Search

We compute the dynamical spin structure factor $S(k,\omega)$ of the SU(3) Heisenberg chain variationally using a truncated Hilbert space spanned by the Gutzwiller projected particle-hole excitations of the Fermi sea, introduced in [B. Dalla Piazza et al., Nature Physics 11, 62 (2015)], with a modified importance sampling. We check the reliability of the method by comparing the $S(k,\omega)$ to exact diagonalization results for 18 sites and to the two-soliton continuum of the Bethe Ansatz for 72 sites. We get an excellent agreement in both cases. Detailed analysis of the finite-size effects shows that the method captures the critical Wess-Zumino-Witten SU(3)$_1$ behavior and reproduces the correct exponent, with the exception of the size dependence of the weight of the bottom of the conformal tower. We also calculate the single-mode approximation for the SU($N$) Heisenberg model and determine the velocity of excitations. Finally, we apply the method to the SU(3) Haldane-Shastry model and find that the variational method gives the exact wave function for the lowest excitation at $k=\pm 2\pi/3$., Comment: 20 pages, 15 figures

Nonreciprocal directional dichroism, also called the optical-diode effect, is an appealing functional property inherent to the large class of noncentrosymmetric magnets. However, the in situ electric control of this phenomenon is challenging as it requires a set of conditions to be fulfilled: Special symmetries of the magnetic ground state, spin excitations with comparable magnetic- and electric-dipole activity, and switchable electric polarization. We demonstrate the isothermal electric switch between domains of ${\mathrm{Ba}}_{2}{\mathrm{CoGe}}_{2}{\mathrm{O}}_{7}$ possessing opposite magnetoelectric susceptibilities. Combining THz spectroscopy and multiboson spin-wave analysis, we show that unbalancing the population of antiferromagnetic domains generates the nonreciprocal light absorption of spin excitations.

Frustration in classical spin models can lead to degenerate ground states without long-range order. In reciprocal space, these degeneracies appear as manifolds of wave vectors, their dimensionality increasing with the degree of frustration and the robustness of the disordered spin-liquid state. Here, we present a recipe to explicitly construct Heisenberg models on Bravais lattices with codimension-one manifolds, i.e., lines in two dimensions and surfaces with different Euler characteristics in three dimensions. Furthermore, we discuss the role of thermal and quantum fluctuations in stabilizing ordered states.

The coexisting magnetic and ferroelectric orders in multiferroic materials give rise to a handful of novel magnetoelectric phenomena, such as the absorption difference for the opposite propagation directions of light called the nonreciprocal directional dichroism (NDD). Usually, these effects are restricted to low temperature, where the multiferroic phase develops. In this paper, we report the observation of NDD in the paramagnetic phase of ${\mathrm{Sr}}_{2}{\mathrm{CoSi}}_{2}{\mathrm{O}}_{7}$ up to temperatures more than 10 times higher than its N\'eel temperature (7 K) and in fields up to 30 T. The magnetically induced polarization and NDD in the disordered paramagnetic phase is readily explained by the single-ion spin-dependent hybridization mechanism, which does not necessitate correlation effects between magnetic ions. The ${\mathrm{Sr}}_{2}{\mathrm{CoSi}}_{2}{\mathrm{O}}_{7}$ provides an ideal system for a theoretical case study, demonstrating the concept of magnetoelectric spin excitations in a paramagnet via analytical as well as numerical approaches. We applied exact diagonalization of a spin cluster to map out the temperature and field dependence of the spin excitations, as well as symmetry arguments of the single ion and lattice problem to get the spectrum and selection rules.

