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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.

The discovery by Kane and Mele of a model of spinful electrons characterized by a $\mathcal{Z}_2$ topological invariant had a lasting effect on the study of electronic band structures. Given this, it is natural to ask whether similar topology can be found in the band-like excitations of magnetic insulators, and recently models supporting $\mathcal{Z}_2$ topological invariants have been proposed for both magnon [Kondo et al. Phys. Rev. B 99, 041110(R) (2019)] and triplet [D. G. Joshi and A. P. Schnyder, Phys. Rev. B 100, 020407 (2019)] excitations. In both cases, magnetic excitations form time--reversal (TR) partners, which mimic the Kramers pairs of electrons in the Kane-Mele model but do not enjoy the same type of symmetry protection. In this paper, we revisit this problem in the context of the triplet excitations of a spin model on the bilayer kagome lattice. Here the triplet excitations provide a faithful analog of the Kane-Mele model as long as the Hamiltonian preserves the TR$\times$U(1) symmetry. We find that exchange anisotropies, allowed by the point group and typical in realistic models, break the required TR$\times$U(1) symmetry and instantly destroy the $\mathcal{Z}_2$ band topology. We further consider the effects of TR breaking by an applied magnetic field. In this case, the lifting of spin-degeneracy leads to a triplet Chern insulator, which is stable against the breaking of TR$\times$U(1) symmetry. Kagome bands realize both a quadratic and a linear band touching, and we provide a thorough characterization of the Berry curvature associated with both cases. We also calculate the triplet-mediated spin Nernst and thermal Hall signals which could be measured in experiments. These results suggest that the $\mathcal{Z}_2$ topology of band-like excitations in magnets may be intrinsically fragile compared to their electronic counterparts., Comment: 19 pages, 16 figures

We provide numerical evidence in favor of spontaneous chiral symmetry breaking and the concomitant appearance of an Abelian chiral spin liquid for three-component fermions on the triangular lattice described by an SU(3) symmetric Hubbard model with hopping amplitude $-t$ ($t>0$) and on-site interaction $U$. This chiral phase is stabilized in the Mott phase with one particle per site in the presence of a uniform $��$-flux per plaquette, and in the Mott phase with two particles per site without any flux. Our approach relies on effective spin models derived in the strong-coupling limit in powers of $t/U$ for general SU$(N)$ and arbitrary uniform charge flux per plaquette, which are subsequently studied using exact diagonalizations and variational Monte Carlo simulations for $N=3$, as well as exact diagonalizations of the SU($3$) Hubbard model on small clusters. Up to third order in $t/U$, and for the time-reversal symmetric cases (flux $0$ or $��$), the low-energy description is given by the $J$-$K$ model with Heisenberg coupling $J$ and real ring exchange $K$. The phase diagram in the full $J$-$K$ parameter range contains, apart from three already known, magnetically long-range ordered phases, two previously unreported phases: i) a lattice nematic phase breaking the lattice rotation symmetry and ii) a spontaneous time-reversal and parity symmetry breaking Abelian chiral spin liquid. For the Hubbard model, an investigation that includes higher-order itinerancy effects supports the presence of a phase transition inside the insulating region, occurring at $(t/U)_{\rm c}\approx 0.07$ [$(U/t)_{\rm c} \approx 13$] between the three-sublattice magnetically ordered phase at small $t/U$ and this Abelian chiral spin liquid., 21 pages, 23 figures

We present a detailed study of the ground state phase diagram of the classical frustrated Heisenberg model on the face-centered-cubic lattice. By considering exchange interactions up till third nearest neighbors, we find commensurate, helimagnetic, as well as noncollinear multi-{\bf Q} orders which include noncoplanar and chiral spin structures. We reveal the presence of subextensively degenerate manifolds that appear at triple points and certain phase boundaries in the phase diagram. Within these manifolds, the spin Hamiltonian can be recast as a complete square of spins on finite motifs, permitting us to identify families of exact ground state spin configurations in real space -- these include randomly stacked ferro- or antiferromagnetically ordered planes and interacting ferromagnetic chains, among others. Finally, we critically investigate the ramifications of our findings on the example of the Ising model, where we exactly enumerate all the states numerically for finite clusters., Comment: 26 pages, 10 figures, 10 tables, small corrections and clarifications

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.

