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We show that spectral walls are common phenomena in the dynamics of kinks in (1+1) dimensions. They occur in models based on two or more scalar fields with a nonempty Bogomol'nyi-Prasam-Sommerfield (BPS) sector, hosting two zero modes, where they are one of the main factors governing the soliton dynamics. We also show that spectral walls appear as singularities of the dynamical vibrational moduli space., Comment: improved, references added

We investigate rectified currents in response to oscillating electric fields in systems lacking inversion and time-reversal symmetries. These currents, in second-order perturbation theory, are inversely proportional to the relaxation rate, and, therefore, naively diverge in the ideal clean limit. Employing a combination of the non-equilibrium Green function technique and Floquet theory, we show that this is an artifact of perturbation theory, and that there is a well-defined periodic steady-state akin to Rabi oscillations leading to finite rectified currents in the limit of weak coupling to a thermal bath. In this Rabi regime the rectified current scales as the square root of the radiation intensity, in contrast with the linear scaling of the perturbative regime, allowing to readily diagnose it in experiments. More generally, our description provides a smooth interpolation from the ideal Periodic Gibbs Ensemble describing the Rabi oscillations of a closed system to the perturbative regime of rapid relaxation due to strong coupling to a thermal bath., 18 pages, 3 figures

We study kink-antikink scattering in a one-parameter variant of the $\phi^4$ theory where the model parameter controls the static intersoliton force. We interpolate between the limit of no static force (BPS limit) and the regime where the static interaction is small (non-BPS). This allows us to study the impact of the strength of the intersoliton static force on the soliton dynamics. In particular, we analyze how the transition of a bound mode through the mass threshold affects the soliton dynamics in a generic process, i.e., when a static intersoliton force shows up. We show that the thin, precisely localized spectral wall which forms in the limit of no static force, broadens in a well-defined manner when a static force is included, giving rise to what we will call a thick spectral wall. This phenomenon just requires that a discrete mode crosses into the continuum at some intermediate stage of the dynamics and, therefore, should be observable in many soliton-antisoliton collisions., Comment: version accepted in Phys. Rev. E

We introduce an operational definition of the Berry Phase Rectification Tensor as the second-order change of polarization of a material in response to an ideal short pulse of an electric field. Under time-reversal symmetry this tensor depends exclusively on the Berry phases of the Bloch bands and not their energy dispersions, making it an intrinsic property to each material which contains contributions from both the inter-band shift currents and the intra-band Berry Curvature Dipole. We also introduce the Solar Rectification Vector as a technologically relevant figure of merit for a bulk photo-current generation under ideal black-body radiation in analogy with the classic solar cell model of Shockley and Queisser. We perform first-principles calculations of the Berry Phase Rectification Tensor and the Solar Rectification Vector for the Weyl semimetal TaAs and the insulator LiAsSe2 which features large shift currents close to the peak of solar radiation intensity., 13 pages, 5 figures

Kink-antikink scattering in the ϕ4 model is investigated in the limit when the static inter-soliton force vanishes. We observe the formation of spectral walls and, further, identify a new phenomenon, the vacuum wall, whose existence gives rise to a bouncing structure for the annihilating solitons. Furthermore, we discover higher order spectral walls, i.e., spectral walls which form when higher harmonics enter the continuous spectrum. These higher order spectral walls not only deform the soliton trajectories, they also can be observed easily as very intense radiation bursts.

We consider a version of the Skyrme model where both the kinetic term and the Skyrme term are multiplied by field-dependent coupling functions. For suitable choices, this "dielectric Skyrme model" has static solutions saturating the pertinent topological bound in the sector of baryon number (or topological charge) $B=\pm 1$ but not for higher $|B|$. This implies that higher charge field configurations are unbound, and loosely bound higher skyrmions can be achieved by small deformations of this dielectric Skyrme model. We provide a simple and explicit example for this possibility. Further, we show that the $|B|=1$ BPS sector continues to exist for certain generalizations of the model like, for instance, after its coupling to a specific version of the BPS Skyrme model, i.e., the addition of the sextic term and a particular potential., Latex file, 13 pages, no figures