Exotic spin-multipolar ordering in spin transition metal insulators has so far eluded unambiguous experimental observation. A less studied, but perhaps more feasible fingerprint of multipole character emerges in the excitation spectrum in the form of quadrupolar transitions. Such multipolar excitations are desirable as they can be manipulated with the use of light or electric field and can be captured by means of conventional experimental techniques. Here we study single crystals of multiferroic ${\mathrm{Sr}}_{2}{\mathrm{CoGe}}_{2}{\mathrm{O}}_{7}$ and observe a two-magnon spin excitation appearing above the saturation magnetic field in electron spin resonance (ESR) spectra. Our analysis of the selection rules reveals that this spin excitation mode does not couple to the magnetic component of the light, but it is excited by the electric field only, in full agreement with the theoretical calculations. Due to the nearly isotropic nature of ${\mathrm{Sr}}_{2}{\mathrm{CoGe}}_{2}{\mathrm{O}}_{7}$, we identify this excitation as a purely spin-quadrupolar two-magnon mode.

The extension of the linear flavor-wave theory (LFWT) to fully antisymmetric irreducible representations (irreps) of $\mathrm{SU}(N)$ is presented in order to investigate the color order of $\mathrm{SU}(N)$ antiferromagnetic Heisenberg models in several two-dimensional geometries. The square, triangular and honeycomb lattices are considered with $m$ fermionic particles per site. We present two different methods: the first method is the generalization of the multiboson spin-wave approach to $\mathrm{SU}(N)$ which consists of associating a Schwinger boson to each state on a site. The second method adopts the Read and Sachdev bosons which are an extension of the Schwinger bosons that introduces one boson for each color and each line of the Young tableau. The two methods yield the same dispersing modes, a good indication that they properly capture the semi-classical fluctuations, but the first one leads to spurious flat modes of finite frequency not present in the second one. Both methods lead to the same physical conclusions otherwise: long-range N��el-type order is likely for the square lattice for $\mathrm{SU}(4)$ with two particles per site, but quantum fluctuations probably destroy order for more than two particles per site, with $N=2m$. By contrast, quantum fluctuations always lead to corrections larger than the classical order parameter for the tripartite triangular lattice (with $N=3m$) or the bipartite honeycomb lattice (with $N=2m$) for more than one particle per site, $m>1$, making the presence of color very unlikely except maybe for $m=2$ on the honeycomb lattice, for which the correction is only marginally larger than the classical order parameter., 13 pages, 4 figures

We show that, in the presence of a $\ensuremath{\pi}/2$ artificial gauge field per plaquette, Mott insulating phases of ultracold fermions with $\mathrm{SU}(N)$ symmetry and one particle per site generically possess an extended chiral phase with intrinsic topological order characterized by an approximate ground space of $N$ low-lying singlets for periodic boundary conditions, and by chiral edge states described by the ${\mathrm{SU}(N)}_{1}$ Wess-Zumino-Novikov-Witten conformal field theory for open boundary conditions. This has been achieved by extensive exact diagonalizations for $N$ between 3 and 9, and by a parton construction based on a set of $N$ Gutzwiller projected fermionic wave functions with flux $\ensuremath{\pi}/N$ per triangular plaquette. Experimental implications are briefly discussed.

Motivated by the numerous examples of 1/3 magnetization plateaux in the triangular lattice Heisenberg an- tiferromagnet with spins ranging from 1/2 to 5/2, we revisit the semiclassical calculation of the magnetization curve of that model, with the aim of coming up with a simple method that allows one to calculate the full mag- netization curve, and not just the critical fields of the 1/3 plateau. We show that it is actually possible to calculate the magnetization curve including the first quantum corrections and the appearance of the 1/3 plateau entirely within linear spin-wave theory, with predictions for the critical fields that agree to order 1/S with those derived a long-time ago on the basis of arguments that required to go beyond linear spin-wave theory. This calculation relies on the central observation that there is a kink in the semiclassical energy at the field where the classical ground state is the collinear up-up-down structure, and that this kink gives rise to a locally linear behavior of the energy with the field when all semiclassical ground states are compared to each other for all fields. The magnetization curves calculated in this way for spin 1/2, 1 and 5/2 are shown to be in good agreement with available experimental data., 11 pages - 7 figures