We report on negative thermal expansion (NTE) in the high-field, half-magnetization plateau phase of the frustrated magnetic insulator CdCr2O4. Using dilatometry, we precisely map the phase diagram at fields of up to 30T, and identify a strong NTE associated with the collinear half-magnetization plateau for B > 27T. The resulting phase diagram is compared with a microscopic theory for spin-lattice coupling, and the origin of the NTE is identified as a large negative change in magnetization with temperature, coming from a nearly-localised band of spin excitations in the plateau phase. These results provide useful guidelines for the discovery of new NTE materials., 6 pages, 2 figures

Resistivity and susceptibility measurements on single crystal samples were used to construct the phase diagram of the 3D Mott system BaVS3 in the pressure- temperature (p-T) plane. The metal to non-magnetic Mott insulator transition is gradually suppressed until it vanishes at the critical pressure p Cr ≈ 20kbar, The high-pressure metallic phase is the first 3d-electron based non-fermi-liquid with a low-T resistivity obeying p—p o ∝ T 1.25 over at least one and a half decade of T. For p p cr, the metal-insulator transition is preceded by a wide precursor range of critically increasing resistivity. We discuss the nature of the various regimes, and point out similarities and dissimilarities to other strongly correlated d-electron systems.

We study the Kitaev-Heisenberg-$\Gamma$-$\Gamma'$ model that describes the magnetism in strong spin-orbit coupled honeycomb lattice Mott insulators. In strong $[111]$ magnetic fields that bring the system into the fully polarized paramagnetic phase, we find that the spin wave bands carry nontrivial Chern numbers over large regions of the phase diagram implying the presence of chiral magnon edge states. In contrast to other topological magnon systems, the topological nontriviality of these systems results from the presence of magnon number non-conserving terms in the Hamiltonian. Since the effects of interactions are suppressed by $J/h$, the validity of the single particle picture is tunable making paramagnetic phases particularly suitable for the exploration of this physics. Using time dependent DMRG and interacting spin wave theory, we demonstrate the presence of the chiral edge mode and its evolution with field., Comment: 16 pages (main text + supplementary material), 10 figures

The ultimate goal of multiferroic research is the development of a new-generation nonvolatile memory devices, where magnetic bits are controlled via electric fields with low energy consumption. Here, we demonstrate the optical identification of magnetoelectric (ME) antiferromagnetic (AFM) domains in the ${\mathrm{LiCoPO}}_{4}$ exploiting the strong absorption difference between the domains. This unusual contrast, also present in zero magnetic field, is attributed to the dynamic ME effect of the spin-wave excitations, as confirmed by our microscopic model, which also captures the characteristics of the observed static ME effect. The control and the optical readout of AFM/ME domains, demonstrated here, will likely promote the development of ME and spintronic devices based on AFM insulators.

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 revisit the SU(6) Heisenberg model on the honeycomb lattice, which has been predicted to be a chiral spin liquid by mean-field theory [G. Szirmai et al., Phys. Rev. A 84, 011611(R) (2011)]. Using exact diagonalizations of finite clusters, infinite projected entangled pair state simulations, and variational Monte Carlo simulations based on Gutzwiller projected wave functions, we provide strong evidence that the model with one particle per site and nearest-neighbor exchange actually develops plaquette order. This is further confirmed by the investigation of the model with a ring-exchange term, which shows that there is a transition between the plaquette state and the chiral state at a finite value of the ring-exchange term.

BaVS3 is a moderately correlated d-electron system with a rich phase diagram. To construct the corresponding minimal electronic model, one has to decide which d-states are occupied, and to which extent. The ARPES experiment presented here shows that the behavior of BaVS_3 is governed by the coexistence of wide-band (A_(1g)) and narrow-band (twofold degenerate E) d-electrons. We sketch a lattice fermion model which may serve as a minimal model of BaVS_3. This serves foremost for the understanding of the metal–insulator in pure BaVS_3 and its absence in some related compounds. The nature of the low-temperature magnetic order differs for several systems which may be described in terms of the same electron model. We describe several recent experiments which give information about magnetic order at high pressures. In particular, we discuss field-induced insulator-to-metal transition at slightly subcritical pressures, and an evidence for magnetic order in the high-pressure metallic phase. The phase diagram of Sr-doped BaVS_3 is also discussed. The complexity of the phases of BaVS_3 arises from the fact that it is simultaneously unstable against several kinds of instabilities.

We introduce a method that allows the evaluation of general expressions for the spectral functions of the one-dimensional Hubbard model for all values of the on-site electronic repulsion U. The spectral weights are expressed in terms of pseudofermion operators such that the spectral functions can be written as a convolution of pseudofermion dynamical correlation functions. Our results are valid for all finite energy and momentum values and are used elsewhere in the study of the unusual finite-energy properties of quasi-one-dimensional compounds and the new quantum systems of ultra-cold fermionic atoms on an optical lattice., Comment: 25 pages, no figures

In this paper we use the pseudofermion dynamical theory (PDT) to study the singular spectral features due to one-electron removal within the one-dimensional Hubbard model. The PDT reveals that in the whole (k, ω)-plane such features are of the power-law type and correspond to well defined lines of three types: charge singular branch lines, spin singular branch lines and border lines. One of our goals is the study of the momentum and energy dependence of the distribution of the spectral weight in the vicinity of such lines. We find that the charge and spin branch lines correspond to the main tetracyanoquinodimethane (TCNQ) peak dispersions observed with angle-resolved photoelectron spectroscopy in the quasi-1D organic conductor tetrathiafulvalene-tetracyanoquinodimethane (TTF-TCNQ). Our expressions refer to all values of the electronic density and on-site repulsion U. The weight distribution in the vicinity of the singular spectral lines is fully controlled by the overall pseudofermion phase shifts. Moreover, the shape of these lines is determined by the bare-momentum dependence of the pseudofermion energy dispersions.