We show that a suitable background field can bring a non-BPS topological soliton into its BPS, self-dual, counterpart. As an example we consider Skyrmions in the minimal Skyrme model. We prove the triviality of the corresponding moduli space. This means that the resulting self-dual Skyrmion does statically interact with the background field. We also show that the originally self-dual Skyrmions (e.g. solutions of the BPS Skyrme model) can preserve the self-duality after a coupling with a background field. In this case, BPS Skyrmions can be effortless moved with respect to the background., Comment: refs added

We discover a new class of topological solitons. These solitons can exist in a space of infinite volume like, e.g., $\mathbb{R}^n$, but they cannot be placed in any finite volume, because the resulting formal solutions have infinite energy. These objects are, therefore, interpreted as totally incompressible solitons. As a first, particular example we consider (1+1) dimensional kinks in theories with a nonstandard kinetic term or, equivalently, in models with the so-called runaway (or vacummless) potentials. But incompressible solitons exist also in higher dimensions. As specific examples in (3+1) dimensions we study Skyrmions in the dielectric extensions both of the minimal and the BPS Skyrme models. In the the latter case, the skyrmionic matter describes a completely incompressible topological perfect fluid., reference added

How a many-body quantum system thermalizes --or fails to do so-- under its own interaction is a fundamental yet elusive concept. Here we demonstrate nuclear magnetic resonance observation of the emergence of prethermalization by measuring out-of-time ordered correlations. We exploit Hamiltonian engineering techniques to tune the strength of spin-spin interactions and of a transverse magnetic field in a spin chain system, as well as to invert the Hamiltonian sign to reveal out-of-time ordered correlations. At large fields, we observe an emergent conserved quantity due to prethermalization, which can be revealed by an early saturation of correlations. Our experiment not only demonstrates a new protocol to measure out-of-time ordered correlations, but also provides new insights in the study of quantum thermodynamics., Comment: 6+12 pages, 3+7 figures

We find a family of (half) self-dual impurity models such that the self-dual (BPS) sector is exactly solvable, for any spatial distribution of the impurity, both in the topologically trivial case and for kink (or antikink) configurations. This allows us to derive the metric on the corresponding one-dimensional moduli space in an analytical form. Also the generalized translational symmetry is found in an exact form. This symmetry provides a motion on moduli space which transforms one BPS solution into another. Finally, we analyse exactly how vibrational properties (spectral modes) of the BPS solutions depend on the actual position on moduli space. These results are obtained both for the nontrivial topological sector (kinks or antikinks) as well as for the topologically trivial sector, where the motion on moduli space represents a kink-antikink annihilation process., sec. 6.1 corrected

We study the problem of a single hole in an Ising antiferromagnet and, using the magnon expansion and analytical methods, determine the expansion coefficients of its wave function in the magnon basis. In the 1D case, the hole is "weakly" confined in a potential well and the magnon coefficients decay exponentially in the absence of a string potential. This behavior is in sharp contrast to the 2D square plane where the hole is "strongly" confined by a string potential and the magnon coefficients decay superexponentially. The latter is identified here to be a fingerprint of the strings in doped antiferromagnets that can be recognized in the numerical or cold atom simulations of the 2D doped Hubbard model. Finally, we attribute the differences between the 1D and 2D cases to the magnon-magnon interactions being crucially important in a 1D spin system., Comment: slightly revised version (following Referee's comments includes correct Fig. 3 and updated discussion of Trugman processes), (re)submission to SciPost

During defect-antidefect scattering, bound modes frequently disappear into the continuous spectrum before the defects themselves collide. This leads to a structural, nonperturbative change in the spectrum of small excitations. Sometimes the effect can be seen as a hard wall from which the defect can bounce off. We show the existence of these spectral walls and study their properties in the $\phi^4$ model with BPS preserving impurity, where the spectral wall phenomenon can be isolated because the static force between the antikink and the impurity vanishes. We conclude that such spectral walls should surround all solitons possessing internal modes., Comment: latex, 5 pages, 3 figures; v2: version published in PRL