We study electrons hopping on a kagome lattice at third filling described by an extended Hubbard Hamiltonian with on-site and nearest-neighbour repulsions in the strongly correlated limit. As a consequence of the commensurate filling and the large interactions, each triangle has precisely two electrons in the effective low energy description, and these electrons form chains of different lengths. The effective Hamiltonian includes the ring exchange around the hexagons as well as the nearest-neighbor Heisenberg interaction. Using large scale exact diagonalization, we find that the effective model exhibits two different phases: If the charge fluctuations are small, the magnetic fluctuations confine the charges to short loops around hexagons, yielding a gapped charge ordered phase. When the charge fluctuations dominate, the system undergoes a quantum phase transition to a resonating plaquette phase with ordered spins and gapless spin excitations. We find that a peculiar conservation law is fulfilled: the electron in the chains can be divided into two sublattices, and this division is conserved by the ring exchange term., Comment: 12 pages, 13 figures, small modifications in the text and in the figures

Static electrical and magnetic properties of single crystal ${\mathrm{BaVS}}_{3}$ were measured over the structural ${(T}_{S}=240\mathrm{K}),$ metal insulator ${(T}_{\mathrm{MI}}=69\mathrm{K}),$ and suspected orbital ordering ${(T}_{X}=30\mathrm{K})$ transitions. The resistivity is almost isotropic both in the metallic and insulating states. An anomaly in the magnetic anisotropy at ${T}_{X}$ signals a phase transition to an ordered low-T state. The results are interpreted in terms of orbital ordering and spin pairing within the lowest crystal-field quasidoublet. The disordered insulator at ${T}_{X}lTl{T}_{\mathrm{MI}}$ is described as a classical liquid of nonmagnetic pairs.

We have determined the dynamical dielectric response of a one-dimensional, correlated insulator by carrying out electron energy-loss spectroscopy on ${\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}$ single crystals. The observed momentum and energy dependence of the low-energy features, which correspond to collective transitions across the gap, are well described by an extended one-band Hubbard model with moderate nearest neighbor Coulomb interaction strength. An excitonlike peak appears with increasing momentum transfer. These observations provide experimental evidence for spin-charge separation in the relevant excitations of this compound, as theoretically expected for the one-dimensional Hubbard model.

We present magnetic-susceptibility measurements on ${\mathrm{MgV}}_{2}{\mathrm{O}}_{5}$, a compound in which the vanadium oxide planes have the same topology as in ${\mathrm{CaV}}_{2}{\mathrm{O}}_{5}$. The most striking property is that there is an energy gap of about 15 K, much smaller than in ${\mathrm{CaV}}_{2}{\mathrm{O}}_{5}$, where the values reported are of the order of 500 K. We show that this may be understood naturally in terms of the phase diagram of the frustrated coupled ladder system. This analysis leads to the prediction that ${\mathrm{MgV}}_{2}{\mathrm{O}}_{5}$ should have incommensurate dynamic spin fluctuations.

We present a theoretical study of the magnetic phase diagram of the frustrated coupled ladder structure realized recently in several materials. This system displays a nondegenerate spin-gap state in the dimer limit and an infinitely degenerate spin-gap state in the regime of weakly coupled zigzag chains. Between these we demonstrate the existence of gapless, magnetically ordered regions whose order is antiferromagnetic close to the honeycomb lattice limit, and incommensurate along the chains when all three magnetic interactions compete.

We give the details of the calculation of the spectral functions of the 1D Hubbard model using the spin-charge factorized wave-function for several versions of the U -> +\infty limit. The spectral functions are expressed as a convolution of charge and spin dynamical correlation functions. A procedure to evaluate these correlation functions very accurately for large systems is developed, and analytical results are presented for the low energy region. These results are fully consistent with the conformal field theory. We also propose a direct method of extracting the exponents from the matrix elements in more general cases.

