arXiv subjects

Andrzej M. Oleś

Publications and source records attributed to Andrzej M. Oleś.

At least 73 records · Page 4Linked to original sources

arXiv2016

Exotic Spin-Orbital Physics in Hybrid Oxides

We compare the effective spin-orbital super\-exchange triggered by magnetic $3d$ impurities with $d^3$ and $d^2$ configurations and either no orbital degree of freedom (orbital dilution) or hole replacing a doublon (charge dilution) in a $4d^4$ Mott insulator with $S=1$ spins. Impurities causing orbital dilution act either as spin defects decoupled from the surrounding ions, or generate orbital polarons along $d^3$-$d^4$ hybrid bonds. The exchange on these bonds determines which orbital is occupied by a doublon on the host site. In case of charge dilution by $3d^2$ impurities additional $\propto T_i^+T_j^+$ terms arise which enhance orbital fluctuations. We show that such terms may radically change orbital pattern at relatively low doping by $x=1/8$ hole defects. Our findings provide new perspective for future theoretical and experimental studies of doped transition metal oxides.

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arXiv2016

Phase diagram and spin correlations of the Kitaev-Heisenberg model: Importance of quantum effects

We explore the phase diagram of the Kitaev-Heisenberg model with nearest neighbor interactions on the honeycomb lattice using the exact diagonalization of finite systems combined with the cluster mean field approximation, and supplemented by the insights from the linear spin-wave and second--order perturbation theories. This study confirms that by varying the balance between the Heisenberg and Kitaev term, frustrated exchange interactions stabilize in this model four phases with magnetic long range order: Néel phase, ferromagnetic phase, and two other phases with coexisting antiferromagnetic and ferromagnetic bonds, zigzag and stripy phases. They are separated by two disordered quantum spin-liquid phases, and the one with ferromagnetic Kitaev interactions has a substantially broader range of stability as the neighboring competing ordered phases, ferromagnetic and stripy, have very weak quantum fluctuations. Focusing on the quantum spin-liquid phases, we study spatial spin correlations and dynamic spin structure factor of the model by the exact diagonalization technique, and discuss the evolution of gapped low-energy spin response across the quantum phase transitions between the disordered spin liquid and magnetic phases with long range order.

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arXiv2016

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

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

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arXiv2016

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

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

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arXiv2016

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

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

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arXiv2016

Multiband $d-p$ model and self-doping in the electronic structure of Ba$_2$IrO$_4$

We introduce and investigate the multiband $d-p$ model describing a IrO$_4$ layer (such as realized in Ba$_2$IrO$_4$) where all $34$ orbitals per unit cell are partly occupied, i.e., $t_{2g}$ and $e_g$ orbitals at iridium and $2p$ orbitals at oxygen ions. The model takes into account anisotropic iridium-oxygen $d-p$ and oxygen-oxygen $p-p$ hopping processes, crystal-field splittings, spin-orbit coupling, and the on-site Coulomb interactions, both at iridium and at oxygen ions. We show that the predictions based on assumed idealized ionic configuration (with $n_0=5+4\times 6=29$ electrons per IrO$_4$ unit) do not explain well the independent \textit{ab initio} data and the experimental data for Ba$_2$IrO$_4$. Instead we find that the total electron density in the $d-p$ states is smaller, $n=29-x 0$). When we fix $x=1$, the predictions for the $d-p$ model become more realistic and weakly insulating antiferromagnetic ground state with the moments lying within IrO$_2$ planes along (110) direction is found, in agreement with experiment and \textit{ab initio} data. We also show that: (i) holes delocalize over the oxygen orbitals and the electron density at iridium ions is enhanced, hence (ii) their $e_g$ orbitals are occupied by more than one electron and have to be included in the multiband $d-p$ model describing iridates.