Critical behavior is very common in many fields of science and a wide variety of many- body systems exhibit emergent critical phenomena. The beauty of critical phase transitions lies in their scale-free properties, such that the temperature dependence of physical parameters of systems differing at the microscopic scale can be described by the same generic power laws. In this work we establish the critical properties of the antiferromagnetic phase transition in artificial square ice, showing that it belongs to the two-dimensional Ising universality class, which extends the applicability of such concepts from atomistic to mesoscopic magnets. Combining soft x-ray resonant magnetic scattering experiments and Monte Carlo simulations, we characterize the transition to the low-temperature long-range order expected for the artificial square-ice system. By measuring the critical scattering, we provide direct quantitative evidence of a continuous magnetic phase transition, obtaining critical exponents which are compatible with those of the two-dimensional Ising universality class. In addition, by varying the blocking temperature relative to the phase transition temperature, we demonstrate its influence on the out-of-equilibrium dynamics due to critical slowing down at the phase transition.

Detection and manipulation of excitations with non-Abelian statistics, such as Majorana fermions, are essential for creating topological quantum computers. To this end, we show the connection between the existence of such localized particles and the phenomenon of unitary subharmonic response (SR) in periodically driven systems. In particular, starting from highly nonequilibrium initial states, the unpaired Majorana modes exhibit spin oscillations with twice the driving period, are localized, and can have exponentially long lifetimes in clean systems. While the lifetime of SR is limited in translationally invariant systems, we show that disorder can be engineered to stabilize the subharmonic response of Majorana modes. A viable observation of this phenomenon can be achieved using modern multiqubit hardware, such as superconducting circuits and cold atomic systems., Comment: 5 pages + 9 pages supplementary information

Electrons moving in a Bloch band are known to acquire an anomalous Hall velocity proportional to the Berry curvature of the band which is responsible for the intrinsic linear Hall effect in materials with broken time-reversal symmetry. Here, we demonstrate that there is also an anomalous correction to the electron acceleration which is proportional to the Berry curvature dipole and is responsible for the Nonlinear Hall effect recently discovered in materials with broken inversion symmetry. This allows us to uncover a deeper meaning of the Berry curvature dipole as a nonlinear version of the Drude weight that serves as a measurable order parameter for broken inversion symmetry in metals. We also derive a quantum rectification sum rule in time reversal invariant materials by showing that the integral over frequency of the rectification conductivity depends solely on the Berry connection and not on the band energies. The intraband spectral weight of this sum rule is exhausted by the Berry curvature dipole Drude-like peak, and the interband weight is also entirely controlled by the Berry connection. This sum rule opens a door to search for alternative photovoltaic technologies based on the Berry geometry of bands. We also describe the rectification properties of Weyl semimetals which are a promising platform to investigate these effects., Comment: 8 pages, 3 figures

In recent experiments, time-dependent periodic fields are used to create exotic topological phases of matter with potential applications ranging from quantum transport to quantum computing. These nonequilibrium states, at high driving frequencies, exhibit the quintessential robustness against local disorder similar to equilibrium topological phases. However, proving the existence of such topological phases in a general setting is an open problem. We propose a universal effective theory that leverages on modern free probability theory and ideas in random matrices to analytically predict the existence of the topological phase for finite driving frequencies and across a range of disorder. We find that, depending on the strength of disorder, such systems may be topological or trivial and that there is a transition between the two. In particular, the theory predicts the critical point for the transition between the two phases and provides the critical exponents. We corroborate our results by comparing them to exact diagonalizations for driven-disordered 1D Kitaev chain and 2D Bernevig-Hughes-Zhang models and find excellent agreement. This Letter may guide the experimental efforts for exploring topological phases., 5 pages + 9 pages supplementary material. 4 Figures