Dynamical properties of the lattice structure were studied by optical spectroscopy in $A$Cr${}_{2}$O${}_{4}$ chromium spinel oxide magnetic semiconductors over a broad temperature region of $T=10$--335 K. The systematic change of the $A$-site ions ($A=$ Mn, Fe, Co, Ni and Cu) showed that the occupancy of 3$d$ orbitals on the $A$ site has strong impact on the lattice dynamics. For compounds with orbital degeneracy (FeCr${}_{2}$O${}_{4}$, NiCr${}_{2}$O${}_{4}$, and CuCr${}_{2}$O${}_{4}$), clear splitting of infrared-active phonon modes and/or activation of silent vibrational modes have been observed upon the Jahn-Teller transition and at the onset of the subsequent long-range magnetic order. Although MnCr${}_{2}$O${}_{4}$ and CoCr${}_{2}$O${}_{4}$ show multiferroic and magnetoelectric character, no considerable magnetoelasticity was found in spinel compounds without orbital degeneracy as they closely preserve the high-temperature cubic spinel structure even in their magnetic ground state. Aside from lattice vibrations, intra-atomic 3$d$-3$d$ transitions of the $A$${}^{2+}$ ions were also investigated to determine the crystal field and Racah parameters and the strength of the spin-orbit coupling.

The dynamical density-density correlation function is calculated for the one-dimensional, half-filled Hubbard model extended with nearest neighbor repulsion using the Lanczos algorithm for finite size systems and analytically for large on site repulsion compared to hopping amplitudes. At the zone boundary an excitonic feature exists for any finite nearest neighbor repulsion and exhausts most of the spectral weight, even for parameters where no exciton is visible at zero momentum., Comment: 5 pages, REVTeX, epsf, 3 postscript figures

We show that the factorized wave-function of Ogata and Shiba can be used to calculate the $k$ dependent spectral functions of the one-dimensional, infinite $U$ Hubbard model, and of some extensions to finite $U$. The resulting spectral function is remarkably rich: In addition to low energy features typical of Luttinger liquids, there is a well defined band, which we identify as the shadow band resulting from $2k_F$ spin fluctuations. This band should be detectable experimentally because its intensity is comparable to that of the main band for a large range of momenta.

We show that the one-particle spectral functions of the one-dimensional Hubbard model diverge at the Fermi energy like $|\ensuremath{\omega}\ensuremath{-}{\ensuremath{\varepsilon}}_{F}{|}^{\ensuremath{-}3/8}$ in the $U\ensuremath{\rightarrow}+\ensuremath{\infty}$ limit. The Luttinger liquid behavior $|\ensuremath{\omega}\ensuremath{-}{\ensuremath{\varepsilon}}_{F}{|}^{\ensuremath{\alpha}}$, where $\ensuremath{\alpha}\ensuremath{\rightarrow}1/8$ as $U\ensuremath{\rightarrow}+\ensuremath{\infty}$, should be limited to $|\ensuremath{\omega}\ensuremath{-}{\ensuremath{\varepsilon}}_{F}|\ensuremath{\sim}{t}^{2}/U$ (for $U$ large but finite), which shrinks to a single point, $\ensuremath{\omega}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}{\ensuremath{\varepsilon}}_{F}$, in that limit. The consequences for the observation of the Luttinger liquid behavior in photoemission and inverse photoemission experiments are discussed.

We consider the square-lattice antiferromagnetic Heisenberg Hamiltonian extended with a single-ion axial anisotropy term as a minimal model for the multiferroic Ba${}_{2}$CoGe${}_{2}$O${}_{7}$. Developing a multiboson spin-wave theory, we investigate the dispersion of the spin excitations in this spin-3/2 system. As a consequence of a strong single-ion anisotropy, a stretching (longitudinal) spin mode appears in the spectrum. The inelastic neutron scattering spectra of Zheludev et al. [Phys. Rev. B 68, 024428 (2003)] are successfully reproduced by the low energy modes in the multiboson spin-wave theory, and we anticipate the appearance of the spin stretching modes at $\ensuremath{\approx}$4 meV that can be identified using the calculated dynamical spin structure factors. We expect the appearance of spin stretching modes for any $Sg1/2$ compound where the single-ion anisotropy is significant.