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arXiv2015

Defects, disorder and strong electron correlations in orbital degenerate, doped Mott insulators

We elucidate the effects of defect disorder and $e$-$e$ interaction on the spectral density of the defect states emerging in the Mott-Hubbard gap of doped transition-metal oxides, such as Y$_{1-x}$Ca$_{x}$VO$_{3}$. A soft gap of kinetic origin develops in the defect band and survives defect disorder for $e$-$e$ interaction strengths comparable to the defect potential and hopping integral values above a doping dependent threshold, otherwise only a pseudogap persists. These two regimes naturally emerge in the statistical distribution of gaps among different defect realizations, which turns out to be of Weibull type. Its shape parameter $k$ determines the exponent of the power-law dependence of the density of states at the chemical potential ($k-1$) and hence distinguishes between the soft gap ($k\geq2$) and the pseudogap ($k<2$) regimes. Both $k$ and the effective gap scale with the hopping integral and the $e$-$e$ interaction in a wide doping range. The motion of doped holes is confined by the closest defect potential and the overall spin-orbital structure. Such a generic behavior leads to complex non-hydrogen-like defect states that tend to preserve the underlying $C$-type spin and $G$-type orbital order and can be detected and analyzed via scanning tunneling microscopy.

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arXiv2015

Quantum entanglement in the one-dimensional spin-orbital SU(2)$\otimes XXZ$ model

We investigate the phase diagram and the spin-orbital entanglement of a one-dimensional SU(2)$\otimes XXZ$ model with SU(2) spin exchange and anisotropic $XXZ$ orbital exchange interactions and negative exchange coupling. As a unique feature, the spin-orbital entanglement entropy in the entangled ground states increases here linearly with system size. In the case of Ising orbital interactions we identify an emergent phase with long-range spin-singlet dimer correlations triggered by a quadrupling of correlations in the orbital sector. The peculiar translational invariant spin-singlet dimer phase has finite von Neumann entanglement entropy and survives when orbital quantum fluctuations are included. It even persists in the isotropic SU(2)$\otimes$SU(2) limit. Surprisingly, for finite transverse orbital coupling the long-range spin singlet correlations also coexist in the antiferromagnetic spin and alternating orbital phase making this phase also unconventional. Moreover we also find a complementary orbital singlet phase that exists in the isotropic case but does not extend to the Ising limit. The nature of entanglement appears essentially different from that found in the frequently discussed model with positive coupling. Furthermore we investigate the collective spin and orbital wave excitations of the disentangled ferromagnetic-spin/ferro-orbital ground state and explore the continuum of spin-orbital excitations. Interestingly one finds among the latter excitations two modes of exciton bound states. Their spin-orbital correlations differ from the remaining continuum states and exhibit logarithmic scaling of the von Neumann entropy with increasing system size.

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arXiv2015

Novel Spin-Orbital Phases Induced by Orbital Dilution

We demonstrate that magnetic $3d$ impurities with $S=3/2$ spins and no orbital degree of freedom induce changes of spin-orbital order in a $4d^4$ Mott insulator with $S=1$ spins. Impurities act either as spin defects which decouple from the surrounding ions, or trigger orbital polarons along $3d$-$4d$ bonds. The $4d$-$4d$ superexchange in the host $J_{\rm host}$ competes with $3d$-$4d$ superexchange $J_{\rm imp}$ --- it depends on which orbital is doubly occupied. The spin-orbital order within the host is totally modified at doping $x=1/4$. Our findings provide new perspective for future theoretical and experimental studies of doped transition-metal oxides.

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arXiv2015

Entanglement Driven Phase Transitions in Spin-Orbital Models

To demonstrate the role played by the von Neumann entropy spectra in quantum phase transitions we investigate the one-dimensional anisotropic SU(2)$\otimes XXZ$ spin-orbital model with negative exchange parameter. In the case of classical Ising orbital interactions we discover an unexpected novel phase with Majumdar-Ghosh-like spin-singlet dimer correlations triggered by spin-orbital entanglement and having $k=π/2$ orbital correlations, while all the other phases are disentangled. For anisotropic $XXZ$ orbital interactions both spin-orbital entanglement and spin-dimer correlations extend to the antiferro-spin/alternating-orbital phase. This quantum phase provides a unique example of two coupled order parameters which change the character of the phase transition from first-order to continuous. Hereby we have established the von Neumann entropy spectral function as a valuable tool to identify the change of ground state degeneracies and of the spin-orbital entanglement of elementary excitations in quantum phase transitions.