Micro/nanomachines capable of propulsion through fluidic environments provide diverse opportunities in important biomedical applications. In this paper, we present a theoretical study on micromotors steered through liquid by an external rotating magnetic field. A purely geometric tight upper bound on the propulsion speed normalized with field frequency, known as propulsion efficiency, δ, for an arbitrarily shaped object is derived. Using this bound, we estimate the maximum propulsion efficiency of previously reported random magnetic aggregates. We introduce a complementary definition of the propulsion efficiency, δ*, that ranks propellers according to their maximal speed in body lengths per unit time and that appears to be preferable over the standard definition in a search for fastest machines. Using a bead-based hydrodynamic model combined with genetic algorithms, we determine that δ*-optimal propeller deviates strongly from the bioinspired slim helix and has a surprising chubby skew-symmetric shape. It is also shown that optimized propellers with preprogrammed shape are substantially more efficient than random magnetic aggregates. We anticipate that the results of the present study will provide guidance toward prospective experimental design of more efficient magnetic micro/nanomachines.

A far-reaching goal of graphene research is exploiting the unique properties of carriers to realize extreme nonclassical electronic transport. Of particular interest is harnessing wavelike carriers to guide and direct them on submicron scales, similar to light in optical fibers. Such modes, while long anticipated, have never been demonstrated experimentally. In order to explore this behavior, we employ superconducting interferometry in a graphene Josephson junction to reconstruct the real-space supercurrent density using Fourier methods. Our measurements reveal charge flow guided along crystal boundaries close to charge neutrality. We interpret the observed edge currents in terms of guided-wave states, confined to the edge by band bending and transmitted as plane waves. As a direct analog of refraction-based confinement of light in optical fibers, such nonclassical states afford new means for information transduction and processing at the nanoscale., 31 pages, including supplementary materials

Electron surface states in solids are typically confined to the outermost atomic layers and, due to surface disorder, have negligible impact on electronic transport. Here, we demonstrate a very different behavior for surface states in graphene. We probe the wavelike character of these states by Fabry-Perot (FP) interferometry and find that, in contrast to theoretical predictions, these states can propagate ballistically over micron-scale distances. This is achieved by embedding a graphene resonator formed by gate-defined p-n junctions within a graphene superconductor-normal-superconductor structure. By combining superconducting Aharanov-Bohm interferometry with Fourier methods, we visualize spatially resolved current flow and image FP resonances due to p-n-p cavity modes. The coherence of the standing-wave edge states is revealed by observing a new family of FP resonances, which coexist with the bulk resonances. The edge resonances have periodicity distinct from that of the bulk states manifest in a repeated spatial redistribution of current on and off the FP resonances. This behavior is accompanied by a modulation of the multiple Andreev reflection amplitude on-and-off resonance, indicating that electrons propagate ballistically in a fully coherent fashion. These results, which were not anticipated by theory, provide a practical route to developing electron analog of optical FP resonators at the graphene edge.

Artificial spin systems consist of mesoscopic single domain magnetic elements, typically arranged on two-dimensional lattices and coupled via magnetostatic interactions. The advantage of such artificial spin systems is the high tunability of the array geometry and nanomagnet parameters available with modern electron beam lithography methods. Well-known examples are frustrated magnetic systems such as the artificial square ice and the artificial kagome ice. Due to the direct and novel physical insight they provide, artificial spin ices have stimulated intense theoretical and experimental work. Despite the great progress in the understanding of the frustration and interactions between the nanomagnets in different lattice geometries, there is very little work reported on magnetic phase transitions in artificial spin ice. Very little is known about the critical properties of artificial square and kagome spin ice. In this thesis, the ordering phenomena under thermodynamic equilibrium conditions of thermally active artificial spin ice systems were characterized. The main goal of this thesis was to achieve a better understanding of ordering phenomena in artificial spin systems, specifically to investigate magnetic correlations and magnetic phase transitions in thermally active square and kagome ice. It was possible for the first time to detect signatures of the predicted phase transitions in artificial kagome spin ice using low energy muon spin rotation, as well as to gain a deeper understanding of these phases using synchrotron x-ray scattering. It was shown that kagome ice II phase is a genuine Coulomb phase and that in the kagome ice I phase, the system exhibits classical spin liquid behaviour. In addition, a first quantitative analysis of a continuous antiferromagnetic phase transition in artificial square ice was performed both experimentally using synchrotron x-ray scattering and theoretically using Monte Carlo simulations. The critical exponents of the transition were obtained that are compatible with the two-dimensional Ising universality class. By taking advantage of the flexibility to vary the nanomagnet parameters in artificial square ice, the role of out of equilibrium dynamics, that originates from the proximity of the blocking temperature to the transition temperature, was also demonstrated. Additionally, thermally active circular Co/Pt nanodisks with out-of-plane magnetization were created that exhibit a transition from a frozen to a superparamagnetic state. This work establishes a framework towards investigations of critical properties and out of equilibrium effects at the phase transitions in artificial spin systems.

