The Hubbard model plays a special role in condensed matter theory as it is considered to be the simplest Hamiltonian model one can write in order to describe anomalous physical properties of some class of real materials. Unfortunately, this model is not exactly solved except in some limits and therefore one should resort to analytical methods, like the Equations of Motion Approach, or to numerical techniques in order to attain a description of its relevant features in the whole range of physical parameters (interaction, filling and temperature). In this paper, the Composite Operator Method, which exploits the above mentioned analytical technique, is presented and systematically applied in order to get information about the behaviour of all relevant properties of the model (local, thermodynamic, single-and two-particle properties) in comparison with many other analytical techniques, the above cited known limits and numerical simulations. Within this approach, the Hubbard model is also shown to be capable of describing some anomalous behaviour of cuprate superconductors.

We study the generation of coherent phonons in a superconductor by ultrafast optical pump pulses. The nonequilibrium dynamics of the coupled Bogoliubov quasiparticle-phonon system after excitation with the pump pulse is analyzed by means of the density-matrix formalism with the phonons treated at a full quantum kinetic level. For ultrashort excitation pulses, the superconductor exhibits a nonadiabatic behavior in which the superconducting order parameter oscillates. We find that in this nonadiabatic regime the generation of coherent phonons is resonantly enhanced when the frequency of the order-parameter oscillation is tuned to the phonon energy, a condition that can be achieved in experiments by varying the integrated pump pulse intensity

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The two-dimensional Hubbard model is analyzed in the framework of the two-pole expansion. It is demonstrated that several theoretical approaches, when considered at their lowest level, are all equivalent and share the property of satisfying the conservation of the first four spectral momenta. It emerges that the various methods differ only in the way of fixing the internal parameters and that it exists a unique way to preserve simultaneously the Pauli principle and the particle-hole symmetry. A comprehensive comparison with respect to some general symmetry properties and the data from quantum Monte Carlo analysis shows the relevance of imposing the Pauli principle.

The composite operator method (COM) is formulated, its internals illustrated in detail and some of its most successful applications reported

We identify and discuss the ground state of a quantum magnet on a triangular lattice with bonddependent Ising-type spin couplings, that is, a triangular analog of the Kitaev honeycomb model. The classical ground-state manifold of the model is spanned by decoupled Ising-type chains, and its accidental degeneracy is due to the frustrated nature of the anisotropic spin couplings. We show how this subextensive degeneracy is lifted by a quantum order-by-disorder mechanism and study the quantum selection of the ground state by treating short-wavelength fluctuations within the linked cluster expansion and by using the complementary spin-wave theory. We find that quantum fluctuations couple next-nearest-neighbor chains through an emergent four-spin interaction, while nearest-neighbor chains remain decoupled. The remaining discrete degeneracy of the ground state is shown to be protected by a hidden symmetry of the model. Frustrated magnets, systems in which every pairwise exchange interaction cannot be simultaneously satisfied, are characterized by accidental degeneracies between various order patterns 1 . Often, these accidental degeneracies are lifted via an order-by-disorder mechanism, driven by thermal and/or quantum fluctuations, selecting an unique ground state 2-4 . In highly frustrated quantum magnets, those with extensive degeneracy, e.g., the isotropic spin one-half kagomé and pyrochlore antiferromagnets (AF), the order-by-disorder mechanism is inactive and they remain disordered down to the lowest temperatures, realizing so-called quantum spin liquids (QSL) in their ground states 1 .In 30 and quantum 31,32 spins has been studied numerically. The obtained rich phase diagram includes a Z 2 -vortex crystal phase near the AF Heisenberg limit, and a nematic phase of decoupled Ising chains with subextensive degeneracy at the Kitaev limit 30,31 . In addition, a chiral spin-liquid phase has been proposed close to the antiferromagnetic Kitaev limit 32 . Here, we study analytically the Kitaev model on the triangular lattice and solve the puzzle of its ground state by analyzing the effects of quantum fluctuations within both the linked-cluster expansion, 33 combined with degenerate perturbation theory, and the linear spin-wave theory. We show that such a deceptively simple model, once realized on a triangular lattice, becomes the host of very interesting and unexpected order-by-disorder effects such as: the quantum selection of the easy axes, the emergence of a specific four-spin interaction, the reduction of the sub-extensive degeneracy of the nematic ground state manifold down to a discrete one protected by a hidden symmetry of the model. I. THE MODELWe consider a triangular lattice lying in the (1, 1, 1) plane of the spin-quantization frame [see Fig. 1(a)] and label by (γ)(= x, y, z) its three non-equivalent NN bonds spanned by the lattice vectors a x = 1 /2, − √ 3 /2 , a y = 1 /2, √ 3 /2 and a z = (1, 0), respectively. On a (γ)-bond, the one perpendicular to the γ spin-quantization axis, only the S γ i components of...

A comprehensive study of the behavior of the Mott insulator Ca2RuO4 under electrical current drive is performed by combining two experimental probes: the macroscopic electrical transport and the microscopic X-Ray diffraction. The resistivity, ρ, vs electric current density, J, and temperature, T , ρ(J,T), resistivity map is drawn. In particular, the meta-stable state, induced between the insulating and the metallic thermodynamic states by current biasing Ca2RuO4 single crystals, is investigated. Such an analysis, combined with the study of the resulting RuO6 octahedra energy levels, reveals that a metallic crystal phase emerges in the meta-stable regime. The peculiar properties of such a phase, coexisting with the well-established orthorhombic insulating and tetragonal metallic phases, allow to explain some of the unconventional and puzzling behaviors observed in the experiments, as a negative differential resistivity. arXiv:1912.01690v1 [cond-mat.str-el]

We address the role played by charged defects in doped Mott insulators with active orbital degrees of freedom. It is observed that defects feature a rather complex and rich physics, which is well captured by a degenerate Hubbard model extended by terms that describe crystal-field splittings and orbital-lattice coupling, as well as by terms generated by defects such as the Coulomb potential terms that act both on doped holes and on electrons within occupied orbitals at undoped sites. We show that the multiplet structure of the excited states generated in such systems by strong electron interactions is well described within the unrestricted Hartree-Fock approximation, once the symmetry breaking caused by the onset of magnetic and orbital order is taken into account. Furthermore, we uncover spectral features that arise within the Mott-Hubbard gap and in the multiplet spectrum at high energies due to the presence of defect states and strong correlations. These features reflect the action on electrons/holes of the generalized defect potential that affects charge and orbital degrees of freedom, and indirectly also spin ones. This study elucidates the mechanism behind the Coulomb gap appearing in the band of defect states and investigates the dependence on the electron-electron interactions and the screening by the orbital-polarization field. As an illustrative example of our general approach, we present explicit calculations for the model describing three t2g orbital flavors in the perovskite vanadates doped by divalent Sr or Ca ions, such as in La1−xSrxVO3 and Y1−xCaxVO3 systems. We analyze the orbital densities at vanadium ions in the vicinity of defects and the excited defect states which determine the optical and transport gaps in doped systems