Ferdinando Mancini - Academia.edu (original) (raw)

Papers by Ferdinando Mancini

Journal of Physical Studies, 1998

The discovery of new materials with properties dominated by strong correlations among electrons h... more The discovery of new materials with properties dominated by strong correlations among electrons has opened the problem of new appropriate calculation schemes. In the case of 1D models the Bethe ansatz provides an exact evaluation of many relevant physical quantities, but not a complete framework. By way of developing new methods appropriate to strongly correlated systems, we study the 1D Hubbard model by means of the Composite Operator Method. We investigate various local quantities. A comparison with exact results and other analytical approaches show a reasonable agreement and determine the applicability range of our approximate scheme.

Physical Review B, 1998

In the low doping region an incommensurate magnetic phase is observed in La2−xSrxCuO4. By means o... more In the low doping region an incommensurate magnetic phase is observed in La2−xSrxCuO4. By means of the composite operator method we show that the single-band 2D Hubbard model describes the experimental situation. In the higher doping region, where experiments are not available, the incommensurability is depressed owing to the van Hove singularity near the Fermi level. A proportionality between the incommensurability amplitude and the critical temperature is predicted, suggesting a close relation between superconductivity and incommensurate magnetism.

Physica B: Condensed Matter, 1999

The charge susceptibility and the specific heat of the 1D Hubbard model are calculated by means o... more The charge susceptibility and the specific heat of the 1D Hubbard model are calculated by means of the composite operator method for finite temperature as functions of filling. A large renormalization of the charge fluctuations appears as the system approaches the metal-insulator transition.

Lettere al Nuovo Cimento, 1970

By using Density Matrix Renormalization Group (DMRG) technique we study the 1D extended anisotrop... more By using Density Matrix Renormalization Group (DMRG) technique we study the 1D extended anisotropic Heisenberg model. We find that starting from the ferromagnetic phase, the system undergoes two quantum phase transitions (QPTs) induced by frustration. By increasing the nextnearest-neighbor (NNN) interaction, the ground state of the system changes smoothly from a completely polarized state to a NNN correlated one. On the contrary, letting the in-plane interaction to be greater than the out-ofplane one, the ground state changes abruptly.

Condensed Matter Physics, 2006

We present the Composite Operator Method (COM) as a modern approach to the study of strongly corr... more 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.

Condensed Matter Physics, 2006

We present a concise and systematic review of the ergodicity issue in strongly correlated systems... more We present a concise and 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 identify the primary source of non-ergodic dynamics for a generic operator as well as to give a recipe for computing unknown quantities characterizing such a behavior within the Composite Operator Method. Finally, we present examples of nontrivial strongly correlated systems where it is possible to find a non-ergodic behavior.

Physics Letters A, 2001

Spin dynamics is calculated in the ferromagnetic (FM) state of the generalized Kondo lattice mode... more Spin dynamics is calculated in the ferromagnetic (FM) state of the generalized Kondo lattice model taking into account strong on-site correlations between eg electrons and antiferromagnetic (AFM) exchange among t2g spins. Our study suggests that competing FM double-exchange and AFM super-exchange interaction lead to a rather nontrivial spin-wave spectrum. While spin excitations have a conventional Dq 2 spectrum in the long-wavelength limit, there is a strong deviation from the spin-wave spectrum of the isotropic Heisenberg model close to the zone boundary. The relevance of our results to the experimental data are discussed.

Physical Review E, 2006

We exactly solve the ferromagnetic spin-1/2 Ising model on the Bethe lattice in the presence of a... more We exactly solve the ferromagnetic spin-1/2 Ising model on the Bethe lattice in the presence of an external magnetic field by means of the equations of motion method within the Green's function formalism. In particular, such an approach is applied to an isomorphic model of localized Fermi particles interacting via an intersite Coulomb interaction. A complete set of eigenoperators is found together with the corresponding eigenvalues. The Green's functions and the correlation functions are written in terms of a finite set of parameters to be self-consistently determined. A procedure is developed, that allows us to exactly fix the unknown parameters in the case of a Bethe lattice with any coordination number z. Non-local correlation functions up to four points are also provided together with a study of the relevant thermodynamic quantities.