The study of magnetic correlations in dipolar-coupled nanomagnet systems with synchrotron x-ray scattering provides a means to uncover emergent phenomena and exotic phases, in particular in systems with thermally active magnetic moments. From the diffuse signal of soft x-ray resonant magnetic scattering, we have measured magnetic correlations in a highly dynamic artificial kagome spin ice with sub-70-nm Permalloy nanomagnets. On comparing experimental scattering patterns with Monte Carlo simulations based on a needle-dipole model, we conclude that kagome ice I phase correlations exist in our experimental system even in the presence of moment fluctuations, which is analogous to bulk spin ice and spin liquid behavior. In addition, we describe the emergence of quasi-pinch-points in the magnetic diffuse scattering in the kagome ice I phase. These quasi-pinch-points bear similarities to the fully developed pinch points with singularities of a magnetic Coulomb phase, and continually evolve into the latter on lowering the temperature. The possibility to measure magnetic diffuse scattering with soft x rays opens the way to study magnetic correlations in a variety of nanomagnetic systems., 8 pages, 5 figures; http://journals.aps.org/prb/abstract/10.1103/PhysRevB.93.224413

We consider coupled atomic-molecular Bose-Einstein condensate system in a quasi-one-dimensional trap. In the vicinity of a Feshbach resonance the system can reveal soliton-like behavior. We analyze bright soliton solutions for the system in the trap and in the presence of the interactions between particles. We show that with increasing number of particles in the system two bright soliton solutions start resembling dark soliton profiles known in an atomic Bose-Einstein condensate with repulsive interactions between atoms. We analyze also methods for experimental preparation and detection of the soliton states.

Materials with interacting magnetic degrees of freedom display a rich variety of magnetic behaviour that can lead to novel collective equilibrium and out-of-equilibrium phenomena. In equilibrium, thermodynamic phases appear with the associated phase transitions providing a characteristic signature of the underlying collective behaviour. Here we create a thermally active artificial kagome spin ice that is made up of a large array of dipolar interacting nanomagnets and undergoes phase transitions predicted by microscopic theory. We use low energy muon spectroscopy to probe the dynamic behaviour of the interacting nanomagnets and observe peaks in the muon relaxation rate that can be identified with the critical temperatures of the predicted phase transitions. This provides experimental evidence that a frustrated magnetic metamaterial can be engineered to admit thermodynamic phases., Recently, periodic arrays of thermally active nanomagnets with bistable magnetization have been built which mimic the behaviour of frustrated magnets and model Ising systems. Here, the authors use muon spin relaxation to evidence thermodynamic phase transitions in an artificial kagome ice system.

