abstract

We apply our new method of approach to electronic states in correlated systems [for a brief review, Part I, see: Acta Phys. Pol. B31, 2879 (2000)] to the analysis of the states and electron localization in nanoscopic chains containing up to \(N=12\) atoms. The Mott and the Hubbard criteria of localization are explicitly evaluated and the importance of the former is stressed. We also define the many-particle wave function and calculate it explicitly for the hydrogen molecule. Further applications of our method are listed at the end.

abstract

We analyze the stability of quantum computations on physically realizable quantum computers by simulating quantum spin models representing quantum computer hardware. Examples of logically identical implementations of the controlled-NOT operation are used to demonstrate that the results of a quantum computation are unstable with respect to the physical realization of the quantum computer. We discuss the origin of these instabilities and discuss possibilities to overcome this, for practical purposes, fundamental limitation of quantum computers.

abstract

High-quality single crystals of YbRh\(_{2}\)(Si\(_{1-x}\)Ge\(_{x}\))\(_{2}\) (\(x=0,\,0.05\)) have been studied by low-temperature (\(T\)) and high-magnetic-field (\(B\)) measurements of the electrical resistivity \(\rho (T,B)\), dc-magnetization \(M(T,B)\) and magnetic ac-susceptibility \(\chi _{\rm ac} (T,B)\). For the undoped compound \((x=0)\) a weak AntiFerromagnetic (AF) transition at \(T_{\text {N}} \simeq 70\,\textrm {mK}\) is observed which can be suppressed for small fields \(B_{\text {c}}\simeq 0.06\,\textrm {T}\) and \(0.7\,\textrm {T}\) applied along the crystallographic \(a\)- and \(c\)-direction, respectively. Below \(T_{\text {N}}\), a \(\rho (T)= \rho _{0} + aT^{2}\) behavior is found with very low residual resistivity \(\rho _{0}\simeq 1\,\mu \Omega \,\textrm {cm}\). Above \(T_{\text {N}}\) pronounced Non-Fermi-Liquid (NFL) effects are observed with a linear \(T\)-dependence of the electrical resistivity. A small volume expansion of \(\Delta V\approx +0.3\,\%\) is sufficient to tune the system YbRh\(_{2}\)(Si\(_{1-x}\)Ge\(_{x}\))\(_{2}\) to its Quantum Critical Point (QCP) at \(x_{\rm c}=(0.06\pm 0.01)\). The \(x=0.05\) compound shows a \(\rho (T) = \rho _{0} + bT\) dependence from below \(10\,\textrm {mK}\) up to above \(10\,\textrm {K}\). The low \(\rho _{0} \approx 5\, \mu \Omega \textrm {cm}\) proves that this NFL behavior is intrinsic due to the proximity to the QCP and not related to the disorder induced by Ge-alloying. No evidence for a metamagnetic phase transition in fields up to \(56\,\textrm {T}\) applied along the magnetic hard direction \(( B\parallel c)\) has been observed.

abstract

A wide variety of strongly correlated insulators ranging from intermediate valence materials, to Kondo insulators, to underdoped high-temperature superconductors display anomalous behavior in their inelastic light scattering. The Raman response in these materials shows a low-temperature transfer of spectral weight from low to high energy (as \(T\) is reduced), the appearance of an isosbestic point (a characteristic frequency where the Raman response is independent of temperature), and a large ratio of twice the “spectral gap” to the “onset temperature” where the low-energy spectral weight begins to deplete. We illustrate how these features generically appear in the Raman response of model systems that are tuned to lie just on the insulating side of the metal–insulator transition. We solve for the Raman response in the Falicov–Kimball model and in the Hubbard model. In the latter case, we find a number of new features arise as one approaches the metal–insulator transition from the metallic Fermi-liquid phase. Such behavior has not yet been seen in experiment.

