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F. P. Mancini

Publications and source records attributed to F. P. Mancini.

18 recordsLinked to original sources
arXiv2010

Magnetic properties of a strongly correlated system on the Bethe lattice

We study the influence of an external magnetic field h on the phase diagram 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 narrow-band limit. Our results establish that the magnetic field may dramatically affect the critical temperature below which a long-range charge ordered phase is observed, as well as the behavior of physical quantities, inducing, for instance, magnetization plateaus in the magnetization curves. Relevant thermodynamic quantities - such as the specific heat and the susceptibility - are also investigated at finite temperature by varying the on-site potential, the particle density and the magnetic field.

cond-mat.str-el↗
arXiv2009

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.

cond-mat.str-el↗
arXiv2009

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.

cond-mat.stat-mech↗
arXiv2009

Extended Hubbard model in the presence of a magnetic field

Within the Green's function and equations of motion formalism it is possible to exactly solve a large class of models useful for the study of strongly correlated systems. Here, we present the exact solution of the one-dimensional extended Hubbard model with on-site $U$ and first nearest neighbor repulsive V interactions in the presence of an external magnetic field h, in the narrow band limit. At zero temperature our results establish the existence of four phases in the three-dimensional space (U, n, h) - n is the filling - with relative phase transitions, as well as different types of charge ordering. The magnetic field may dramatically affect the behavior of thermodynamic quantities, inducing, for instance, magnetization plateaus in the magnetization curves, and a change from a single to a double-peak structure in the specific heat. According to the value of the particle density, we find one or two critical fields, marking the beginning of full or partial polarization. A detailed study of several thermodynamic quantities is also presented at finite temperature.

cond-mat.str-el↗
arXiv2008

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.

cond-mat.str-el↗
arXiv2008

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.

cond-mat.str-el↗
arXiv2008

Magnetic and thermal properties of a one-dimensional spin-1 model

We study the one-dimensional S=1 Blume-Emery-Griffiths model. Upon transforming the spin model into an equivalent fermionic model, we provide the exact solution within the Green's function and equations of motion formalism. We show that the relevant response functions as well as thermodynamic quantities can be determined, in the whole parameters space, in terms of a finite set of local correlators. Furthermore, considering the case of an antiferromagnetic chain with single-ion anisotropy in the presence of an external magnetic field, we find three plateaus in the magnetization curve; in the neighborhood of the endpoints of the intermediate plateau, the specific heat shows a double peak structure.

cond-mat.str-el↗
arXiv2007

Exact solution of the extended Hubbard model in the atomic limit on the Bethe Lattice

We study the phase diagram at finite temperature of a system of Fermi particles on the sites of the Bethe lattice with coordination number z and interacting through onsite U and nearest-neighbor V interactions. This is a physical realization of the extended Hubbard model in the atomic limit. By using the equations of motion method, we exactly solve the model. For an attractive intersite potential, we find, at half filling, a phase transition towards a broken particle-hole symmetry state. The critical temperature, as a function of the relevant parameters, has a re-entrant behavior as already observed in the equivalent spin-1 Ising model on the Bethe lattice.

cond-mat.str-el↗
arXiv2007

Spatially Inhomogeneous Superconducting and Bosonic Networks With Emergent Complex Behaviors

The spontaneous emergence of enhanced responses and local orders are properties often associated with complex matter where nonlinearities and spatial inhomogeneities dominate. We discuss these phenomena in quantum devices realized with superconducting Josephson junction networks and cold atoms in optical lattices. We evidence how the pertinent engineering of the network's shape induces the enhancement of the zero-voltage Josephson critical currents in superconducting arrays as well as the emergence of spatially localized condensates for cold atoms in inhomogeneous optical lattices.

cond-mat.supr-con↗
arXiv2006

BEC in a star-comb graph

We investigate the properties of free bosons hopping on a star-comb network, discussing the single-particle spectrum and the main thermodynamic equilibrium properties: Bose-Einstein critical temperature, fraction of condensate, and spatial boson distribution. We find an enhancement of the critical temperature with respect to other inhomogeneous networks.

cond-mat.stat-mech↗
arXiv2006

One-step replica symmetry breaking solution of the quadrupolar glass model

We consider the quadrupolar glass model with infinite-range random interaction. Introducing a simple one-step replica symmetry breaking ansatz we investigate the para-glass continuous (discontinuous) transition which occurs below (above) a critical value of the quadrupole dimension m*. By using a mean-field approximation we study the stability of the one-step replica symmetry breaking solution and show that for m>m* there are two transitions. The thermodynamic transition is discontinuous but there is no latent heat. At a higher temperature we find the dynamical or glass transition temperature and the corresponding discontinuous jump of the order parameter.

cond-mat.dis-nn↗
arXiv2004

Topology Induced Spatial Bose-Einstein Condensation for Bosons on Star-Shaped Optical Networks