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arXiv2015

Fermi-liquid Landau parameters for a nondegenerate band: Spin and charge instabilities in the extended Hubbard model

We investigate the Landau parameters for the instabilities in spin and charge channels in the nondegenerate extended Hubbard model with intersite Coulomb and exchange interactions. To this aim we use the spin rotationally invariant slave boson approach and we determine the necessary inverse propagator matrix. The analytically derived spin Landau parameter $F_0^a$ for the half filled band uncovers the intrinsic instability of the nondegenerate Hubbard model towards ferromagnetism --- negative intersite exchange interaction triggers a ferromagnetic instability at half filling before the metal-insulator transition, indicated by the divergence of the magnetic susceptibility at $F_0^a=-1$. This result is general and the instability occurs in the strongly correlated metallic regime for any lattice, in three or two dimensions. Next as an illustrative example we present numerical results obtained for the cubic lattice with nearest neighbor exchange $J$ and Coulomb $V$ elements and arbitrary electron density. One finds that the range of small doping near half filling is the most unstable one towards spin polarization, but only in the case of ferromagnetic intersite exchange $J<0$. Charge Landau parameter $F_0^s$ is lowered near half filling by increasing $U$ when the intersite Coulomb interaction $V$ is attractive, but in contrast to $F_0^a$ at $J<0$ it requires an attraction beyond a critical value $V_c$ to generate the divergence of the charge susceptibility at $F_0^s=-1$ in the metallic phase. This instability was found for a broad range of electronic filling away from half filling for moderate attraction.

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arXiv2015

Charge transfer model for the electronic structure of layered ruthenates

Motivated by the earlier experimental results and \textit{ab initio} studies on the electronic structure of layered ruthenates (Sr$_2$RuO$_4$ and Ca$_2$RuO$_4$) we introduce and investigate the multiband $d-p$ charge transfer model describing a single RuO$_4$ layer, similar to the charge transfer model for a single CuO$_2$ plane including apical oxygen orbitals in high $T_c$ cuprates. The present model takes into account nearest-neighbor anisotropic ruthenium-oxygen $d-p$ and oxygen-oxygen $p-p$ hopping elements, crystal-field splittings and spin-orbit coupling. The intraorbital Coulomb repulsion and Hund's exchange are defined not only at ruthenium but also at oxygen ions. Our results demonstrate that the RuO$_4$ layer cannot be regarded to be a pure ruthenium $t_{2g}$ system. We examine a different scenario in which ruthenium $e_g$ orbitals are partly occupied and highlight the significance of oxygen orbitals. We point out that the predictions of an idealized model based on ionic configuration (with $n_0=4+4\times 6=28$ electrons per RuO$_4$ unit) do not agree with the experimental facts for Sr$_2$RuO$_4$ which support our finding that the electron number in the $d-p$ states is significantly smaller. In fact, we find the electron occupation of $d$ and $p$ orbitals for a single RuO$_4$ unit $n=28-x$, being smaller by at least 1--1.5 electrons from that in the ionic model and corresponding to self-doping with $x\simeq 1.5$.

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arXiv2015

Polaron states in a CuO chain

We introduce a one-dimensional model for a CuO chain, with holes and $S=1/2$ spins localized in $3d_{x^2-y^2}$ orbitals, and $p_σ$ oxygen orbitals without holes in the ground state. We consider a single hole doped at an oxygen site and study its propagation by spin-flip processes. We develop the Green's function method and treat the hole-spin coupling in the self-consistent Born approximation, similar to that successfully used to study polarons in the regular $t$-$J$ model. We present an analytical solution of the problem and investigate whether the numerical integration is a good approximation to this solution.

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arXiv2015

Quantum phase transitions in the Kitaev--Heisenberg model on a single hexagon

We present a detailed analysis of the Kitaev--Heisenberg model on a single hexagon. The energy spectra and spin--spin correlations obtained using exact diagonalisation indicate quantum phase transitions between antiferromagnetic and anisotropic spin correlations when the Kitaev interactions increase. In cluster mean-field approach frustrated nearest neighbor exchange stabilizes the stripe phase in between the Néel phase and frustrated one which evolves towards the Kitaev spin liquid.

