arXiv subjects

Andrzej M. Oles

Publications and source records attributed to Andrzej M. Oles.

At least 37 records · Page 2Linked to original sources

arXiv2009

Exact solution for a quantum compass ladder

We introduce a spin ladder with antiferromagnetic Ising ZZ interactions along the legs, and interactions on the rungs which interpolate between the Ising ladder and the quantum compass ladder. We show that the entire energy spectrum of the ladder may be determined exactly for finite number of spins 2N by mapping to the quantum Ising chain and using Jordan-Wigner transformation in invariant subspaces. We also demonstrate that subspaces with spin defects lead to excited states using finite size scaling, and the ground state corresponds to the quantum Ising model without defects. At the quantum phase transition to maximally frustrated interactions of the compass ladder, the ZZ spin correlation function on the rungs collapses to zero and the ground state degeneracy increases by 2. We formulate a systematic method to calculate the partition function for a mesoscopic system, and employ it to demonstrate that fragmentation of the compass ladder by kink defects increases with increasing temperature. The obtained heat capacity of a large compass ladder consisting of 2N=104 spins reveals two relevant energy scales and has a broad maximum due to dense energy spectrum. The present exact results elucidate the nature of the quantum phase transition from ordered to disordered ground state found in the compass model in two dimensions.

cond-mat.str-el↗

arXiv2009

Compass model on a ladder and square clusters

We obtained exact heat capacities of the quantum compass model on the square L x L clusters with L=2,3,4,5 using Kernel Polynomial Method and compare them with heat capacity of a large compass ladder. Intersite correlations found in the ground state for these systems demonstrate that the quantum compass model differs from its classical version.

cond-mat.str-el↗

arXiv2009

Spin-wave theory for dimerized ferromagnetic chains

We describe a Peierls dimerization which occurs in ferromagnetic spin chains at finite temperature, within the modified spin-wave theory. Usual spin-wave theory is modified by introducing a Lagrange multiplier which enforces a nonmagnetic state at finite temperature. It is shown that this method gives results in excellent agreement with the density--matrix renormalization group applied to transfer matrices for dimerized ferromagnetic chains. We study bond correlation functions and explore the characteristic features of dimerization in the specific heat.

cond-mat.str-el↗

arXiv2009

Orbitally induced string formation in the spin-orbital polarons

We study the spectral function of a single hole doped into the (a,b) plane of the Mott insulator LaVO$_3$, with antiferromagnetic (AF) spin order of S=1 spins accompanied by alternating orbital (AO) order of active $\{d_{yz},d_{zx}\}$ orbitals. Starting from the respective t-J model, with spin-orbital superexchange and effective three-site hopping terms, we derive the polaron Hamiltonian and show that a hole couples simultaneously to the collective excitations of the AF/AO phase, magnons and orbitons. Next, we solve this polaron problem using the self-consistent Born approximation and find a stable quasiparticle solution -- a spin-orbital polaron. We show that the spin-orbital polaron resembles the orbital polaron found in $e_g$ systems, as e.g. in K$_2$CuF$_4$ or (to some extent) in LaMnO$_3$, and that the hole may be seen as confined in a string-like potential. However, the spins also play a crucial role in the formation of this polaron -- we explain how the orbital degrees of freedom: (i) confine the spin dynamics acting on the hole as the classical Ising spins, and (ii) generate the string potential which is of the joint spin-orbital character. Finally, we discuss the impact of the results presented here on the understanding of the phase diagrams of the lightly doped cubic vanadates.

cond-mat.str-el↗

arXiv2009

Spin--orbital physics in transition metal oxides

We present the main features of the spin-orbital superexchange which describes the magnetic and optical properties of Mott insulators with orbital degrees of freedom. In contrast to the SU(2) symmetry of spin superexchange, the orbital part of the superexchange obeys the lower cubic symmetry of the lattice and is intrinsically frustrated. This intrinsic frustration and spin-orbital entanglement induce enhanced quantum fluctuations, and we point out a few situations where this leads to disordered states. Strong coupling between the spin and orbital degrees of freedom is discussed on the example of the $R$VO$_3$ perovskites, with $R$ standing for rare-earth ion, La,...,Lu. We explain the observed evolution of the orbital $T_{\rm OO}$ and Néel $T_{N1}$ transition temperature in the $R$VO$_3$ series with decreasing ionic radius $r_R$. A few open problems and the current directions of research in the field of spin-orbital physics are pointed out.

