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These lectures review the large N Schwinger Bosons Mean Field approach to the quantum Heisenberg model. The method applies to ordered and disordered phases in all dimensions, at zero and at finite temperature. Extension to frustrated models is explained. An example for an experimentally useful application, is the temperature dependent staggered magnetization of the layered antiferromagnet.
We investigate the lattice Coulomb glass model in three dimensions via Monte Carlo simulations. No evidence for an equilibrium glass phase is found down to very low temperatures, although the correlation length increases rapidly near T=0. A charge-ordered phase (COP) exists at low disorder. The transition to this phase is consistent with the Random Field Ising universality class, which shows that the interaction is effectively screened at moderate temperature. For large disorder, the single-particle density of states near the Coulomb gap satisfies the scaling relation g(e,T)=T^δf(|e|/T) with δ= 2.01 +/- 0.05 in agreement with the prediction of Efros and Shklovskii. For decreasing disorder, a crossover to a larger effective exponent occurs due to the proximity of the COP.
This thesis poses a selection of recent research of the author in a common context. It starts with a selected review on research concerning the role entanglement might play at quantum phase transitions and introduces measures for entanglement used for this analysis. A selection of results from this research is given and proposed as evidence for the relevance of multipartite entanglement in this context. A constructive method for an SLOCC classification and quantification of multipartite qubit entanglement is outlined and results for convex roof extensions of the resulting measures are briefly discussed on a specific example. At the end, a transformation of antilinear expectation values into linear expectation values is presented which admits an expression of the aforementioned measures of genuine multipartite entanglement in terms of spin correlation function, hence making them experimentally accessible.
This is extended version of a previously submitted paper, in which special solutions of the Hartree-Fock (HF) problem for Coulomb interacting electrons, being described by a simple model of the Cu-O planes in La2CuO4, are presented. One of the mean field states obtained, is able to predict some of the basic properties of this material, such as its insulator character and the antiferromagnetic order. The natural appearance of pseudogaps in some states of this compound is also indicated by another of the HF states obtained. These surprising results follow after eliminating spin and crystal symmetry restrictions which are usually imposed on the single particle HF orbitals, by means of employing a rotational invariant formulation of the HF scheme which was originally introduced by Dirac. Therefore, it is exemplified how, up to now being considered strong correlation effects, can be described by improving the HF solution of the physical systems. In other words, defining the correlation effects as such ones shown by the physical system and which are not predicted by the best HF (lowest energy) solution, allows to explain currently assumed as strong correlation properties, as simple mean field ones. The discussion also helps to clarify the role of the antiferromagnetism and pseudogaps in the physics of the HTSC materials and indicates a promising way to start conciliating the Mott and Slater pictures for the description of the transition metal oxides and other strongly correlated electron systems.
The nature of the polarons in the optimally doped colossal magnetoresistive (CMR) materials La0.7Ba0.3MnO3 (LBMO) and La0.7Sr0.3MnO3 (LSMO) is studied by elastic and inelastic neutron scattering. In both materials, dynamic nanoscale polaron correlations develop abruptly in the ferromagnetic state. However, the polarons are not able to lock-in to the lattice and order, in contrast to the behavior of La0.7Ca0.3MnO3. Therefore ferromagnetic order in LBMO and LSMO survives their formation, explaining the conventional second order nature of the ferromagnetic--paramagnetic transition. Nevertheless, the results demonstrate that the fundamental mechanism of polaron formation is a universal feature of these ferromagnetic perovskite manganites.
The phase diagram of Sr3Ru2O7 contains a metamagnetic transition that bifurcates to enclose an anomalous phase with intriguing properties - a large resistivity with anisotropy that breaks the crystal-lattice symmetry. We propose that this is a magnetic analogue of the spatially inhomogeneous superconducting Fulde-Ferrel-Larkin-Ovchinnikov state. We show - through a Ginzburg-Landau expansion where the magnetisation transverse to the applied field can become spatially inhomogeneous - that a Stoner model with electronic band dispersion can reproduce this phase diagram and transport behaviour.