We analyze the role of orbital degeneracy in possible magnetic and orbital instabilities by solving exactly a two-site molecule with two orbitals of either $e_g$ or $t_{2g}$ symmetry at quarter-filling. As a generic feature of both models one finds that the spin and orbital correlations have opposite signs in the low temperature regime when the orbitals are degenerate, in agreement with the Goodenough-Kanamori rules. While Hund's exchange coupling $J_H$ induces ferromagnetic spin correlations in both models, it is more efficient for $t_{2g}$ orbitals where the orbital quantum number is conserved along the hopping processes. We show that the ground state and finite temperature properties may change even qualitatively with increasing Coulomb interaction when the crystal field splitting of the two orbitals is finite, and the Goodenough-Kanamori rules may not be followed., 25 pages, 12 figures, JPCM style

The variational wave function proposed by Bartkowski (1972) to treat the ground state of a quantum antiferromagnet is generalized to arbitrary spin. We derive the fundamental equations of this method for the energy and magnetization by using a local cluster expansion. The leading order corrections to the wave function in the limit of either large spin S or lattice dimension D are identified. The good quality of the wave function is confirmed by the ground state energy of E0 = -0.3340J obtained for the Heisenberg S = 1/2 antiferromagnet on the square lattice. We present results obtained for the system of two planes and for three-dimensional SC and BCC lattices, as well as for the three-dimensional anisotropic Heisenberg model. It is found that the quantum fluctuations in a two-plane system are already closer to a three-dimensional than to a two-dimensional antiferromagnet while a weak interplane coupling in the latter case hardly influences the nearest-neighbour spin correlations within the planes.

We summarize some characteristic features of the frustrated magnetic interactions in spin-orbital models adequate for cubic transition metal oxides with orbital degeneracy. A generic tendency towards dimerization, found already in the degenerate Hubbard model, is confirmed for $t_{2g}$ but not for $e_g$ systems. In the $t_{2g}$ case the quantum orbital fluctuations are more pronounced and contribute to a stronger competition between different magnetic and orbital states. Therefore the orbital liquid states exist in some undoped $t_{2g}$ systems, while in the manganites such states can be triggered only by doping., 9 pages, 5 figures

We investigate the stability of the charge exchange (CE) phase within a microscopic model which describes a single plane as in La$_{0.5}$Sr$_{1.5}$MnO$_4$. The model includes Coulomb interactions (on-site and intersite), the Jahn-Teller term and the superexchange interactions due to $e_g$ and $t_{2g}$ electrons. By investigating the phase diagram at T=0 in mean-field approximation we conclude that the superexchange interactions can stabilize the CE phase, but only if they are stronger than estimated from spectroscopy., 4 pages, 3 figures

${\mathrm{CoAl}}_{2}{\mathrm{O}}_{4}$ spinel with magnetic ${\mathrm{Co}}^{2+}$ ions on the diamond lattice is known to be magnetically frustrated. We compare neutron single-crystal diffraction patterns measured in zero and applied magnetic fields with the ones obtained from classical Monte Carlo models. In simulations we test the influence of various parameters on diffraction patterns: the ratio of nearest-, ${J}_{1}$, and next-nearest-, ${J}_{2}$, neighbor interactions, magnetic field applied along the principal crystallographic directions, and random disorder on the $A({\mathrm{Co}}^{2+})$ and $B({\mathrm{Al}}^{3+})$ sites. We conclude that the models considered so far explain the broadening of magnetic Bragg peaks in zero magnetic field and their anisotropic response to applied magnetic field only partly. As bulk properties of our single crystal are isotropic, we suggest that its microstructure, specifically $\ensuremath{\langle}111\ensuremath{\rangle}$-twin boundaries, could be a reason for the nonconventional magnetic order in ${\mathrm{CoAl}}_{2}{\mathrm{O}}_{4}$.

In a recent experimental paper [Bid et al., Nature 466, 585 (2010)] a qualitative confirmation of the existence of upstream neutral modes at the $\ensuremath{\nu}=\frac{2}{3}$ quantum Hall edge was reported. Using the chiral Luttinger liquid theory of the quantum Hall edge we develop a quantitative model of the experiment of Bid et al. A good quantitative agreement of our theory with the experimental data reinforces the conclusion of the existence of the upstream neutral mode. Our model also enables us to extract important quantitative information about nonequilibrium processes in Ohmic and tunneling contacts from the experimental data. In particular, for $\ensuremath{\nu}=\frac{2}{3}$, we find a power-law dependence of the neutral mode temperature on the charge current injected from the Ohmic contact.