abstract

The two models of short coherence length superconductors with anisotropic pairing symmetry are discussed. First, we examine superconducting properties of the extended Hubbard model with intersite attraction on a 2D square lattice with nearest- and next-nearest-neighbor hopping. The effects of phase fluctuations on the extended \(s\) and \(d_{x^2-y^2}\)-wave as well as on the mixed \(s \pm id\) state are studied within the Kosterlitz–Thouless scenario. This leads to a new phase with a pseudogap, and the universal linear scaling of the critical temperature versus zero temperature phase stiffness can occur on the Uemura type plots due to the separation of scales for pairing and for the phase coherence. The second model is that of local electron pairs and itinerant fermions coupled via charge exchange mechanism, which mutually induces superconductivity in both subsystems. The phase diagram of this two-component system is presented for anisotropic pairing on a 2D square lattice.

abstract

32 years have passed since Falicov and Kimball proposed a model of correlated electrons attempting to explaine such cooperative phenomena as metal–insulator transitions in some solids. We present a telegraph-style review of the development of the theory and applications of models based on the Falicov and Kimball idea which has taken place during the last 15 years of increased interest in these models. The list of collective phenomena that have been discussed in the framework of Falicov–Kimball models includes crystallization, segregation, phase separation, formation of molecules, flux phases, mixed-valence states, Peierls instability and metal-insulator transitions. We point out new trends and some open problems.

abstract

The exact solution of the multi-component Falicov–Kimball model in infinite-dimensions is presented and used to discuss a new fixed point of valence fluctuating intermetallics with Yb and Eu ions. In these compounds, temperature, external magnetic field, pressure, or chemical pressure induce a transition between a metallic state with the \(f\)-ions in a mixed-valent (non-magnetic) configuration and a semi-metallic state with the \(f\)-ions in an integral-valence (paramagnetic) configuration. The zero-field transition occurs at the temperature \(T_{\rm V}\), while the zero-temperature transition sets in at the critical field \(H_{\rm c}\). We present the thermodynamic and dynamic properties of the model for an arbitrary concentration of \(d\)- and \(f\)-electrons. For large \(U\), we find a MI transition, triggered by the temperature or field-induced change in the \(f\)-occupancy.

abstract

The extended Hubbard model with pair-hopping (intersite charge exchange) interaction is studied. The effects of phase fluctuations on the \(s\)-wave superconductivity of this system are discussed within the Kosterlitz–Thouless scenario. For two-dimensional (SQ) lattice the evolution of the superconducting critical temperature \(T_{\rm c},\) the pair formation temperature \(T_{\rm p}\) and the Uemura-type plots (i.e. the plots of \(T_{\rm c}\) vs superfluid stiffness at \(T=0\)) with pairing strength is determined.

abstract

We present the quasi-two dimensional Fermi surface studies in rare earth and uranium compounds such as UX\(_2\) (X: Bi, Sb, As and P) and RTIn\(_5\) (R: rare earth, T: Co, Rh and Ir), together with UTGa\(_5\). The present quasi-two dimensionality is closely related to the magnetic unit cell and/or the unique crystal structure elongated along the tetragonal [001] direction, which bring about a flat Brillouin zone and produce cylindrical but highly corrugated Fermi surfaces along [001].

abstract

Recent experiments on single crystals of the compounds CeRh\(_{1-x}\)Co\(_{ x}\)In\(_{5}\) and PrOs\(_{4}\)Sb\(_{12}\) are briefly reviewed. The temperature-composition (\(T-x\)) phase diagram of the heavy fermion pseudoternary system CeRh\(_{1-x}\)Co\(_{ x}\)In\(_{5}\), delineating the regions in which superconductivity, antiferromagnetism, and the coexistence of these two phenomena occur, has been established. Superconductivity has been observed in single crystals of the filled skutterudite compound PrOs\(_{4}\)Sb\(_{12}\) below \(T_{\rm c}\) = 1.85 K and appears to involve heavy fermion quasiparticles with an effective mass \(m^* \sim 50 m_e\), where \(m_e\) is the mass of the free electron.

abstract

We investigate the frustrated magnetic interactions in cubic transition metal oxides with orbital degeneracy. The \(e_g\) orbitals order easier and their ordering explains the \(A\)-type antiferromagnetic phase in KCuF\(_3\) and LaMnO\(_3\). In \(t_{2g}\) systems the magnetic order changes at a transition from an orbital liquid to orbital ordered states. The fluctuations of \(t_{2g}\) orbitals play a prominent role in LaVO\(_3\) and YVO\(_3\), where they compete with the Jahn-Teller effect and trigger the \(C\)-type antiferromagnetic order.