Using angle-integrated photoemission spectroscopy we have probed the novel LaO$_{0.9}$F$_{0.1}$FeAs superconductor over a wide range of photon energies and temperatures. We have provided the first full characterization of the orbital character of the VB DOS and of the magnitude of the d-p hybridization energy. Finally, we have identified two characteristic temperatures: 90K where a pseudogap-like feature appears to close and 120K where a sudden change in the DOS near E$_F$ occurs. We associate these phenomena with the SDW magnetic ordering and the structural transition seen in the parent compound, respectively. These results suggest the important role of electron correlation, spin physics and structural distortion in the physics of Fe-based superconductors.
On the basis of self-consistent Born approximation, we present a theory of weak localization of Dirac fermions under finite-range scatters in graphene. With an explicit solution to the ground state of singlet pseudospin Cooperons, we solve the Bethe-Salpeter matrix equation for all the singlet and triplet pseudospin Cooperons at long-wave length states by perturbation treatment. The solution to the Cooperon in the presence of the external weak magnetic field is also obtained. We calculate the quantum interference correction to the conductivity and present the comparison with experiments. It is shown that the present calculation for the magnetoconductivity is in good agreement with some of the experimental measurements.
Recent advanced Monte Carlo simulations have not found superconductivity and phase separation in the Hubbard model with on-site repulsive electron-electron correlations. We argue that microscopic phase separations in cuprate superconductors and colossal magnetoresistance (CMR) manganites originate from a strong electron-phonon interaction (EPI) combined with unavoidable disorder. Attractive electron correlations, caused by an almost unretarded EPI, are sufficient to overcome the direct inter-site Coulomb repulsion in these charge-transfer Mott-Hubbard insulators, so that low energy physics is that of small polarons and small bipolarons (real-space electron (hole) pairs dressed by phonons). They form clusters localised by disorder below the mobility edge, but propagate as the Bloch states above the mobility edge. I identify the Froehlich finite-range EPI with optical phonons as the most essential for pairing and phase separation in superconducting layered cuprates. The pairing of oxygen holes into heavy bipolarons in the paramagnetic phase (current-carrier density collapse (CCDC)) explains also CMR of doped manganites due to magnetic break-up of bipolarons in the ferromagnetic phase. Here I briefly present an explanation of high and low-resistance phase coexistence near the ferromagnetic transition as a mixture of polaronic ferromagnetic and bipolaronic paramagnetic domains due to unavoidable disorder in doped manganites.
We investigate thermopower and thermoelectric coefficient of nano-granular materials at large tunneling conductance between the grains, g_{T} >> 1. We show that at intermediate temperatures, T >= g_{T}δ, where δis the mean energy level spacing for a single grain, electron-electron interaction leads to an increase of the thermopower with decreasing grain size. We discuss our results in the light of new types of thermoelectric materials and present the behavior of the figure of merit depending on system parameters.
We studied the oxygen isotope effect (OIE) on the zero point motion and the thermal motion as well as on structural parameters in La$_2$CuO$_4$ by means of high-resolution neutron diffraction experiments. We found a negative OIE on the lattice parameters (-0.01%). The OIE on the isotropic thermal parameters turned out to be positive for lanthanum, copper and negative for the oxygen atoms, respectively. The Rietvield refinement of the anisotropic thermal parameters of the different directions yielded the same sign of the OIE for each ion. Our analysis shows that the OIE on isotropic thermal parameters is most pronounced for La at 15 K (up to 100%) which we found to be originating mainly from the thermal motion in x-direction as determined from the refinement of the anisotropic thermal parameters.
The experimental results for ZrZn$_{2}$, URhGe, and in some pressure ranges also for UGe$_{2}$, have shown that the ferromagnetic superconductors are weak itinerant ferromagnets. Guided by these results we describe the phenomenon of coexistence between equal spin triplet pairing superconductivity (SC) and ferromagnetism (F) using the extended Stoner model, which includes in Hamiltonian the on-site Coulomb interaction, $U$, and occupation dependent hopping integral. We use Hartree-Fock (H-F) approximation and the Green functions technique. In the H-F approximation the on-site Coulomb interaction plays the role of the on-site exchange (Hund's) field. All inter-site interactions will have included the inter-site kinetic correlation, $ $, within the H-F approximation. We introduce the pressure-dependence to the hopping integral. Numerical results are compared with experimental data for ZrZn$_{2}$. The kinetic correlation creates the superconductivity without help of negative values of Coulomb interactions. The model can explain stimulation of triplet SC by the weak itinerant ferromagnetism. This effect was observed experimentally in ZrZn$_{2}$. Numerical analysis also confirms the experimental effect of decrease in critical temperatures (Curie and superconducting) with increasing external pressure.
