arXiv subjects

Ferdinando Mancini

Publications and source records attributed to Ferdinando Mancini.

At least 19 recordsLinked to original sources

arXiv2015

Analysis of the magnetic response of the edge-sharing chain cuprate Li$_2$CuO$_2$ within TMRG

It is widely accepted that the low-energy physics in edge-sharing cuprate materials has one-dimensional (1D) character. The relevant model to study such systems is believed to be the 1D extended Heisenberg model with ferromagnetic nearest-neighbor (NN) interaction and antiferromagnetic next-nearest-neighbor one. Thus far, however, theoretical studies of such materials have been confined to the case of isotropic interactions. In the present work, we compare the spin susceptibility of the 1D extended Heisenberg model with anisotropy in the NN channel, obtained by means of the Transfer Matrix Renormalization Group method, with that of the edge-sharing chain cuprate Li$_2$CuO$_2$.

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arXiv2015

The phase diagram of the extended anisotropic ferromagnetic-antiferromagnetic Heisenberg chain

By using Density Matrix Renormalization Group (DMRG) technique we study the phase diagram of 1D extended anisotropic Heisenberg model with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions. We analyze the static correlation functions for the spin operators both in- and out-of-plane and classify the zero-temperature phases by the range of their correlations. On clusters of $64,100,200,300$ sites with open boundary conditions we isolate the boundary effects and make finite-size scaling of our results. Apart from the ferromagnetic phase, we identify two gapless spin-fluid phases and two ones with massive excitations. Based on our phase diagram and on estimates for the coupling constants known from literature, we classify the ground states of several edge-sharing materials.

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arXiv2013

Exact solution of the 1D Hubbard model with NN and NNN interactions in the narrow-band limit

We present the exact solution, obtained by means of the Transfer Matrix (TM) method, of the 1D Hubbard model with nearest-neighbor (NN) and next-nearest-neighbor (NNN) Coulomb interactions in the atomic limit (t=0). The competition among the interactions ($U$, $V_1$, and $V_2$) generates a plethora of T=0 phases in the whole range of fillings. $U$, $V_1$, and $V_2$ are the intensities of the local, NN and NNN interactions, respectively. We report the T=0 phase diagram, in which the phases are classified according to the behavior of the principal correlation functions, and reconstruct a representative electronic configuration for each phase. In order to do that, we make an analytic limit $T\to 0$ in the transfer matrix, which allows us to obtain analytic expressions for the ground state energies even for extended transfer matrices. Such an extension of the standard TM technique can be easily applied to a wide class of 1D models with the interaction range beyond NN distance, allowing for a complete determination of the T=0 phase diagrams.

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arXiv2013

Emery vs. Hubbard model for cuprate superconductors: a Composite Operator Method study

Within the Composite Operator Method (COM), we report the solution of the Emery model (also known as p-d or three band model), which is relevant for the cuprate high-Tc superconduc- tors. We also discuss the relevance of the often-neglected direct oxygen-oxygen hopping for a more accurate, sometimes unique, description of this class of materials. The benchmark of the solution is performed by comparing our results with the available quantum Monte Carlo ones. Both single- particle and thermodynamic properties of the model are studied in detail. Our solution features a metal-insulator transition at half filling. The resulting metal-insulator phase diagram agrees qual- itatively very well with the one obtained within Dynamical Mean-Field Theory. We discuss the type of transition (Mott-Hubbard (MH) or charge-transfer (CT)) for the microscopic (ab-initio) parameter range relevant for cuprates getting, as expected a CT type. The emerging single-particle scenario clearly suggests a very close relation between the relevant sub-bands of the three- (Emery) and the single- band (Hubbard) models, thus providing an independent and non-perturbative proof of the validity of the mapping between the two models for the model parameters optimal to describe cuprates. Such a result confirms the emergence of the Zhang-Rice scenario, which has been recently questioned. We also report the behavior of the specific heat and of the entropy as functions of the temperature on varying the model parameters as these quantities, more than any other, depend on and, consequently, reveal the most relevant energy scales of the system.

