape Cod, Massachusetts

Three well-known perturbative approaches to deriving low-energy effective theories, the degenerate Brillouin-Wigner perturbation theory (projection method), the canonical transformation, and the resolvent methods, are compared. We use the Hubbard model as an example to show how, to fourth order in hopping $t$, all methods lead to the same effective theory, namely the $t\text{\ensuremath{-}}J$ model with ring exchange and various correlated hoppings. We emphasize subtle technical difficulties that make such a derivation less trivial to carry out for orders higher than second. We also show that in higher orders, different approaches can lead to seemingly different forms for the low-energy Hamiltonian. All of these forms are equivalent since they are connected by an additional unitary transformation whose generator is given explicitly. The importance of transforming the operators is emphasized and the equivalence of their transformed structure within the different approaches is also demonstrated.

We study the effect of spin anisotropies on a frustrated quantum antiferromagnet using the ${J}_{1}\mathrm{\text{\ensuremath{-}}}{J}_{2}^{XXZ}$ model on the square lattice. The $T=0$ and finite-$T$ phase diagrams of this model are obtained utilizing spin-wave theory, exact diagonalization, and quantum Monte Carlo calculations. We find that anisotropic frustration tends to stabilize $XY$- and Ising-like ordered phases, while the disordered spin-liquid phase is restricted to a small region of the phase diagram. The ordered phases are separated by first-order transitions and exhibit a nontrivial reentrance phenomenon.

We study competition between different phases in a strongly correlated nano-structure with an edge. Making use of the self-consistent Green's function and density matrix renormalization group methods, we study a system described by the t-Jz and t-J models on a strip of a square lattice with a linear hole density n_||. At intermediate interaction strength J/t we find edge stripe-like states, reminiscent of the bulk stripes that occur at smaller J/t. We find that stripes attach to edges more readily than hole pairs, and that the edge stripes can exhibit a peculiar phase separation., Comment: 4+ pages, 3 Figures, published version