In this paper we show that the general finite-energy spectral-function expressions provided by the pseudofermion dynamical theory for the one-dimensional Hubbard model lead to the expected low-energy Tomonaga–Luttinger liquid correlation function expressions. Moreover, we use the former general expressions to derive correlation-function asymptotic expansions in space and time which go beyond those obtained by conformal-field theory and bosonization: we derive explicit expressions for the pre-factors of all terms of such expansions and find that they have an universal form, as the corresponding critical exponents. Our results refer to all finite values of the on-site repulsion U and to a chain of length L very large and with periodic boundary conditions for the above model, but are of general nature for many integrable interacting models. The studies of this paper clarify the relation of the low-energy Tomonaga–Luttinger liquid behavior to the scattering mechanisms which control the spectral properties at all energy scales and provide a broader understanding of the unusual properties of quasi-one-dimensional nanostructures, organic conductors, and optical lattices of ultracold fermionic atoms. Furthermore, our results reveal the microscopic mechanisms which are behind the similarities and differences of the low-energy and finite-energy spectral properties of the model metallic phase.

The momentum and energy dependence of the weight distribution in the vicinity of the one-electron spectral-function singular branch lines of the 1D Hubbard model is studied for all values of the electronic density and on-site repulsion $U$. To achieve this goal we use the recently introduced pseudofermion dynamical theory. Our predictions agree quantitatively for the whole momentum and energy bandwidth with the peak dispersions observed by angle-resolved photoelectron spectroscopy in the quasi-1D organic conductor TTF-TCNQ., Comment: Replaced with shortened version; 4 figures

We present a method for the calculation of few-electron spectral functions of the one-dimensional Hubbard model which relies on a pseudofermion description introduced recently in Ref. [6]. The spectral functions are expressed as a convolution of pseudofermion dynamical correlation functions. Our general method involves the direct evaluation of the matrix elements of pseudofermion operators between the ground state and the excited states. We briefly discuss the application of our general method to the study of the unusual finite-energy spectral properties observed in the quasi-one-dimensional organic conductor TTF-TCNQ.

The classical ground states of the SU(4) Heisenberg model on the face-centered-cubic lattice constitute a highly degenerate manifold. We explicitly construct all the classical ground states of the model. To describe quantum fluctuations above these classical states, we apply linear flavor-wave theory. At zero temperature, the bosonic flavor waves select the simplest of these SU(4) symmetry-breaking states, the four-sublattice-ordered state defined by the cubic unit cell of the fcc lattice. Due to geometrical constraints, flavor waves interact along specific planes only, thus rendering the system effectively two dimensional and forbidding ordering at finite temperatures. We argue that longer-range interactions generated by quantum fluctuations can shift the transition to finite temperatures.

A pyrochlore lattice is considered where the average electron number of electrons per site is half--integer, concentrating on the case of exactly half an electron per site. Strong on-site repulsions are assumed, so that all sites are either empty or singly occupied. Where there are in addition strong nearest--neighbour repulsions, a tetrahedron rule comes into effect, as previously suggested for magnetite. We show that in this case, there exist excitations with fractional charge (+/-) e/2. These are intimately connected with the high degeneracy of the ground state in the absence of kinetic energy terms. When an additional electron is inserted into the system, it decays into two point like excitations with charge -e/2, connected by a Heisenberg spin chain which carries the electron's spin., Comment: 10 pages, 4 eps figures. To appear in Decemeber issue of Annalen der Physik

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 Sr2CoGe2O7 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 Sr2CoGe2O7, we identify this excitation as a purely spin-quadrupolar two-magnon mode.

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

The celebrated Shastry Sutherland model has a gapped dimer singlet ground state. The material SrCu$_2$(BO$_3$)$_2$ serves as a good realization of this model, upto small anisotropies arising from Dzyaloshinskii-Moriya (DM) interactions. The DM interactions admix a triplet component into the singlet ground state and give rise to weakly dispersing triplon bands. We show that an applied magnetic field splits the triplon modes and opens band gaps. Surprisingly, we are left with topological bands with Chern numbers $\pm 2$. SrCu$_2$(BO$_3$)$_2$ thus supports topologically protected triplonic edge modes and is a magnetic analogue of the integer quantum Hall effect. At a critical value of the magnetic field set by the strength of DM interactions, the three triplon bands touch once again in a spin-1 generalization of a Dirac cone, and lose their topological character. We predict a strong thermal Hall signature in the topological regime., 4 pages + 3 pages supplementary material

We briefly review the 1D lattice models that are most often used to understand the physics of one-dimensional or quasi-one-dimensional conductors and their low-temperature instabilities. We discuss the physical relevance of the different models, ranging from anisotropic crystals to quantum wires, and we emphasize the specific physics present in each of the models reviewed.