Physica C: Superconductivity, 1999

In order to describe the variety of results observed in different cuprates the original Hubbard m... more In order to describe the variety of results observed in different cuprates the original Hubbard model is too simple. In this paper we consider a generalization of it, where correlated hopping and intersite Coulomb interaction are considered. By using the Composite Operator Method we analyze the effect of these extra terms on the Fermi surface and the relative position of the van Hove singularity with respect to the Fermi level. Comparison with recent ARPES data on La Sr CuO 2yx x 4 is discussed.

Physica C: Superconductivity, 2007

A fermionic model, built up of q species of localized Fermi particles, interacting by charge corr... more 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 Tc, the fermionic system for T < Tc is unstable against the formation of inhomogeneous phases with charge separation.

Physica B: Condensed Matter, 1989

A new method for solving the Anderson model is proposed. The method is based on a perturbation ex... more A new method for solving the Anderson model is proposed. The method is based on a perturbation expansion in the kinetic energy of the conduction electrons. In the limit of zero width the model is exactly solvable. By means of the path integral formalism exact analytic expressions for the n-point Green's functions at finite temperature are derived. The analysis is also extended to the case of time-dependent situations by means of Thermo Field Dynamics. A new diagram method to compute the n-point functions is also proposed.

Journal of Physics: Conference Series, 2011

The orbital degrees of freedom are of vital importance in explanation of various phenomena. Among... more The orbital degrees of freedom are of vital importance in explanation of various phenomena. Among them is the orbital-selective Mott transition (OSMT), which is thought to occur in several materials as Ca2−xSrxRuO4 and Lan+1NinO3n+1. OSMT is usually studied in the infinite-dimension limit, and for the time being, it is not clear if it could survive in onedimensional (1D) case. There exist two scenarios for the OSMT: upon increasing the interaction in a two-band system i) one of the bands becomes insulating, while the other remains metallic and ii) one of the bands becomes empty, while the other may eventually undergo a singleband Mott insulator transition. In this work, we present a preliminary study of the two-orbital Hubbard model by means of Density Matrix Renormalization Group in 1D at quarter-filling, where the second scenario seems to be realized. In particular, we study the orbital densities, double occupancies and form-factors also in the case of finite inter-orbital inter-site hopping.

International Journal of Quantum Chemistry, 1980

By using quantum-field theory techniques and the boson transformation method, we study systems th... more By using quantum-field theory techniques and the boson transformation method, we study systems that exhibit macroscopic ordered states. As an illustration, we apply the method to the study of superconducting systems by taking into account the quantization of the vector potential. The results of a dynamical calculation, performed in the pair approximation, are presented. The Higgs phenomenon is also discussed in the framework of a fully quantum theory. A(+) is a derivative operator and F[+] is a functional of J,. We look for solutions of Eq. (1) such that J, can be expressed in terms of normal products of a set of free fields {4}: This expression has to be read as a weak relation, the Hilbert space being chosen as the Fock space of free fields. A realization of Eq. (2) can be obtained by means of the Lsz-formula, the free fields being determined by the condition that the Heisenberg equation [Eq. (l)] be satisfied.

The European Physical Journal B - Condensed Matter, 2003

The Green's function formalism in Condensed Matter Physics is reviewed within the equation of mot... more The Green's function formalism in Condensed Matter Physics is reviewed within the equation of motion approach. Composite operators and their Green's functions naturally appear as building blocks of generalized perturbative approaches and require fully self-consistent treatments in order to be properly handled. It is shown how to unambiguously set the representation of the Hilbert space by fixing both the unknown parameters, which appear in the linearized equations of motion and in the spectral weights of non-canonical operators, and the zero-frequency components of Green's functions in a way that algebra and symmetries are preserved. To illustrate this procedure some examples are given: the complete solution of the two-site Hubbard model, the evaluation of spin and charge correlators for a narrow-band Bloch system, the complete solution of the three-site Heisenberg model, and a study of the spin dynamics in the Double-Exchange model.