abstract

CeCu\(_{6-x}\)Au\(_x\) has become a prototype heavy-fermion system where, starting from not magnetically ordered CeCu\(_6\), Au doping introduces long-range incommensurate antiferromagnetism for \(x\gt x_{\rm c} \approx 0.1\). At the critical concentration \(x_{\rm c}\), the unusual magnetic fluctuations probed by inelastic neutron scattering lead to non-Fermi-liquid behavior, i.e. to anomalous low-temperature thermodynamic and transport properties. In magnetically ordered alloys, hydrostatic pressure can be employed to tune the magnetic–nonmagnetic transition. The effect of pressure in suppressing the antiferromagnetic order is contrasted by the effect of a magnetic field by way of a detailed study for \(x = 0.2\).

abstract

In this work we have discussed electronic structure, structural and magnetic properties of the CeMX-type compounds, where M is a transition metal and X is an \(sp\) element. The main goal of this presentation is to find the influence of metal M on the coherent gap formation at the Fermi level in the Ce-Kondo insulators. We also discuss a similar semiconductor-like resistance anomaly of Fe\(_2\)TiSn and CeNiSn-type Kondo insulators.

abstract

Heavy-fermion systems are modelled by the Periodic Anderson Model (PAM) in the limit of infinite dimensions (\(d \rightarrow \infty \)), in which the local approximation for the selfenergy or the Dynamical Mean-Field Theory (DMFT), respectively, become exact. As a consequence, vertex corrections for transport quantities vanish, which means that transport quantities like the conductivity (resistivity) and the thermoelectric power can be calculated from the selfenergy. Different approximations are used to determine the selfenergy, namely the Second Order Perturbation Theory (SOPT) for the PAM and a Modified Perturbation Theory (MPT) within a DMFT-mapping of the PAM on an effective Single-Impurity Anderson Model (SIAM). The MPT reproduces the SOPT for the SIAM for weak interactions and simultaneously fulfills the atomic limit. Both approximations yield an \(f\)-electron spectral function at the chemical potential which is strongly temperature dependent and decreases on a characteristic temperature scale \(T^*\) approaching a constant value for high temperatures. This characteristic low temperature \(T^*\) can be interpreted as the Kondo temperature within these approximations, but \(T^*\) does not yet have the characteristic (exponential, non-analytic) dependence on the model parameters expected from the Schrieffer–Wolff transformation. The resistivity \(R(T)\) obtained shows qualitatively exactly the behavior, which is characteristic for heavy-fermion systems, namely a low value for zero temperature, a \(T^2\) increase for low temperatures, a maximum exactly at \(T^*\), and \(R(T)\) decreases with increasing \(T\) for higher temperatures \(T \gt T^*\). The thermoelectric power obtained is absolutely very large (of the magnitude \(10^{-4}\) V/K), and it has an extremum at a temperature, which scales linearly with \(T^*\); the absolute value at the extremum even becomes larger with increasing \(T^*\). The influence of impurity scattering (alloying) was also investigated treating the disorder within the Coherent Potential Approximation (CPA). Possible extensions of these investigations to include crystal-field effects are discussed.

abstract

We discuss phase transitions and critical behavior deviating from the standard scheme based on a mean-field theory renormalizing only the mass of the critical excitations completed with a perturbative scaling renormalization of the interaction strength. On examples of mean-field theories for spin glasses and for quantum phase transitions we show that coupling constants are relevant variables in these systems and are to be renormalized already within the mean-field approximations.