We studied spin excitations in the magnetically ordered phase of the noncentrosymmetric Ba(2)CoGe(2)O(7) in high magnetic fields up to 33 T. In the electron spin resonance and far infrared absorption spectra we found several spin excitations beyond the two conventional magnon modes expected for such a two-sublattice antiferromagnet. We show that a multiboson spin-wave theory describes these unconventional modes, including spin-stretching modes, characterized by an oscillating magnetic dipole and quadrupole moment. The lack of inversion symmetry allows each mode to become electric dipole active. We expect that the spin-stretching modes can be generally observed in inelastic neutron scattering and light absorption experiments in a broad class of ordered S > 1/2 spin systems with strong single-ion anisotropy and/or noncentrosymmetric lattice structure.

We propose a quantitative estimate of the charge gap that opens in the one-dimensional dimerized Hubbard model at quarter-filling due to dimerization, which makes the system effectively half--filled, and to repulsion, which induces umklapp scattering processes. Our estimate is expected to be valid for any value of the repulsion and of the parameter describing the dimerization. It is based on analytical results obtained in various limits (weak coupling, strong coupling, large dimerization) and on numerical results obtained by exact diagonalization of small clusters. We consider two models of dimerization: alternating hopping integrals and alternating on--site energies. The former should be appropriate for the Bechgaard salts, the latter for compounds where the stacks are made of alternating $TMTSF$ and $TMTTF$ molecules. % $(TMTSF)_2 X$ and $(TMTTF)_2 X$ ($X$ denotes $ClO_4$, $PF_6$, $Br$...)., 33 pages, RevTeX 3.0, figures on request

We investigate the spin induced polarization in the multiferroic compound Ba${}_{2}$CoGe${}_{2}$O${}_{7}$ using variational and finite-temperature mean field approaches, with the aim to reproduce the peculiar behavior of the induced polarization in a magnetic field observed experimentally in Murakawa et al. [Phys. Rev. Lett. 105, 137202 (2010)]. The compound is usually described by a spin-3/2 Heisenberg model extended with easy-plane anisotropy and Dzyaloshinskii-Moriya (DM) interaction. By applying a magnetic field parallel to the $[110]$ axis, three phases can be distinguished in this model: (i) At high magnetic field, we find a partially magnetized phase with spins parallel to the fields and uniform polarization. (ii) Below a critical field, the ground state is a twofold-degenerate canted antiferromagnet, where the degeneracy can be lifted by a finite DM interaction. (iii) At zero field, a U$(1)$ symmetry-breaking phase takes place, exhibiting a Goldstone mode. We find that extending the Hamiltonian with an antiferroelectric term results in the appearance of a canted ferrimagnetic phase for $h\ensuremath{\lesssim}1$ T. This phase is characterized by a finite staggered polarization, as well as by a magnetization closing a finite angle with the applied field leading to torque anomalies.

We study the spin-$3/2$ Heisenberg model including easy-plane and exchange anisotropies in one and two dimensions. In the Ising limit, when the off-diagonal exchange interaction $J$ is zero, the phase diagram in magnetic field is characterized by magnetization plateaus that are either translationally invariant or have a two-sublattice order, with phase boundaries that are macroscopically degenerate. Using a site-factorized variational wave function and perturbational expansion around the Ising limit, we find that superfluid and supersolid phases emerge between the plateaus for small finite values of $J$. The variational approach is complemented by a density matrix renormalization group study of a one-dimensional chain and exact diagonalization calculations on small clusters of a square lattice. The studied model may serve as a minimal model for the layered Ba${}_{2}$CoGe${}_{2}$O${}_{7}$ material compound, and we believe that the vicinity of the uniform 1/3 plateau in the model parameter space can be observed as an anomaly in the measured magnetization curve.

We study the crossover from the one-dimensional to the two-dimensional Hubbard model in the photoemission spectra of weakly coupled chains. The chains with on-site repulsion are treated using the spin-charge factorized wave function, known to provide an accurate description of the dynamics of the model in the strong coupling limit, while the hoppings between the chains are considered as a perturbation. We calculate dynamical spectral functions at all energies in the random-phase approximation by resuming an infinite set of diagrams. Even though the hoppings drive the system from a fractionalized Luttinger-liquid-like system to a Fermi-liquid-like system at low energies, significant characteristics of the one-dimensional system remain in the two-dimensional system. Furthermore, we find that, of introducing (frustrated) hoppings beyond the nearest-neighbor one, the interference effects increase the energy and momentum range of the one-dimensional character.