The European Physical Journal B, 2008

We consider the extended Hubbard model in the atomic limit on a Bethe lattice with coordination n... more 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.

The European Physical Journal B, 2013

Within the Composite Operator Method (COM), we report the solution of the Emery model (also known... more 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 superconductors. 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 singleparticle 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 qualitatively 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.

The European Physical Journal B, 2013

In this paper we present for the first time the exact solution in the narrow-band limit of the 1D... more In this paper we present for the first time the exact solution in the narrow-band limit of the 1D extended Hubbard model with nearest-neighbour spin-spin interactions described by an exchange constant J. An external magnetic field h is also taken into account. This result has been obtained in the framework of the Green's functions formalism, using the Composite Operator Method. By means of this theoretical background, we have studied some relevant features such as double occupancy, magnetization, spin-spin and charge-charge correlation functions and derived a phase diagram for both ferro (J > 0) and anti-ferro (J < 0) coupling in the limit of zero temperature. We also report a study on density of states, specific heat, charge and spin susceptibilities. In the limit of zero temperature, we show that the model exhibits a very rich phase diagram characterized by different magnetic orders and by the coexistence of charge and spin orderings at commensurate filling. Moreover, our analysis at finite temperature of density of states and response functions shows the presence of low-temperature charge and spin excitations near the phase boundaries.

The European Physical Journal B, 2008

By means of the Density Matrix Renormalization Group technique, we have studied the region where ... more 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.

Open Physics, 2012

In this paper we study a generalization of the Hubbard model by considering spin-spin interaction... more In this paper we study a generalization of the Hubbard model by considering spin-spin interactions described by the exchange constant J. An external magnetic field his also taken into account. In the narrowband limit and for the 1D case, we present the exact solution obtained in the framework of the Green’s function formalism, using the Composite Operator Method. We report the T = 0 phase diagram for both ferro (J > 0) and anti-ferro (J < 0) couplings. The competition of the different energy scales (U, J, and h; being U the local charge interaction) generates a variety of phases and different charge and spin orderings.

Journal of Physical Studies, 1998

The discovery of new materials with properties dominated by strong correlations among electrons h... more The discovery of new materials with properties dominated by strong correlations among electrons has opened the problem of new appropriate calculation schemes. In the case of 1D models the Bethe ansatz provides an exact evaluation of many relevant physical quantities, but not a complete framework. By way of developing new methods appropriate to strongly correlated systems, we study the 1D Hubbard model by means of the Composite Operator Method. We investigate various local quantities. A comparison with exact results and other analytical approaches show a reasonable agreement and determine the applicability range of our approximate scheme.

Physical Review B, 1998

In the low doping region an incommensurate magnetic phase is observed in La2−xSrxCuO4. By means o... more In the low doping region an incommensurate magnetic phase is observed in La2−xSrxCuO4. By means of the composite operator method we show that the single-band 2D Hubbard model describes the experimental situation. In the higher doping region, where experiments are not available, the incommensurability is depressed owing to the van Hove singularity near the Fermi level. A proportionality between the incommensurability amplitude and the critical temperature is predicted, suggesting a close relation between superconductivity and incommensurate magnetism.

Physica B: Condensed Matter, 1999

The charge susceptibility and the specific heat of the 1D Hubbard model are calculated by means o... more The charge susceptibility and the specific heat of the 1D Hubbard model are calculated by means of the composite operator method for finite temperature as functions of filling. A large renormalization of the charge fluctuations appears as the system approaches the metal-insulator transition.

Lettere al Nuovo Cimento, 1970

By using Density Matrix Renormalization Group (DMRG) technique we study the 1D extended anisotrop... more By using Density Matrix Renormalization Group (DMRG) technique we study the 1D extended anisotropic Heisenberg model. We find that starting from the ferromagnetic phase, the system undergoes two quantum phase transitions (QPTs) induced by frustration. By increasing the nextnearest-neighbor (NNN) interaction, the ground state of the system changes smoothly from a completely polarized state to a NNN correlated one. On the contrary, letting the in-plane interaction to be greater than the out-ofplane one, the ground state changes abruptly.