abstract

AC magnetic susceptibility, electrical resistivity and X-ray Photoelectron Spectroscopy (XPS) measurements have been performed on the Ho(Co\(_{1-x}\)Cr\(_{x})_{2}\) compounds with \(x\)= 0.0, 0.03, 0.05, 0.10, 0.15 and 0.20. A strengthening of the HoCo\(_{2}\) ferrimagnetism shows up through a rapid increase at small Cr concentration \(x\) of the Curie temperature \(T_{\rm C}\) which reaches a maximum around \(x\)= 0.15. The lattice parameters also go through a maximum for the same concentration of Cr. A remarkable decrease of the density of states near the Fermi level is observed for the sample with \(x\)= 0.20. We correlate the changes of the Curie temperature with the decrease of \(d\)-electron concentration when Cr substitutes for Co.

abstract

We show that the spectral functions in the ferromagnetic planes of orbitally ordered LaMnO\(_3\) strongly depend on the Jahn–Teller interaction and on the polarization of orbitals around the hole. Using realistic parameters and available experimental information we suggest that the incoherent spectral weight and the mass enhancement in LaMnO\(_3\) might be quite large.

abstract

The microscopic nature of the magnetic phase transitions in ordered states observed in TbTSb\(_2\) (T = Cu, Pd) and TbTGe\(_2\) (T = Pt, Ir) are discussed on the basis of neutron diffraction and magnetometric measurements.

abstract

TbAuIn and HoAuIn compounds crystallize in the hexagonal ZrNiAl-type structure and order magnetically below 35 K for R = Tb and 4.8 K for R = Ho. In the case of TbAuIn a noncollinear antiferromagnetic structure described by the propagation vector \({k}=(0,0,\frac {1}{2})\) is stable in the temperature range from 1.5 K up to \(T_{\rm N}\). The magnetic structure of HoAuIn determined at 1.5 K is noncollinear antiferromagnetic one. This low temperature magnetic structure could be described by two propagation vectors \({k}_1=(0,\frac {1}{2},\frac {1}{2})\) and \({k}_2=(0,0,\frac {1}{2})\). At \(T=2.5\) K an additional phase transition to a modulated structure is observed.

abstract

Polycrystalline samples of Ce\(_2\)Co\(_{1-x}\)Au\(_x\)Si\(_3\) for \(x\) equal to 0.4, 0.6, 0.8 and 1.0 have been studied by neutron diffraction. All compounds exhibit the hexagonal crystal structure derived from the AlB\(_2\)-type. For \(x=0.4\) the Ce magnetic moments equal to 0.6(1) \(\mu _{\rm B}\) form a simple antiferromagnetic structure and are parallel to the \(b\)-axis. In Ce\(_2\)Co\(_{0.2}\)Au\(_{0.8}\)Si\(_3\) a short range magnetic order is observed. For \(x=0.6\) and 1.0 the Ce-moments do not order up to 1.5 K.

abstract

Specific heat and thermal expansion measured along the \(c\)-axis are reported for the UAsSe single crystals with \(T_{\rm C}=101.5\,{\rm K}\), which display the pronounced low-\(T\) upturn in the electrical resistivity. Besides the ferromagnetic transition, no additional anomaly has been found that could affect the low-\(T\) physics of UAsSe. The investigated \(^{77}\)Se NMR spectra give evidence for a systematic development of the disorder caused by a small change of the sample composition. The appearance of electron-assisted tunneling of the atoms in UAsSe and related compounds is discussed.

abstract

The Double EXchange (DEX) model for ferromagnetism is studied by means of the flow equation method. The initial Hamiltonian is lead through a set of the infinitesimal unitary transformations which eliminate from it the part responsible for violation of the magnon number. Basic properties of the effective Hamiltonian are discussed.

abstract

We study the effect of site diagonal disorder on the pairing amplitude by a perturbation method. Using an extended Hubbard model with the inter-site attraction we analyze fluctuations of order parameter in the presence of non-magnetic disorder and discuss the instability of various solutions with \(p\)-wave pairing.

abstract

In the limit of infinite spatial dimensions a thermodynamically consistent theory of the strongly correlated electron systems, which is valid for arbitrary value of the Coulombic interaction (\(U\lt \infty \)), is built. For the Hubbard model the total auxiliary single-site problem exactly splits into four subspaces, which describe Fermi and non-Fermi liquid components. Such analytical approach allows to construct different thermodynamically consistent approximations: alloy-analogy approximation, Hartree–Fock approximation, and further, that which describes the self-consistent renormalization of the bosonic excitations (magnons and doublons).