The one-dimensional Hubbard model in a magnetic field is equivalent under renormalization-group transformation to a multicomponent Tomonaga-Luttinger model. The mapping between the Coulomb repulsion U of the Hubbard model and the couplings of the Tomonaga-Luttinger model is obtained for aribitrary magnetic field h and band filling n from a comparison of the correlation function exponents. These quantities are calculated for the Hubbard model from the finite-size corrections to the excitation energies, since the assumption of conformal invariance relates them to the critical exponents. On the other hand, the correlation functions of the multicomponent Tomonaga-Luttinger model are determined by solving the exact equation of motion derived by the use of generalized Ward identities.

Combining a semi-classical analysis with exact diagonalizations, we show that the ground state of the SU(3) Heisenberg model on the square lattice develops three-sublattice long-range order. This surprising pattern for a bipartite lattice with only nearest-neighbor interactions is shown to be the consequence of a subtle quantum order-by-disorder mechanism. By contrast, thermal fluctuations favor two-sublattice configurations via entropic selection. These results are shown to extend to the cubic lattice, and experimental implications for the Mott-insulating states of three-flavor fermionic atoms in optical lattices are discussed., 4 pages, 3 figures, minor changes, references added

The classical bilinear-biquadratic nearest-neighbor Heisenberg antiferromagnet on the pyrochlore lattice does not exhibit conventional N\'eel-type magnetic order at any temperature or magnetic field. Instead spin correlations decay algebraically over length scales $r\ensuremath{\lesssim}{\ensuremath{\xi}}_{c}\ensuremath{\sim}1/\sqrt{T}$, behavior characteristic of a Coulomb phase arising from a strong local constraint. Despite this, its thermodynamic properties remain largely unchanged if N\'eel order is restored by the addition of a degeneracy-lifting perturbation, e.g., further neighbor interactions. Here we show how these apparent contradictions can be resolved by a proper understanding of way in which long-range N\'eel order emerges out of well-formed local correlations and identify nematic and vector-multipole orders hidden in the different Coulomb phases of the model. So far as experiment is concerned, our results suggest that where long-range interactions are unimportant, the magnetic properties of Cr spinels which exhibit half-magnetization plateaux may be largely independent of the type of magnetic order present.

We consider a one-dimensional model of interacting electrons. The Fermi surface crosses two bands, with light and heavy masses, respectively. Both intraband and interband interactions are assumed. The earlier renormalization-group treatment of the model by Varma and Zawadowski is extended to check the validity of the scaling assumption and to calculate the next corrections to the scaling equations. These corrections indicate a Fermi-velocity renormalization. Depending on the initial parameters, two kinds of behavior can appear. Either the interband charge fluctuations are negligible and then the dominant instabilities are determined by the interband exchange and the intraband backscattering with the two velocities remaining different, or the interband charge fluctuations become dominant and the velocities scale to a common value. The phase diagram of the model is also determined.

We examine the influence of weak anisotropic interactions on the T=0 phase diagram of the frustrated two-leg Heisenberg ladder, a well-studied spin model exhibiting integer and fractional magnetization plateaux separated by gapless incommensurate states. We find that the Dzyaloshinskii--Moriya coupling may substantially modify the phase diagram so that the half-integer plateau and the surrounding gapless phases merge into a single Ising-ordered phase breaking the translational symmetry of the lattice. A different Ising order is found for a weakly frustrated ladder. Implications for experimental ladder and dimer systems are discussed., Comment: 5 pages, 5 figures

In the limit of large nearest--neighbor and on--site Coulomb repulsions, the Hubbard model on the planar pyrochlore lattice maps, near quarter-filling, onto a doped quantum fully packed loop model. The phase diagram exhibits at quarter filling a novel quantum state of matter, the Resonating Singlet-Pair Crystal, an insulating phase breaking lattice symmetry. Properties of a few doped holes are investigated. In contrast to the doped quantum antiferromagnet, phase separation is restricted to very small hopping leaving an extended``window'' for superconducting pairing. However the later is more fragile for large hopping than in the case of the antiferromagnet., 4 pages, 5 figures