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arXiv2011

The Composite Operator Method (COM)

The Composite Operator Method (COM) is formulated, its internals illustrated in detail and some of its most successful applications reported. COM endorses the emergence, in strongly correlated systems (SCS), of composite operators, optimally deals with their unusual features and implements algebra constraints, and other relevant symmetries, in order to properly compute the unconventional properties of SCS.

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arXiv2011

Spin and charge orderings in the atomic limit of the U-V-J model

In this paper we study a generalization of the 1D Hubbard model by considering density-density and Ising-type spin-spin nearest neighbor (NN) interactions, parameterized by $V$ and $J$, respectively. We present the T=0 phase diagram for both ferro ($J>0$) and anti-ferro ($J<0$) coupling obtained in the narrow-band limit by means of an extension to zero-temperature of the transfer-matrix method. Based on the values of the Hamiltonian parameters, we identify a number of phases that involve orderings of the double occupancy, NN density and spin correlations, being these latter very fragile.

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arXiv2009

The two-orbital Hubbard model and the OSMT

We analyze the two-orbital Hubbard model by means of the Composite Operator Method with the aim at studying the phenomenon of orbital selective Mott transition (OSMT). The model contains an interorbital interaction $U'$, in addition to the usual intraorbital one $U$. As warming-up approximation, we use a basis of two operators only, the Hubbard operators. The analysis of the density of states at the chemical potential as a function of the ratio between the bandwidths of the two orbitals shows the clear signature of an orbital selective Mott transition as expected.

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arXiv2008

XXZ-like phase in the F-AF anisotropic Heisenberg chain

By means of the Density Matrix Renormalization Group technique, we have studied the region where $XXZ$-like behavior is most likely to emerge within the phase diagram of the F-AF anisotropic extended ($J-J'$) Heisenberg chain. We have analyzed, in great detail, the equal-time two-spin correlation functions, both in- and out-of- plane, as functions of the distance (and momentum). Then, we have extracted, through an accurate fitting procedure, the exponents of the asymptotic power-law decay of the spatial correlations. We have used the exact solution of $XXZ$ model ($J'=0$) to benchmark our results, which clearly show the expected agreement. A critical value of $J'$ has been found where the relevant power-law decay exponent is independent of the in-plane nearest-neighbor coupling.

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arXiv2007

Inhomogeneous charge ordering of a spinless fermionic system on the Bethe lattice

We show that a system of spinless Fermi particles, localized on the sites of the Bethe lattice with coordination number z and interacting through a repulsive nearest-neighbor interaction, exhibits a phase transition to a charge-ordered state. The phase diagram in the n-T plane is derived. Relevant thermodynamic quantities, such as the free energy, the specific heat, the entropy and the compressibility are analyzed in detail.

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arXiv2007

Fermionic systems with charge correlations on the Bethe lattice

A fermionic model, built up of q species of localized Fermi particles, interacting by charge correlations, is isomorphic to a spin-q/2 Ising model. However, the equivalence is only formal and the two systems exhibit a different physical behavior. By considering a Bethe lattice with q=1, we have exactly solved the models. There exists a critical temperature below which there is a spontaneous breakdown of the particle-hole symmetry for the first model, and of the spin symmetry for the second. While the spin system is always stable and exhibits a homogeneous ferromagnetic phase below T_{c}, the fermionic system for T<T_{c} is unstable against the formation of inhomogeneous phases with charge separation.

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arXiv2007

Entanglement in the F-AF zig-zag Heisenberg chain

We present a study of the entanglement properties of the F-AF zig-zag Heisenberg chain done by means of the Density Matrix Renormalization Group method. In particular, we have selected the concurrence as measure of entanglement and checked its capability to signal the presence of quantum phase transitions within the previously found ergodicity phase diagram [E. Plekhanov, A. Avella, and F. Mancini, Phys. Rev. B \textbf{74}, 115120 (2006)]. By analyzing the behavior of the concurrence, we have been able not only to determine the position of the transition lines within the phase diagram of the system, but also to identify a well defined region in the parameter space of the model that shows a complex spin ordering indicating the presence of a new phase of the system.