Condensed Matter Physics, 2006

We present the Composite Operator Method (COM) as a modern approach to the study of strongly corr... more 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.

Condensed Matter Physics, 2006

We present a concise and systematic review of the ergodicity issue in strongly correlated systems... more We present a concise and 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 identify the primary source of non-ergodic dynamics for a generic operator as well as to give a recipe for computing unknown quantities characterizing such a behavior within the Composite Operator Method. Finally, we present examples of nontrivial strongly correlated systems where it is possible to find a non-ergodic behavior.

Physics Letters A, 2001

Spin dynamics is calculated in the ferromagnetic (FM) state of the generalized Kondo lattice mode... more Spin dynamics is calculated in the ferromagnetic (FM) state of the generalized Kondo lattice model taking into account strong on-site correlations between eg electrons and antiferromagnetic (AFM) exchange among t2g spins. Our study suggests that competing FM double-exchange and AFM super-exchange interaction lead to a rather nontrivial spin-wave spectrum. While spin excitations have a conventional Dq 2 spectrum in the long-wavelength limit, there is a strong deviation from the spin-wave spectrum of the isotropic Heisenberg model close to the zone boundary. The relevance of our results to the experimental data are discussed.

Physical Review E, 2006

We exactly solve the ferromagnetic spin-1/2 Ising model on the Bethe lattice in the presence of a... more We exactly solve the ferromagnetic spin-1/2 Ising model on the Bethe lattice in the presence of an external magnetic field by means of the equations of motion method within the Green's function formalism. In particular, such an approach is applied to an isomorphic model of localized Fermi particles interacting via an intersite Coulomb interaction. A complete set of eigenoperators is found together with the corresponding eigenvalues. The Green's functions and the correlation functions are written in terms of a finite set of parameters to be self-consistently determined. A procedure is developed, that allows us to exactly fix the unknown parameters in the case of a Bethe lattice with any coordination number z. Non-local correlation functions up to four points are also provided together with a study of the relevant thermodynamic quantities.

Physica C: Superconductivity, 1999

In order to describe the variety of results observed in different cuprates the original Hubbard m... more In order to describe the variety of results observed in different cuprates the original Hubbard model is too simple. In this paper we consider a generalization of it, where correlated hopping and intersite Coulomb interaction are considered. By using the Composite Operator Method we analyze the effect of these extra terms on the Fermi surface and the relative position of the van Hove singularity with respect to the Fermi level. Comparison with recent ARPES data on La Sr CuO 2yx x 4 is discussed.

Physica C: Superconductivity, 2007

A fermionic model, built up of q species of localized Fermi particles, interacting by charge corr... more 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 Tc, the fermionic system for T < Tc is unstable against the formation of inhomogeneous phases with charge separation.

Physica B: Condensed Matter, 1989

A new method for solving the Anderson model is proposed. The method is based on a perturbation ex... more A new method for solving the Anderson model is proposed. The method is based on a perturbation expansion in the kinetic energy of the conduction electrons. In the limit of zero width the model is exactly solvable. By means of the path integral formalism exact analytic expressions for the n-point Green's functions at finite temperature are derived. The analysis is also extended to the case of time-dependent situations by means of Thermo Field Dynamics. A new diagram method to compute the n-point functions is also proposed.

Journal of Physics: Conference Series, 2011

The orbital degrees of freedom are of vital importance in explanation of various phenomena. Among... more The orbital degrees of freedom are of vital importance in explanation of various phenomena. Among them is the orbital-selective Mott transition (OSMT), which is thought to occur in several materials as Ca2−xSrxRuO4 and Lan+1NinO3n+1. OSMT is usually studied in the infinite-dimension limit, and for the time being, it is not clear if it could survive in onedimensional (1D) case. There exist two scenarios for the OSMT: upon increasing the interaction in a two-band system i) one of the bands becomes insulating, while the other remains metallic and ii) one of the bands becomes empty, while the other may eventually undergo a singleband Mott insulator transition. In this work, we present a preliminary study of the two-orbital Hubbard model by means of Density Matrix Renormalization Group in 1D at quarter-filling, where the second scenario seems to be realized. In particular, we study the orbital densities, double occupancies and form-factors also in the case of finite inter-orbital inter-site hopping.