cond-mat.str-el↗

arXiv2008

Reiter's polaron wavefunction applied to a $t_{2g}$ orbital t-J model

Using the self-consistent Born approximation we calculate Reiter's wavefunction for a single hole introduced into the undoped and orbitally ordered ground state of the t-J model with $t_{2g}$ orbital degrees of freedom. While the number of excitations is similar to the spin t-J model for a given J/t, a distinct structure of the calculated wavefunction and its momentum dependence is identified suggesting the formation of a novel type of mobile polarons.

cond-mat.str-el↗

arXiv2008

Spectral properties of orbital polarons in Mott insulators

We address the spectral properties of Mott insulators with orbital degrees of freedom, and investigate cases where the orbital symmetry leads to Ising-like superexchange in the orbital sector. The paradigm of a hole propagating by its coupling to quantum fluctuations, known from the spin t-J model, then no longer applies. We find instead that when one of the two orbital flavors is immobile, as in the Falicov-Kimball model, trapped orbital polarons coexist with free hole propagation emerging from the effective three-site hopping in the regime of large on-site Coulomb interaction U. The spectral functions are found analytically in this case within the retraceable path approximation in one and two dimensions. On the contrary, when both of the orbitals are active, as in the model for $t_{2g}$ electrons in two dimensions, we find propagating polarons with incoherent scattering dressing the moving hole and renormalizing the quasiparticle dispersion. Here, the spectral functions, calculated using the self-consistent Born approximation, are anisotropic and depend on the orbital flavor. Unbiased conclusions concerning the spectral properties are established by comparing the above results for the orbital t-J models with those obtained using the variational cluster approximation or exact diagonalization for the corresponding Hubbard models. The present work makes predictions concerning the essential features of photoemission spectra of certain fluorides and vanadates.

cond-mat.str-el↗

arXiv2008

Superconductivity of Mo3Sb7 from first principles

Superconductivity in Mo3Sb7 is analyzed using the combined electronic structure and phonon calculations, and the electron--phonon coupling constant λ_{ph}=0.54 is determined from first principles. This value explains the experimental value of the superconducting critical temperature T_c=2.2 K. The possible influence of spin fluctuations and spin gap on the superconductivity in Mo3Sb7 is discussed, and electron--paramagnon interaction is found to be weak.

cond-mat.supr-con↗

arXiv2008

Quantum Phase Transition in the One-Dimensional XZ Model

We introduce a one-dimensional (1D) XZ model with alternating $σ_i^zσ_{i+1}^z$ and $σ_i^xσ_{i+1}^x$ interactions on even/odd bonds, interpolating between the Ising model and the quantum compass model. We present two ways of its exact solution by: ($i$) mapping to the quantum Ising models, and ($ii$) using fermions with spin 1/2. In certain cases the nearest neighbor pseudospin correlations change discontinuously at the quantum phase transition, where one finds highly degenerate ground state of the 1D compass model.

cond-mat.str-el↗

arXiv2008

Frustration and entanglement in the $t_{2g}$ spin--orbital model on a triangular lattice: valence--bond and generalized liquid states