Using mean-field theory, exact diagonalizations and SU(3) flavour theory, we have precisely mapped out the phase diagram of the S=1 bilinear-biquadratic Heisenberg model on the triangular lattice in a magnetic field, with emphasis on the quadrupolar phases and their excitations. In particular, we show that ferroquadrupolar order can coexist with short-range helical magnetic order, and that the antiferroquadrupolar phase is characterized by a remarkable 2/3 magnetization plateau, in which one site per triangle retains quadrupolar order while the other two are polarized along the field. Implications for actual S=1 magnets are discussed., Comment: 4 pages, 5 figures, published version

We show that the prefactors of all terms of the one-dimensional (1D) Hubbard model correlation-function asymptotic expansions have a universal form, as the corresponding critical exponents. In addition to calculating such prefactors, our study clarifies the relation of the low-energy Tomonaga-Luttinger-liquid behavior to the scattering mechanisms which control the spectral properties of the model at all energy scales. Our results are of general nature for many integrable interacting models and provide a broader understanding of the unusual properties of quasi-1D nanostructures, organic conductors, and optical lattices of fermionic atoms.

Magnetization plateaus, visible as anomalies in magnetic susceptibility at low temperatures, are one of the hallmarks of frustrated magnetism. We show how an extremely robust half-magnetization plateau can arise from coupling between spin and lattice degrees of freedom in a pyrochlore antiferromagnet, and develop a detailed symmetry of analysis of the simplest possible scenario for such a plateau state. The application of this theory to the spinel oxides CdCr2O4 and HgCr2O4, where a robust half magnetization plateau has been observed, is discussed., 4 pages, 4 figures

Motivated by the absence of cooperative Jahn-Teller effect and of magnetic ordering in LiNiO$_2$, a layered oxide with triangular planes, we study a general spin-orbital model on the triangular lattice. A mean-field approach reveals the presence of several singlet phases between the SU(4) symmetric point and a ferromagnetic phase, a conclusion supported by exact diagonalizations of finite clusters. We argue that one of the phases, characterized by a large number of low-lying singlets associated to dimer coverings of the triangular lattice, could explain the properties of LiNiO$_2$, while a ferro-orbital phase that lies nearby in parameter space leads to a new prediction for the magnetic properties of NaNiO$_2$., 18 pages, 17 figures

The antiferromagnetic Ising model on a checkerboard lattice has an ice-like ground state manifold with extensive degeneracy. and, to leading order in ${J}_{xy}$, deconfined spinon excitations. We explore the role of cyclic exchange arising at order ${J}_{xy}^{2}∕{J}_{z}$ on the ice states and their associated spinon excitations. By mapping the original problem onto an equivalent quantum six-vertex model, we identify three different phases as a function of the chemical potential for flippable plaquettes---a phase with long range N\'eel order and confined spinon excitations, a nonmagnetic state of resonating square plaquettes, and a quasicollinear phase with gapped but deconfined spinon excitations. The relevance of the results to the square-lattice quantum dimer model is also discussed.

Motivated by the absence of cooperative Jahn-Teller effect in LiNiO2 and BaVS3, two layered oxides with triangular planes, we study the SU(4) symmetric spin-orbital model on the triangular lattice. Upon reducing the next-nearest neighbour coupling, we show that the system undergoes a quantum phase transition to a liquid phase. A variational approach to this liquid phase shows that simple types of long-range correlations are suppressed, suggesting that it is stable against lattice distortions., 5 pages, 5 figures, RevTex4

We study the exact one-electron propagator and spectral function of a solvable model of interacting electrons due to Schulz and Shastry. The solution previously found for the energies and wave functions is extended to give spectral functions that turn out to be computable, interesting, and nontrivial. They provide one of the few examples of cases where the spectral functions are known asymptotically as well as exactly.