International Journal of Quantum Chemistry, 1980

By using quantum-field theory techniques and the boson transformation method, we study systems th... more By using quantum-field theory techniques and the boson transformation method, we study systems that exhibit macroscopic ordered states. As an illustration, we apply the method to the study of superconducting systems by taking into account the quantization of the vector potential. The results of a dynamical calculation, performed in the pair approximation, are presented. The Higgs phenomenon is also discussed in the framework of a fully quantum theory. A(+) is a derivative operator and F[+] is a functional of J,. We look for solutions of Eq. (1) such that J, can be expressed in terms of normal products of a set of free fields {4}: This expression has to be read as a weak relation, the Hilbert space being chosen as the Fock space of free fields. A realization of Eq. (2) can be obtained by means of the Lsz-formula, the free fields being determined by the condition that the Heisenberg equation [Eq. (l)] be satisfied.

The European Physical Journal B - Condensed Matter, 2003

The Green's function formalism in Condensed Matter Physics is reviewed within the equation of mot... more The Green's function formalism in Condensed Matter Physics is reviewed within the equation of motion approach. Composite operators and their Green's functions naturally appear as building blocks of generalized perturbative approaches and require fully self-consistent treatments in order to be properly handled. It is shown how to unambiguously set the representation of the Hilbert space by fixing both the unknown parameters, which appear in the linearized equations of motion and in the spectral weights of non-canonical operators, and the zero-frequency components of Green's functions in a way that algebra and symmetries are preserved. To illustrate this procedure some examples are given: the complete solution of the two-site Hubbard model, the evaluation of spin and charge correlators for a narrow-band Bloch system, the complete solution of the three-site Heisenberg model, and a study of the spin dynamics in the Double-Exchange model.

The European Physical Journal B, 2008

We consider the extended Hubbard model in the atomic limit on a Bethe lattice with coordination n... more 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.

The European Physical Journal B, 2013

Within the Composite Operator Method (COM), we report the solution of the Emery model (also known... more 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 superconductors. 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 singleparticle 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 qualitatively 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.

The European Physical Journal B, 2013

In this paper we present for the first time the exact solution in the narrow-band limit of the 1D... more In this paper we present for the first time the exact solution in the narrow-band limit of the 1D extended Hubbard model with nearest-neighbour spin-spin interactions described by an exchange constant J. An external magnetic field h is also taken into account. This result has been obtained in the framework of the Green's functions formalism, using the Composite Operator Method. By means of this theoretical background, we have studied some relevant features such as double occupancy, magnetization, spin-spin and charge-charge correlation functions and derived a phase diagram for both ferro (J > 0) and anti-ferro (J < 0) coupling in the limit of zero temperature. We also report a study on density of states, specific heat, charge and spin susceptibilities. In the limit of zero temperature, we show that the model exhibits a very rich phase diagram characterized by different magnetic orders and by the coexistence of charge and spin orderings at commensurate filling. Moreover, our analysis at finite temperature of density of states and response functions shows the presence of low-temperature charge and spin excitations near the phase boundaries.

The European Physical Journal B, 2008

By means of the Density Matrix Renormalization Group technique, we have studied the region where ... more 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.

Open Physics, 2012

In this paper we study a generalization of the Hubbard model by considering spin-spin interaction... more In this paper we study a generalization of the Hubbard model by considering spin-spin interactions described by the exchange constant J. An external magnetic field his also taken into account. In the narrowband limit and for the 1D case, we present the exact solution obtained in the framework of the Green’s function formalism, using the Composite Operator Method. We report the T = 0 phase diagram for both ferro (J > 0) and anti-ferro (J < 0) couplings. The competition of the different energy scales (U, J, and h; being U the local charge interaction) generates a variety of phases and different charge and spin orderings.