abstract

Using the two-dimensional Jordan–Wigner fermionization we calculate the \(zz\) dynamic structure factor \(S_{zz}({k},\omega )\) for the \(s=\frac {1}{2}\) isotropic \(XY\) model on a spatially anisotropic square lattice. We discuss the dispersion relations for different modes which contribute to \(S_{zz}({k},\omega )\).

abstract

Using the two-dimensional Jordan–Wigner fermionization we calculate the thermodynamic quantities of the (spatially anisotropic) square-lattice spin 1/2 anisotropic \(XY\) (\(XZ\)) model. We compare the results of different approaches for the ground-state and thermodynamic properties of the model.

abstract

Thermodynamical properties of the one-dimensional \(S=1/2\) Heisenberg model with dimerized nearest and uniform next-nearest neighbors interactions, applicable to CuGeO\(_3\) and Pb[Cu(SO\(_4\))(OH)\(_2\)] compounds, are studied by the numerically exact quantum transfer-matrix method. Suzuki–Trotter formula is used to obtain a classical system with spin \(\sigma \)=\(3/2\) and effective interactions between nearest neighbors only. Magnetic specific heat and magnetic susceptibility curves are calculated and compared with experimental results in a wide temperature range giving estimates of the coupling parameters in the model proposed for CuGeO\(_3\) and Pb[Cu(SO\(_4\))(OH)\(_2\)].

abstract

The Monte Carlo simulations allowing a distinction between the 1st and the 2nd order phase transitions in the three-dimensional Ashkin–Teller spin-lattice model, a system with three order parameters, are described. The applied method allows a precise location of points on the phase diagram. Some critical points on the phase boundaries have been calculated in the regions complementary to the results recently described in literature.

abstract

Second order perturbation theory for the free energy of the \(s\)–\(d\) exchange Hamiltonian \(H_{\rm K}\) is applied to CuCr. The temperature dependence of the cutoff \(D(T)\) for \(H_{\rm K}\) is adjusted to obtain agreement between theory and the experimental plot of specific heat for CuCr found by Tripplett and Philips. We find that the function \(D(T)\) follows approximately the rule \(D(T)=10^3 k_{\rm B} T+\gamma (k_{\rm B} T)^2\).

abstract

An argument is given showing that in the limit of small impurity concentrations, the statistical sum \(Z_{\rm K}\) of the \(M\)-impurity \(s\)–\(d\) model equals \(Z_{\rm K}(M)=M(Z_{{\rm K}r}(1)-Z_r(0))+Z_r(0),\) where \(Z_r(M)\) denotes the statistical sum of the \(M\)-impurity reduced \(s\)–\(d\) model and \(Z_{{\rm K}r}(1)\) that of a single impurity interacting with the free electron gas and mean field of the reduced \(s\)–\(d\) model.

abstract

We present a theory of combined nonmagnetic and magnetic momentum-dependent impurity scattering in the \(d\)-wave superconductor. After deriving a formula for the initial suppression of the critical temperature we discuss the experimental data for Zn and Ni substitutions as well as electron irradiation defects in cuprates. We suggest, that the unequal pair-breaking effect of Zn and Ni may be related to a different structure of the magnetic moments induced by these impurities.

abstract

Two-dimensional spinless Falicov–Kimball Model (FKM) with a generalized correlated hopping is studied perturbatively in the limit of large on-site Coulomb interaction \(U\). In the half-filled case (i.e. \(\rho _i+\rho _e=1\), where \(\rho _i, \rho _e\) are densities of ions and electrons, respectively,) an effective Hamiltonian in spin variables is derived up to terms proportional to \(U^{-3}\). Unlike the simplest FKM case, it contains odd parity terms (resulting from the correlated hopping) in addition to even parity ones. The ground-state phase diagram of the effective Hamiltonian is examined in the \((a,g,h)\) parameter space, where \(a,g\) are parameters characterizing strength of the correlated hopping and \(h\) is a difference of chemical potentials of two sorts of particles present in the system. It appears to be asymmetric with respect to the change \(h\to -h\) and a new ordered phases are found for certain values of \(a\) and \(g\).