Using the Jordan-Wigner fermionization, Green function approach and continued fractions we examine rigorously the local magnetizations and the local static susceptibilities of the spin-1/2 XX chain in a transverse field with regularly varying exchange interactions. We discuss our findings from a viewpoint of the strong-coupling approach.

Using an exact diagonalization method within the dynamical mean-field theory we found stable stripe phases in the two-dimensional Hubbard model doped by $0.03l\ensuremath{\delta}l0.2$ holes, with a crossover from diagonal to vertical site-centered stripes at doping $\ensuremath{\delta}\ensuremath{\simeq}0.05$. The doping dependence of the size of magnetic domains and chemical potential shift $\ensuremath{\Delta}\ensuremath{\mu}\ensuremath{\propto}\ensuremath{-}{\ensuremath{\delta}}^{2}$ are in quantitative agreement with the experimental results for ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}$. The one-dimensional metallic behavior along the domain walls explains the observed suppression of spectral weight along the Brillouin zone diagonal.

We use continued fractions for a study of the thermodynamic properties of the periodic nonuniform spin-1/2 isotropic XY chain in a non-random/random (Lorentzian) transverse field. The obtained results permit to examine the influence of a magnetic field and randomness on the spin-Peierls dimerization.

We present the charge and magnetization density distribution in various stripe phases obtained for twodimensional models of correlated electrons solved within the Hartree-Fock approximation and a variational local ansatz. Apart from the Hubbard model with local Coulomb interaction U, we investigate its two extensions by adding either static Peierls electron-lattice coupling, or the correlated hopping term in the so-called Hirsch model. It has been found that the stripe ordering is robust and occurs in underdoped ( d51/8) and overdoped (d51/4) systems. At intermediate values of U in underdoped systems (d51/8) local correlations stabilize the vertical ~01! antiferromagnetic domains, separated by nonmagnetic domain walls filled by one doped hole per two wall atoms. A stripe phase with the same size of magnetic domains and an increased filling of one hole per one wall atom is stable for overdoped (d51/4) systems. At larger values of U, both structures are replaced by more extended magnetic domain walls oriented along the ~11! direction. These findings agree qualitatively with the experimental results. @S0163-1829~99!13733-0# Nonhomogeneous charge and spin ordering in real space, so-called stripe phases, attracted much attention due to their possible role in the high-temperature superconductivity of the cuprates. In contrast to the high-temperature superconductivity itself, the stripe instability of the effective Hubbard model describing a normal phase of the cuprates was first predicted in the theory within Hartree-Fock ~HF! calculations on finite clusters with periodic boundary conditions, 1 and later verified experimentally. The theoretical discovery was soon followed by the experimental observation of incommensurate spin correlations in La22xSrxCuO4 by neutron scattering experiments. 2 However, a clear identification of a stripe phase was possible only more recently in La1.62xNd0.4SrxCuO4, where the stripe structures are pinned. Neutron scattering experiments 3‐5 performed on La1.62xNd0.4SrxCuO4 demonstrate the existence of the stripe phases, with antiferromagnetic ~AF! spin domains, separated by charged domain walls. Neutron diffraction measurements on single crystals with the hole doping ratio d.1/8 revealed the existence of two kinds of incommensurate superlattices peaks. 4 In the reciprocal space the magnetic peaks are satellites of the AF Bragg reflection at k5(p,p); they are displaced along the (10) and (01) directions to k5@p(1 62h),p# and k5@p,p(162h)#, respectively, while at the same time the charge-order x-ray satellite diffraction peaks are displaced by 4h with respect to the peak at k5(0,0) found for a uniform distribution. Experiments at low temperature for La1.62xNd0.4SrxCuO4 showed that h.d at small doping d