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arXiv2015

Spin-Orbital Order Modified by Orbital Dilution in Transition Metal Oxides: From Spin Defects to Frustrated Spins Polarizing Host Orbitals

We study the $3d$ substitution in $4d$ transition metal oxides in the cases of $3d^3$ doping at either $3d^2$ or $4d^4$ sites which realize orbital dilution. We derive the effective $3d-4d$ (or $3d-3d$) superexchange in a Mott insulator with different ionic valencies, underlining the emerging structure of the spin-orbital coupling between the impurity and the host sites and demonstrate that it is qualitatively different from that encountered in the host itself. This derivation shows that the interaction between the host and the impurity depends in a crucial way on the type of doubly occupied $t_{2g}$ orbital. One finds that in some cases, due to the quench of the orbital degree of freedom at the $3d$ impurity, the spin and orbital order within the host is drastically modified by doping. The impurity acts either as a spin defect accompanied by an orbital vacancy in the spin-orbital structure when the host-impurity coupling is weak, or it favors doubly occupied active orbitals (orbital polarons) along the $3d-4d$ bond leading to antiferromagnetic or ferromagnetic spin coupling. This competition between different magnetic couplings leads to quite different ground states. We find that magnetic frustration and spin degeneracy can be lifted by the quantum orbital flips of the host but they are robust in special regions of the incommensurate phase diagram. The spin-orbit coupling can lead to anisotropic spin and orbital patterns along the symmetry directions and cause a radical modification of the order imposed by the spin-orbital superexchange. Our findings are expected to be of importance for future theoretical understanding of experimental results for doped $4d$ transition metal oxides doped with $3d^3$ ions. We suggest how the local or global changes of the spin-orbital order induced by such impurities could be detected experimentally.

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arXiv2014

Quantum versus classical polarons in a ferromagnetic CuO$_3$-like chain

We present an exact solution for an itinerant hole added into the oxygen orbitals of a CuO$_{3}$-like ferromagnetic chain. Using the Green's function method, the quantum polarons obtained for the Heisenberg SU(2) interaction between localized Cu spins are compared with the polarons in the Ising chain. We find that magnons with large energy are favorable towards quasiparticle existence, even in the case of relatively modest electron-magnon coupling. We observe two quasiparticle states with dispersion $\sim 2t$ each, which emerge from the incoherent continuum when the exchange coupling $J$ increases. Quantum fluctuations in the spin system modify the incoherent part of the spectrum and change the spectral function qualitatively, beyond the bands derived from the perturbation theory.

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arXiv2014

Frustration and Entanglement in Compass and Spin-Orbital Models

We review the consequences of intrinsic frustration of the orbital superexchange and of spin-orbital entanglement. While Heisenberg perturbing interactions remove frustration in the compass model, the lowest columnar excitations are robust in the nanoscopic compass clusters and might be used for quantum computations. Entangled spin-orbital states determine the ground states in some cases, while in others concern excited states and lead to measurable consequences, as in the $R$VO$_3$ perovskites. On-site entanglement for strong spin-orbit coupling generates the frustrated Kitaev-Heisenberg model with a rich magnetic phase diagram on the honeycomb lattice. Frustration is here reflected in hole propagation which changes from coherent in an antiferromagnet via hidden quasiparticles in zigzag and stripe phases to entirely incoherent one in the Kitaev spin liquid.

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arXiv2014

Exact treatment of magnetism-driven ferroelectricity in the one-dimensional compass model

We consider a class of one-dimensional compass models with antisymmetric Dzyaloshinskii-Moriya exchange interaction in an external magnetic field. Based on the exact solution derived by means of Jordan-Wigner transformation, we study the excitation gap, spin correlations, ground-state degeneracy, and critical properties at phase transitions. The phase diagram at finite electric and magnetic field consists of three phases: ferromagnetic, canted antiferromagnetic, and chiral. Dzyaloshinskii-Moriya interaction induces an electrical polarization in the ground state of the chiral phase, where the nonlocal string order and special features of entanglement spectra arise, while strong chiral correlations emerge at finite temperature in the other phases and are controlled by a gap between the nonchiral ground state and the chiral excitations. We further show that the magnetoelectric effects in all phases disappear above a typical temperature corresponding to the total bandwidth of the effective fermionic model. To this end we explore the entropy, specific heat, magnetization, electric polarization, and the magnetoelectric tensor at finite temperature. We identify rather peculiar specific-heat and polarization behavior of the compass model which follows from highly frustrated interactions.

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