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arXiv2007

Ergodicity in Strongly Correlated Systems

We present a concise, but systematic, review of the ergodicity issue in strongly correlated systems. After giving a brief historical overview, we analyze the issue within the Green's function formalism by means of the equations of motion approach. By means of this analysis, we are able to individuate the primary source of non-ergodic dynamics for a generic operator and also to give a recipe to compute unknown quantities characterizing such a behavior within the Composite Operator Method. Finally, we present examples of non-trivial strongly correlated systems where it is possible to find a non-ergodic behavior.

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arXiv2007

A class of solvable models in Condensed Matter Physics

In this paper, we show that there is a large class of fermionic systems for which it is possible to find, for any dimension, a finite closed set of eigenoperators and eigenvalues of the Hamiltonian. Then, the hierarchy of the equations of motion closes and analytical expressions for the Green's functions are obtained in terms of a finite number of parameters, to be self-consistently determined. Several examples are given. In particular, for these examples it is shown that in the one-dimensional case it is possible to derive by means of algebraic constraints a set of equations which allow us to determine the self-consistent parameters and to obtain a complete exact solution.

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arXiv2007

Green's Function Formalism for Highly Correlated Systems

We present the Composite Operator Method (COM) as a modern approach to the study of strongly correlated electronic systems, based on the equation of motion and Green's function method. COM uses propagators of composite operators as building blocks at the basis of approximate calculations and algebra constrains to fix the representation of Green's functions in order to maintain the algebraic and symmetry properties.

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arXiv2007

Study of the spin-$\frac32$ 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.

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arXiv2007

The charge and spin sectors of the $t$-$t'$ Hubbard model

The charge and spin sectors, which are intimately coupled to the fermionic one, of the $t$-$t'$ Hubbard model have been computed self-consistently within the two-pole approximation. The relevant unknown correlators appearing in the causal bosonic propagators have been computed by enforcing the constraints dictated by the hydrodynamics and the algebra of the composite operators coming into play. The proposed scheme of approximation extends previous calculations made for the fermionic sector of the $t$-$t'$ Hubbard model and the bosonic sector of the Hubbard model, which showed to be very effective to describe the overdoped region of cuprates (the former) and the magnetic response of their parent compounds (the latter).

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arXiv2007

The Hubbard model: bosonic excitations and zero-frequency constants

A fully self-consistent calculation of the bosonic dynamics of the Hubbard model is developed within the Composite Operator Method. From one side we consider a basic set of fermionic composite operators (Hubbard fields) and calculate the retarded propagators. On the other side we consider a basic set of bosonic composite operators (charge, spin and pair) and calculate the causal propagators. The equations for the Green's functions (GF) (retarded and causal), studied in the polar approximation, are coupled and depend on a set of parameters not determined by the dynamics. First, the pair sector is self-consistently solved together with the fermionic one and the zero-frequency constants (ZFC) are calculated not assuming the ergodic value, but fixing the representation of the GF in such a way to maintain the constrains required by the algebra of the composite fields. Then, the scheme to compute the charge and spin sectors, ZFCs included, is given in terms of the fermionic and pair correlators.

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arXiv2007

Ergodicity of the extended anisotropic 1D Heisenberg model: response at low temperatures

We present the results of exact diagonalization calculations of the isolated and isothermal on-site static susceptibilities in the anisotropic extended Heisenberg model on a linear chain with periodic boundary conditions. Based on the ergodicity considerations we conclude that the isothermal susceptibility will diverge as $T\to 0$ both in finite clusters and in the bulk system in two non-ergodic regions of the phase diagram of the system.

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