We have studied the zero and low-temperature behavior of anisotropic alternating antiferromagnetic-ferromagnetic Heisenberg spin-1/2 chains in a transverse magnetic field. Using the analytical spinless fermion approach, the thermodynamic behavior of the model has been studied. We have introduced a new order parameter to distinguish the gapless Luttinger liquid phase from the other gapped phases. The exact diagonalization Lanczos results are also used to compare with the spinless fermion ones. We have found a double peak structure in the specific heat curves for the region between the two quantum critical points. Using the numerical full diagonalization results, the existence of the double peak structure is confirmed.
In frustrated antiferromagnets with isotropic exchange interactions, there is typically a manifold of degenerate classical ground states. This degeneracy is broken by the (free) energy of quantum or thermal fluctuations, or the uniform effects of bond disorder. We derive effective Hamiltonians to express each kind of selection effect, in both exact forms and convenient approximate forms. It is argued that biquadratic terms, representing the collinear-selecting effects of quantum fluctuations, should be included in classical simulations of large-$S$ frustrated magnets at low temperatures
We have presented the role of the Coulomb interaction ($U$) and the magnetic field ($\vec{B}$) on the ground state properties of the quasi-one dimensional graphite ribbon structures at half-filling. Mean field Hartree-Fock Approximation is used to study the systems. To understand the boundary effects in graphite structures, we have compared the results of these systems with those of the square lattice ribbon structures. Studying the density of states, the Drude weight and the charge gap, we have drawn the $U-B$ phase diagrams for the zigzag and the armchair graphite ribbons.
The metal to insulator transition in the charge transfer NiS{2-x}Se{x} compound has been investigated through infrared reflectivity. Measurements performed by applying pressure to pure NiS2 (lattice contraction) and by Se-alloying (lattice expansion) reveal that in both cases an anomalous metallic state is obtained. We find that optical results are not compatible with the linear Se-alloying vs Pressure scaling relation previously established through transport, thus pointing out the substantially different microscopic origin of the two transitions.
We examine a possible spin Hall effect for localized spin systems with no charge degrees of freedom. In this scenario, a longitudinal magnetic field gradient induces a transverse spin current carried by spin wave excitations with an anomalous velocity which is associated with the Berry curvature raised by spin chirality, in analogy with anomalous Hall effects in itinerant electron systems. Our argument is based on a semiclassical equations of motion applicable to general spin systems. Also, a microscopic model of frustrated magnets which exhibits the anamalous spin Hall effect is presented.
A detailed exposition is made of recent transport and 'quantum oscillation' results from HTSC systems covering the full range from overdoped to underdoped material. This now very extensive and high quality data set is interpreted here within the framework developed by the author of local pairs and boson-fermion resonance, arising in the context of negative-U behaviour in an inhomogeneous electronic environment. The strong inhomogeneity comes with the mixed-valent condition of these materials, which when underdoped lie in close proximity to the Mott-Anderson transition. The observed intense scattering is presented as resulting from pair formation and electron-boson collisions in the resonant crossover circumstance. The high level of scattering brings the systems to incoherence in the pseudogapped state, p < pc (= 0.183). In a high magnetic field the striped partition of the inhomogeneous charge distribution is much strengthened and regularized. Magnetization and resistance oscillations, of period dictated by the favoured positioning of the square fluxon array within the real space environment of the diagonal 2D charge striping array, are demonstrated to be responsible for the recently reported behaviour hitherto widely attributed to the quantum oscillation response of a much more standard Fermi liquid condition. A detailed analysis embracing all the experimental data serves to indicate that in the given conditions of very high field, low temperature, 2D-striped, underdoped, d-wave superconducting, HTSC material the flux quantum becomes doubled to h/e.