abstract

Ground state phase diagrams in the canonical ensemble of the one-dimensional Falicov-Kimball Model (FKM) with the correlated hopping are presented for several values of the model parameters. As compare to the conventional FKM, the diagrams exhibit a loss of the particle–hole symmetry.

abstract

We show that patterns of the current-current correlation function in the form of the staggered flux indicate that spin bipolarons form in doped antiferromagnets. Holes which form a spin bipolaron reside at opposite ends of a line (string) formed by the defects in the antiferromagnetic spin background. The string is relatively highly mobile, because the motion of a hole at its end does not raise extensively the number of defects, provided that the hole at the other end of the line follows along the same track. Appropriate coherent combinations of string states realize some irreducible representations of the point group \(C_{4v}\). Creep of strings favors \(d\)- and \(p\)-wave states. Some more subtle processes decide the symmetry of pairing. The pattern of the current correlation function, that defines the structure of flux, emerges from motion of holes at string ends and coherence factors with which string states appear in the wave function of the bound state. Condensation of bipolarons and phase coherence between them puts to infinity the correlation length of the current correlation function and establishes the flux in the system.

abstract

Results of thermal conductivity measurements of PrSn\(_{3}\) are presented. The measurements were curried out in the temperature range 4–300 K on a single crystal sample oriented along the [100] direction. It was found that the thermal conductivity \(\mathit {\lambda }\) is dominated by scattering electrons in the whole temperature range under examination. The magnetic contribution to the thermal conductivity \(\mathit {\lambda }_{\rm e, m}\) has been separated and its temperature dependence \(\mathit {\lambda }_{\rm e,m}\)(T) has been obtained. The thermal conductivity of PrSn\(_{3}\) was found as a linear function of temperature at higher temperatures, whereas an anomaly was observed below \(T_{N}\). In ordered state, the \(\mathit {\lambda }_{\rm e,m}\)(T) changes in the opposite way as the total thermal conductivity does. The temperature dependence of the Lorenz number exhibits a pronounced maximum at about 20 K.

abstract

It is shown that crystals of some uranium and thorium compounds, grown in off-stoichiometric composition, show single-ion Kondo type behaviour of the resistivity, thermoelectric power and the Hall coefficient. The data for off-stoichiometric crystals of uranium monoantimonide (antiferromagnet) and thorium arsenosulphide (diamagnet) are presented. The behaviour is discussed in terms of the two-level-system Kondo model.

abstract

Single crystals of uranium phosphorosulfide, UPS, have been obtained by the chemical transport method. Their thermoelectric power, \(S(T)\), and electrical resistivity, \(\rho (T)\), have been measured from \(\sim 2\) K to room temperature. The transport properties of UPS show some anomalies, which could be ascribed to the Kondo-like scattering of the conduction electrons.

abstract

The de Haas van Alphen effect was investigated in the antiferromagnatic compound GdIn\(_3\). A number of Fermi surface branches were observed. The list of the all detected frequencies and related cyclotron masses is given. The anisotropy of the critical field connected with the observed metamagnetic transition was measured. The angular dependence of this anisotropy shows that magnetic moment alignment in GdIn\(_3\) is probably tilted by 5 degree from the \([111]\) direction.

abstract

We have investigated the anisotropy and off-stoichiometry effects on the thermoelectric power \(S(T)\) of uranium dipnictides — UP\(_{1.7}\)As\(_{0.3}\) and UAs\(_2\) and arsenoselenide — UAs\(_{1-x}\)Se\(_{1+x}\). These two groups of compounds have tetragonal PbFCl-type structure and order at low temperatures anti- or ferromagnetically, respectively. The \(S(T)\) curves are strongly anisotropic for all the examined systems. The \(a\)-axis thermopower of the ferromagnetic UAs\(_{1-x}\)Se\(_{1+x}\) system shows a spectacular dependence of the shape of \(S(T)\) curve on \(x\). This behaviour is discussed in the frame of the multi-channel Kondo model.