The mixed valence character of the holes at $\mathrm{Cu}{(3d}_{{x}^{2}\ensuremath{-}{y}^{2}})$ and $\mathrm{O}{(2p}_{\ensuremath{\sigma}})$ orbitals in copper oxides is implemented by wave-function corrections to the spin-fermion model. We show that the hybridization effects lead to drastic changes in the distribution of spectral weight and the dispersion of the quasiparticle band with decreasing charge-transfer energy \ensuremath{\Delta}. For $\ensuremath{\Delta}=2.0--3.0\mathrm{eV}$ the quasiparticle dispersion resembles that of the $t\ensuremath{-}J$ model with extended hopping and agrees qualitatively with the experimental data in insulating ${\mathrm{Sr}}_{2}{\mathrm{CuO}}_{2}{\mathrm{Cl}}_{2},$ demonstrating that the quasiparticle states due to ${p}_{\ensuremath{\sigma}}$ orbitals play the dominating role for the realistic parameters.

We have studied the phase diagram and excitations of the spin-orbital model derived for a three dimensional perovskite lattice, as in KCuF_3. The results demonstrate that the orbital degeneracy drastically increases quantum fluctuations and suppresses the classical long-range order near the multicritical point in the mean-field phase diagram. This generates a qualitatively new spin liquid, providing the first example of a valence bond ground state in three dimensions., Comment: 4 pages, ReVTeX, 4 figures, submitted to Phys. Rev. Lett

Using the formalism introduced by Harris and Lange [Phys. Rev. 157, 295 (1967)] explicit expressions for partial sum rules of the individual Hubbard bands in the large-negative-U limit are derived. The one-particle spectrum, optical spectrum, as well as charge- and spin-response functions are considered. The approach gives a transparent description of the main features of these spectra. The main sum rules depend on only two independent nearest-neighbor expectation values which are estimated in the ground state using numerical calculations, exact results, and linear-spin-wave theory. Simple expressions for the intensities of the upper and lower Hubbard bands in the optical conductivity show that this spectrum is extremely sensitive on details of the ground state. The charge-density wave and superconducting phases are clearly distinguishable and even the transition to the broken-symmetry state may have a detectable influence on the conductivity.

We investigate the influence of frustration on the quasiparticle dispersion in the {ital t}-{ital J} and {ital t}-{ital t}{sup {prime}}-{ital J} models using the linear spin-wave theory and self-consistent Born approximation. The next-neighbor antiferromagnetic interactions, simulating the effect of doping within CuO{sub 2} planes of high-{ital T}{sub {ital c}} superconductors, lead to a drastic reduction of the quasiparticle bandwidth with the increasing frustration in a wide range of {ital t}, {ital t}{sup {prime}}, and {ital J} parameters. The low-energy quasiparticle band (with the width only {approximately}0.3 eV) obtained for the realistic values of parameters and a very weak quasiparticle state at the (0,0) point in the Brillouin zone agree quite well with the flat band observed at the Fermi level in the angle-resolved photoemission experiments for Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub 8+{delta}}. {copyright} {ital 1996 The American Physical Society.}

Treating the hole-magnon interaction within the self-consistent Born approximation, we demonstrate that the low-energy quasiparticles that occur in the t-J model due to quantum fluctuations of the spin system survive in the models including free hole propagation on the sublattices. The quasiparticle dispersion and weight are found to be strongly dependent on the next-neighbor hopping parameter. The flat band observed near the X point in the high-temperature superconductors is reproduced, but not for the realistic parameters that correspond to the hole-doped system.

The three-band Hubbard Hamiltonian with an attractive oxygen-oxygen interaction [ital U][sub [ital p][ital p]] is investigated using the Hartree-Fock approximation. Such a Hamiltonian is assumed to be a generic model for CuO[sub 2] planes of high-[ital T][sub [ital c]] superconductors. Both superconducting and antiferromagnetic phases are found in the separate regions of the numerically obtained ([ital U][sub [ital p][ital p]],[delta]) phase diagrams, where [delta] is the hole doping. It is found that the region of stability of the superconducting phase is enhanced with decreasing values of the charge-transfer gap, in good qualitative agreement with the experimental findings.