We consider the spin--orbital model for a magnetic system with singly occupied but triply degenerate $t_{2g}$ orbitals coupled into a planar, triangular lattice, as would be exemplified by NaTiO$_2$. We investigate the ground states of the model for interactions which interpolate between the limits of pure superexchange and purely direct exchange interactions. By considering ordered and dimerized states at the mean--field level, and by interpreting the results from exact diagonalization calculations on selected finite systems, we demonstrate that orbital interactions are always frustrated, and that orbital correlations are dictated by the spin state, manifesting an intrinsic entanglement of these degrees of freedom. In the absence of Hund coupling, the ground state changes from a highly resonating, dimer--based, symmetry--restored spin and orbital liquid phase, to one based on completely static, spin--singlet valence bonds. The generic properties of frustration and entanglement survive even when spins and orbitals are nominally decoupled in the ferromagnetic phases stabilized by a strong Hund coupling. By considering the same model on other lattices, we discuss the extent to which frustration is attributable separately to geometry and to interaction effects.

cond-mat.str-el↗

arXiv2007

Unidirectional d-wave superconducting domains in the two-dimensional t-J model

Motivated by the recently observed pattern of unidirectional domains in high-T_c superconductors [Y. Kohsaka et al., Science 315, 1380 (2007)], we investigate the emergence of spontaneous modulations in the d-wave superconducting resonating valence bond phase using the t-J model at x=1/8 doping. Half-filled charge domains separated by four lattice spacings are found to form along one of the crystal axis leading to modulated superconductivity with out-of-phase d-wave order parameters in neighboring domains. Both renormalized mean-field theory and variational Monte Carlo calculations yield that the energies of modulated and uniform phases are very close to each other.

cond-mat.str-el↗

arXiv2007

Origin of the Verwey transition in magnetite: Group theory, electronic structure, and lattice dynamics study

The Verwey phase transition in magnetite has been analyzed using the group theory methods. It is found that two order parameters with the symmetries $X_3$ and $Δ_5$ induce the structural transformation from the high-temperature cubic to the low-temperature monoclinic phase. The coupling between the order parameters is described by the Landau free energy functional. The electronic and crystal structure for the cubic and monoclinic phases were optimized using the {\it ab initio} density functional method. The electronic structure calculations were performed within the generalized gradient approximation including the on-site interactions between 3d electrons at iron ions -- the Coulomb element $U$ and Hund's exchange $J$. Only when these local interactions are taken into account, the phonon dispersion curves, obtained by the direct method for the cubic phase, reproduce the experimental data. It is shown that the interplay of local electron interations and the coupling to the lattice drives the phonon order parameters and is responsible for the opening of the gap at the Fermi energy. Thus, it is found that the metal-insulator transition in magnetite is promoted by local electron interactions, which significantly amplify the electron-phonon interaction and stabilize weak charge order coexisting with orbital order of the occupied $t_{2g}$ states at Fe ions. This provides a scenario to understand the fundamental problem of the origin of the Verwey transition in magnetite.

cond-mat.str-el↗

arXiv2007

Spin-orbital entanglement near quantum phase transitions

Spin-orbital entanglement in the ground state of a one-dimensional SU(2)$\otimes$SU(2) spin-orbital model is analyzed using exact diagonalization of finite chains. For $S=1/2$ spins and $T=1/2$ pseudospins one finds that the quantum entanglement is similar at the SU(4) symmetry point and in the spin-orbital valence bond state. We also show that quantum transitions in spin-orbital models turn out to be continuous under certain circumstances, in constrast to the discontinuous transitions in spin models with SU(2) symmetry.

cond-mat.str-el↗

arXiv2007

One-dimensional orbital fluctuations and the exotic magnetic properties of YVO$_3$

Starting from the Mott insulator picture for cubic vanadates, we derive and investigate the model of superexchange interactions between V$^{3+}$ ions, with nearly degenerate $t_{2g}$ orbitals occupied by two electrons each. The superexchange interactions are strongly frustrated and demonstrate a strong interrelation between possible types of magnetic and orbital order. We elucidate the prominent role played by fluctuations of $yz$ and $xz$ orbitals which generate ferromagnetic superexchange interactions even in the absence of Hund's exchange. In this limit we find orbital valence bond state which is replaced either by $C$-type antiferromagnetic order with weak $G$-type orbital order at increasing Hund's exchange, or instead by $G$-type antiferromagnetic order when the lattice distortions stabilize $C$-type orbital order. Both phases are observed in YVO$_3$ and we argue that a dimerized $C$-type antiferromagnetic phase with stronger and weaker FM bonds alternating along the c axis may be stabilized by large spin-orbital entropy at finite temperature. This suggests a scenario which explains the origin of the exotic $C$-AF order observed in YVO$_3$ in the regime of intermediate temperatures and allows one to specify the necessary ingredients of a more complete future theory.