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.

The strong coupling limit of one-dimensional correlated systems is nontrivial, but simple in some sense. Here we demonstrate it, discussing the wave functions for the 1D U→ +∞ Hubbard model, which are factorized as a direct product of the charge part and the spin part and determining the one-particle spectral functions explicitly.

We report studies of the electronic structure and elementary excitations of undoped, one- and two-dimensional cuprates. Using high-energy spectroscopies such as X-ray absorption, photoemission and electron energy-loss spectroscopy, important information regarding the charge distribution, hole dynamics and dielectric response has been obtained. The comparison of the experimental data with suitable theoretical models sets constraints on the parameters entering into the model calculations.

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 investigate the effect of the Berry phase on quadrupoles that occur for example in the low-energy description of spin models. Specifically we study here the one-dimensional bilinear-biquadratic spin-one model. An open question for many years about this model is whether it has a non-dimerized fluctuating nematic phase. The dimerization has recently been proposed to be related to Berry phases of the quantum fluctuations. We use an effective low-energy description to calculate the scaling of the dimerization according to this theory, and then verify the predictions using large scale density-matrix renormalization group (DMRG) simulations, giving good evidence that the state is dimerized all the way up to its transition into the ferromagnetic phase. We furthermore discuss the multiplet structure found in the entanglement spectrum of the ground state wave functions., 4.5 pages + 4 pages supplementary material, 4 figures

Recent experiments on the spin-ice material Dy2Ti2O7 suggest that the Pauling "ice entropy", characteristic of its classical Coulombic spin-liquid state, may be lost at low temperatures [D. Pomaranski et al., Nature Phys. 9, 353 (2013)]. However, despite nearly two decades of intensive study, the nature of the equilibrium ground state of spin ice remains uncertain. Here we explore how long-range dipolar interactions D, short-range exchange interactions, and quantum fluctuations combine to determine the ground state of dipolar spin ice. We identify a new organisational principle, namely that ordered ground states are selected from a set of "chain states" in which dipolar interactions are exponentially screened. Using both quantum and classical Monte Carlo simulation, we establish phase diagrams as a function of quantum tunneling g, and temperature T, and find that only a very small g_c << D is needed to stabilize a quantum spin-liquid ground state. We discuss the implications of these results for Dy2Ti2O7., 24 pages

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.

We present an analysis of a system of weakly coupled Hubbard chains based on combining an exact study of spectral functions of the uncoupled chain system by means of the pseudofermion dynamical theory with a renormalization group method for the coupled chains. Our theoretical predictions are consistent with the phase diagram observed in the ( TMTTF ) 2 X and ( TMTSF ) 2 X series of organic compounds.

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.

The SU(4) Heisenberg model can serve as a low energy model of the Mott insulating state in materials where the spins and orbitals are highly symmetric, or in systems of alkaline-earth atoms on optical lattice. Recently, it has been argued that on the honeycomb lattice the model exhibits a unique spin-orbital liquid phase with an algebraic decay of correlations [P. Corboz et al., Phys. Rev. X 2, 041013 (2012)]. Here we study the instability of the algebraic spin-orbital liquid toward spontaneous formation of SU(4) singlet plaquettes (tetramerization). Using a variational Monte Carlo approach to evaluate the projected wave-function of fermions with $\pi$-flux state, we find that the algebraic liquid is robust, and that a finite value of the next nearest exchange is needed to induce tetramerization. We also studied the phase diagram of a model which interpolates between the nearest neighbor Heisenberg model and a Hamiltonian for which the singlet-plaquette product state is an exact ground state., Comment: 10 pages, 11 figures

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 present a numerical study of the SU(3) Heisenberg model of three-flavor fermions on the triangular and square lattice by means of the density-matrix renormalization group (DMRG) and infinite projected entangled-pair states (iPEPS). For the triangular lattice we confirm that the ground state has a three-sublattice order with a finite ordered moment which is compatible with the result from linear flavor wave theory (LFWT). The same type of order has recently been predicted also for the square lattice [PRL 105, 265301 (2010)] from LFWT and exact diagonalization. However, for this case the ordered moment cannot be computed based on LFWT due to divergent fluctuations. Our numerical study clearly supports this three-sublattice order, with an ordered moment of m=0.2-0.4 in the thermodynamic limit., Published version. 11 pages, 6 figures