Magnetic behavior of a spin-1 Blume-Emery-Griffiths model

I study the one-dimensional spin-1 Blume-Emery-Griffiths model with bilinear and biquadratic exchange interactions and single-ion crystal field under an applied magnetic field. This model can be exactly mapped into a tight-binding Hubbard model - extended to include intersite interactions - provided one renormalizes the chemical and the on-site potentials, which become temperature dependent. After this transformation, I provide the exact solution of the Blume-Emery-Griffiths model in one dimension by means of the Green's functions and equations of motion formalism. I investigate the magnetic variations of physical quantities - such as magnetization, quadrupolar moment, susceptibility - for different values of the interaction parameters and of the applied field, focusing on the role played by the biquadratic interaction in the breakdown of the magnetization plateaus.Comment: 4 pages, 5 figures. ICM 2009 (Karlsruhe) Conference proceeding

Different orderings in the narrow-band limit of the extended Hubbard model on the Bethe lattice

We present the exact solution of a system of Fermi particles living on the sites of a Bethe lattice with coordination number z and interacting through on-site U and nearest-neighbor V interactions. This is a physical realization of the extended Hubbard model in the atomic limit. Within the Green's function and equations of motion formalism, we provide a comprehensive analysis of the model and we study the phase diagram at finite temperature in the whole model's parameter space, allowing for the on-site and nearest-neighbor interactions to be either repulsive or attractive. We find the existence of critical regions where charge ordering (V>0) and phase separation (V<0) are observed. This scenario is endorsed by the study of several thermodynamic quantities.Comment: 17 pages, 20 figure

One-dimensional extended Hubbard model in the atomic limit

We present the exact solution of the one-dimensional extended Hubbard model in the atomic limit within the Green's function and equation of motion formalism. We provide a comprehensive and systematic analysis of the model by considering all the relevant response and correlation functions as well as thermodynamic quantities in the whole parameter space. At zero temperature we identify four phases in the plane (U,n) [U is the onsite potential and n is the filling] and relative phase transitions as well as different types of charge ordering. These features are endorsed by investigating at T=0 the chemical potential and pertinent local correlators, the particle and double occupancy correlation functions, the entropy, and by studying the behavior in the limit T going to zero of the charge and spin susceptibilities. A detailed study of the thermodynamic quantities is also presented at finite temperature. This study evidences that a finite-range order persists for a wide range of the temperature, as shown by the behavior of the correlation functions and by the two-peak structure exhibited by the charge susceptibility and by the entropy. Moreover, the equation of motion formalism, together with the use of composite operators, allows us to exactly determine the set of elementary excitations. As a result, the density of states can be determined exactly and a detailed analysis of the specific heat allows for identifying the excitations and for ascribing its two-peak structure to a redistribution of the charge density.Comment: 28 pages;added references and corrected typos. This paper is an extended version of Phys. Rev. E 77, 061120 (2008

Role of the attractive intersite interaction in the extended Hubbard model

We consider the extended Hubbard model in the atomic limit on a Bethe lattice with coordination number z. By using the equations of motion formalism, the model is exactly solved for both attractive and repulsive intersite potential V. By focusing on the case of negative V, i.e., attractive intersite interaction, we study the phase diagram at finite temperature and find, for various values of the filling and of the on-site coupling U, a phase transition towards a state with phase separation. We determine the critical temperature as a function of the relevant parameters, U/|V|, n and z and we find a reentrant behavior in the plane (U/|V|,T). Finally, several thermodynamic properties are investigated near criticality.Comment: 7 pages, 7 figures. EPJB Topical Issue on Novel Quantum Phases and Mesoscopic Physics in Quantum Gase

Study of the spin-32\frac32 Hubbard-Kondo lattice model by means of the Composite Operator Method

We study the spin-$\frac32$ Hubbard-Kondo lattice model by means of the Composite Operator Method, after applying a Holstein-Primakov transformation. The spin and particle dynamics in the ferromagnetic state are calculated by taking into account strong on-site correlations between electrons and antiferromagnetic exchange among $\frac32$ spins, together with usual Hund coupling between electrons and spins

The sn-pole approximation in the Composite Operator Method

A well-established method to deal with highly correlated systems is based on the expansion of the Green's function in terms of spectral moments. In the context of the Composite Operator Method one approximation is proposed: a set of n composite fields is assumed as fundamental basis and the dynamics is considered up to the order s. The resulting Green's function has a sn-pole structure. The truncation of the hierarchy of the equations of motion is made at the s-th order and the first s-1 equations are treated exactly. A theorem, which rules the conservation of the spectral moments, is presented. The procedure is applied to the Hubbard model and a recurrence relation for the calculation of its electronic spectral moments is derived.Comment: 16 RevTeX page

Effects of two-site composite excitations in the Hubbard model

The electronic states of the Hubbard model are investigated by use of the Composite Operator Method. In addition to the Hubbard operators, two other operators related with two-site composite excitations are included in the basis. Within the present formulation, higher-order composite excitations are reduced to the chosen operatorial basis by means of a procedure preserving the particle-hole symmetry. The positive comparison with numerical simulations for the double occupancy indicates that such approximation improves over the two-pole approximation.Comment: 2 pages, 1 figur

The Mott-Hubbard transition and the paramagnetic insulating state in the two-dimensional Hubbard model

The Mott-Hubbard transition is studied in the context of the two-dimensional Hubbard model. Analytical calculations show the existence of a critical value Uc of the potential strength which separates a paramagnetic metallic phase from a paramagnetic insulating phase. Calculations of the density of states and double occupancy show that the ground state in the insulating phase contains always a small fraction of empty and doubly occupied sites. The structure of the ground state is studied by considering the probability amplitude of intersite hopping. The results indicate that the ground state of the Mott insulator is characterized by a local antiferromagnetic order; the electrons keep some mobility, but this mobility must be compatible with the local ordering. The vanishing of some intersite probability amplitudes at U=Uc puts a constrain on the electron mobility. It is suggested that such quantities might be taken as the quantities which control the order in the insulating phase.Comment: 7 pages, 5 EPS figures, EuroTeX, to be published in EuroPhysics Letters; content changed, references remove

Different realizations of tomographic principle in quantum state measurement

We establish a general principle for the tomographic approach to quantum state reconstruction, till now based on a simple rotation transformation in the phase space, which allows us to consider other types of transformations. Then, we will present different realizations of the principle in specific examples.Comment: 17 pages, Latex file, no figures, accepted by J. of Mod. Op