cond-mat.str-el↗

arXiv2007

Orbital liquid in ferromagnetic manganites: The orbital Hubbard model for $e_g$ electrons

We have analyzed the symmetry properties and the ground state of an orbital Hubbard model with two orbital flavors, describing a partly filled spin-polarized $e_g$ band on a cubic lattice, as in ferromagnetic manganites. We demonstrate that the off-diagonal hopping responsible for transitions between $x^2-y^2$ and $3z^2-r^2$ orbitals, and the absence of SU(2) invariance in orbital space, have important implications. One finds that superexchange contributes in all orbital ordered states, the Nagaoka theorem does not apply, and the kinetic energy is much enhanced as compared with the spin case. Therefore, orbital ordered states are harder to stabilize in the Hartree-Fock approximation (HFA), and the onset of a uniform ferro-orbital polarization and antiferro-orbital instability are similar to each other, unlike in spin case. Next we formulate a cubic (gauge) invariant slave boson approach using the orbitals with complex coefficients. In the mean-field approximation it leads to the renormalization of the kinetic energy, and provides a reliable estimate for the ground state energy of the disordered state. Using this approach one finds that the HFA fails qualitatively in the regime of large Coulomb repulsion $U\to\infty$ -- the orbital order is unstable, and instead a strongly correlated orbital liquid with disordered orbitals is realized at any electron filling.

cond-mat.str-el↗

arXiv2007

Origin of charge density wave in the coupled spin ladders in Sr$_{14-x}$Ca$_x$Cu$_{24}$O$_{41}$

We formulate a d-p multiband charge transfer model for Cu$_2$O$_5$ coupled spin ladders, relevant for Cu$_2$O$_3$ plane of Sr$_{14-x}$Ca$_x$Cu$_{24}$O$_{41}$, and solve it using Hartree-Fock approximation. The results explain that (i) the charge density wave (CDW) with its periodicity dependent on doping is stabilized by purely electronic many-body interactions in a single spin ladder and (ii) the inclusion of the interladder interactions favors (disfavors) the stability of the CDW with odd (even) periodicity, respectively. This stays in agreement with recent experimental results and suggests the structure of the minimal microscopic model which should be considered in future more sophisticated studies.

cond-mat.str-el↗

arXiv2007

Quantum phase transition in the one-dimensional compass model

We introduce a one-dimensional model which interpolates between the Ising model and the quantum compass model with frustrated pseudospin interactions $σ_i^zσ_{i+1}^z$ and $σ_i^xσ_{i+1}^x$, alternating between even/odd bonds, and present its exact solution by mapping to quantum Ising models. We show that the nearest neighbor pseudospin correlations change discontinuosly and indicate divergent correlation length at the first order quantum phase transition. At this transition one finds the disordered ground state of the compass model with high degeneracy $2\times 2^{N/2}$ in the limit of $N\to\infty$.

cond-mat.str-el↗

arXiv2007

Spin-rotationally symmetric domain flux phases in underdoped cuprates

We propose a new form of inhomogeneous phases consisting of out-of-phase staggered flux domains separated by diagonal charged domain walls centered on bonds or on sites. Remarkably, such domain flux phases are spin-rotationally symmetric and exhibit cone-like quasiparticle dispersion as well as incommensurate order of orbital currents. Such features are consistent with the pseudogap behavior and the diagonal stripes observed experimentally in lightly doped cuprates. A renormalized mean field theory shows that such solutions are competitive candidates within the $t$--$J$ model.

cond-mat.str-el↗