New coherent states may be induced by pertinently engineering the topology of a network. As an example, we consider the properties of non-interacting bosons on a star network, which may be realized with a dilute atomic gas in a star-shaped deep optical lattice. The ground state is localized around the star center and it is macroscopically occupied below the Bose-Einstein condensation temperature T_c. We show that T_c depends only on the number of the star arms and on the Josephson energy of the bosonic Josephson junctions and that the non-condensate fraction is simply given by the reduced temperature T/T_c.

cond-mat.stat-mech↗
arXiv2004

Topology Induced Macroscopic Quantum Coherence in Josephson Junction Networks

We argue that Josephson junction networks may be engineered to allow for the emergence of new and robust quantum coherent states. We provide a rather intuitive argument showing how the change in topology may affect the quantum properties of a bosonic particle hopping on a network. As a paradigmatic example, we analyze in detail the quantum and thermodynamic properties of non-interacting bosons hopping on a comb graph. We show how to explicitly compute the inhomogeneities in the distribution of bosons along the comb's fingers, evidencing the effects of the topology induced spatial Bose-Einstein condensation characteristic of the system. We propose an experiment enabling to detect the spatial Bose-Einstein condensation for Josephson networks built on comb graphs.

cond-mat.stat-mech↗
arXiv2004

On the Phase Diagram of Josephson Junction Arrays with Offset Charges

We study the effects of external offset charges on the phase diagram of Josephson junction arrays. Using the path integral approach, we provide a pedagogical derivation of the equation for the phase boundary line between the insulating and the superconducting phase within the mean-field theory approximation. For a uniform offset charge q=e the superconducting phase increases with respect to q=0 and a characteristic lobe structure appears in the phase diagram when the critical line is plotted as a function of q at fixed temperature. We review our analysis of the physically relevant situation where a Josephson network feels the effect of random offset charges. We observe that the Mott-insulating lobe structure of the phase diagram disappears for large variance (σ> e) of the offset charges probability distribution; with nearest-neighbor interactions, the insulating lobe around q=e is destroyed even for small values of σ. Finally, we study the case of random self-capacitances: here we observe that, until the variance of the distribution reaches a critical value, the superconducting phase increases in comparison to the situation in which all self-capacitances are equal.

cond-mat.supr-con↗
arXiv2003

Self-Consistent Mean-Field Theory for Frustrated Josephson Junction Arrays

We review the self-consistent mean-field theory for charge-frustrated Josephson junction arrays. Using (ϕis the phase of the superconducting wavefunction) as order parameter and imposing the self-consistency condition, we compute the phase boundary line between the superconducting region ( not equal to zero) and the insulating one ( = 0). For a uniform offset charge q=e the superconducting phase increases with respect to the situation in which q=0. Here, we generalize the self-consistent mean-field theory to include the effects induced by a random distribution of offset charges and/or of diagonal self-capacitances. For most of the phase diagram, our results agree with the outcomes of Quantum Monte Carlo simulations as well as with previous studies using the path-integral approach.

cond-mat.supr-con↗
arXiv2003

Phase diagram of Josephson junction arrays with capacitive disorder

We study the phase diagram at finite temperature of Josephson junction arrays with capacitive disorder (i.e., random offset charges and/or random charging energies): in the limit of large particle numbers per junction, this is a remarkable physical realization of the disordered boson Hubbard model. By using a mean-field approximation, we compute the average free energy and the equation for the phase boundary line between the insulating and the superconducting phase. We find that the Mott-insulating lobe structure disappears for large variance ($σ\gtrsim e$) of the offset charges probability distribution. Further, with nearest-neighbor interactions, the insulating lobe around $q=e$ is destroyed even for small values of $σ$. In the case of random charging energies, until the variance of the distribution reaches some critical value the superconducting phase increases in comparison to the situation in which all self-capacitances are equal.

cond-mat.supr-con↗
arXiv2000

Phase Diagrams of the Harper Map and the Golden Staircase

We present phase diagrams of the Harper map, which is equivalent to the problem of Bloch electrons in a uniform magnetic field (Azbel-Hofstadter model). We consider the cases where the magnetic flux $ω$ assumes either the continued fraction approximations towards the golden mean or the golden mean itself. The phase diagrams for rational values of $ω$ show a finite number of Arnol'd tongues of localized electronic states with rational winding numbers and regions of extended phases in between them. For the particular case of $ω= \frac{\sqrt{5}-1}{2}$, we find an infinite number of Arnol'd tongues of localized phases with extended phases in between. In this case, the study of the winding number gives rise to a Golden Staircase, where the plateaux represent localized phases with winding numbers equal to sums of powers of the golden mean. We also present evidence of the existence of an infinite number of strange nonchaotic attractors for $ε=1$ in points analogous to critical points in the pressure-temperature phase diagram of the water.

cond-mat.dis-nn↗