The half-filled Hubbard chain in the Composite Operator Method: A comparison with Bethe Ansatz (original) (raw)

The 1D Hubbard model within the Composite Operator Method

The European Physical Journal B, 2002

Although effective for two dimensional (2D) systems, some approximations may fail in describing the properties of one-dimensional (1D) models, which belong to a different universality class. In this paper, we analyze the adequacy of the Composite Operator Method (COM ), which provides a good description of many features of 2D strongly correlated systems, in grasping the physics of 1D models. To this purpose, the 1D Hubbard model is studied within the framework of the COM by considering a two-pole approximation and a paramagnetic ground state. The local, thermodynamic and single-particle properties, the correlation functions and susceptibilities are calculated in the case of half filling and arbitrary filling. The results are compared with those obtained by the Bethe Ansatz (BA) as well as by other numerical and analytical techniques. The advantages and limitations of the method are analyzed in detail.

The Hubbard model with intersite interaction within the Composite Operator Method

The European Physical Journal B Condensed Matter Physics, 2004

We study the one- and two- dimensional extended Hubbard model by means of the Composite Operator Method within the 2-pole approximation. The fermionic propagator is computed fully self-consistently as a function of temperature, filling and Coulomb interactions. The behaviors of the chemical potential (global indicator) and of the double occupancy and nearest-neighbor density- density correlator (local indicators) are analyzed in detail as primary sources of information regarding the instability of the paramagnetic (metal and insulator) phase towards charge ordering driven by the intersite Coulomb interaction. Very rich phase diagrams (multiple first and second order phase transitions, critical points, reentrant behavior) have been found and discussed with respect to both metal-insulator and charge ordering transitions: the connections with the experimental findings relative to some manganese compounds are analyzed. Moreover, the possibility of improving the capability of describing cuprates with respect to the simple Hubbard model is discussed through the analysis of the Fermi surface and density of states features. We also report about the specific heat behavior in presence of the intersite interaction and the appearance of crossing points.

The N-chain Hubbard model in the composite operator method

Physica B: Condensed Matter, 1999

We propose a theoretical framework to describe the ladder systems. The N-chain Hubbard model has been studied within the Composite Operator Method. In this scheme of calculations the single-particle Green's function for any number of coupled chains is obtained by solving self-consistently a system of integral equations.

Local quantities for the 1D Hubbard model in the composite operator method

Journal of Physical Studies, 1998

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.

A 4-pole approach to the Hubbard model within the Composite Operator Method

Journal of Physics: Conference Series, 2012

The Hubbard model is studied within the Composite Operator Method framework in a 4-pole approximation. The operatorial basis is chosen according to both the hierarchy of equations of motion and the exact solution of the model reduced to the minimal cluster (2 sites) where all Hamiltonian terms are still active. Such a recipe amounts to include into the basis not only the two Hubbard operators, which usually take care of the scale of energy related to the on-site Coulomb repulsion U , but also two other non-local operators describing the Hubbard operators dressed by charge, spin and pair fluctuations on the nearest-neighboring sites and addressing the dynamically generated scale of energy related to the exchange J = 4t 2 /U . The calculation framework is outlined and a very first comparison to numerical simulations, showing very good qualitative and quantitative agreement, is reported. As reference, the results in the 2-pole approximation are also reported and the differences discussed.

Antiferromagnetic phase in the Hubbard model by means of the composite operator method

Physical Review B, 2001

We have investigated the antiferromagnetic phase of two-dimensional ͑2D͒, three-dimensional ͑3D͒, and extended Hubbard models on a bipartite cubic lattice by means of the composite operator method within a two-pole approximation. This approach yields a fully self-consistent treatment of the antiferromagnetic state that respects the symmetry properties of both the model and the algebra. The complete phase diagram, as regards the antiferromagnetic and paramagnetic phases, has been drawn. We first reported, within a pole approximation, three kinds of transitions at half-filling: Mott-Hubbard, Mott-Heisenberg, and Heisenberg transitions. We have also found a metal-insulator transition, driven by doping, within the antiferromagnetic phase. This latter is restricted to a very small region near half-filling, and has, in contrast to what has been found by similar approaches, a finite critical Coulomb interaction as a lower bound at half-filling. Finally, it is worth noting that our antiferromagnetic gap has two independent components: one due to the antiferromagnetic correlations, and another coming from the Mott-Hubbard mechanism.

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

2007

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\frac32frac32 spins, together with usual Hund coupling between electrons and spins.

Study of the spin- Hubbard–Kondo lattice model by means of the Composite Operator Method

2006

We study the spin-3 2 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 3 2 spins, together with usual Hund coupling between electrons and spins.

Study of the spin- 3 2 Hubbard�Kondo lattice model by means of the Composite Operator Method

Physica B Condensed Matter, 2006

We study the spin- {3}/{2} 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 {3}/{2} spins, together with usual Hund coupling between electrons and spins.

Properties of the half-filled Hubbard model investigated by the strong coupling diagram technique

International Journal of Modern Physics B

The equation for the electron Green's function of the fermionic Hubbard model, derived using the strong coupling diagram technique, is solved self-consistently for the near-neighbor form of the kinetic energy and for half-filling. In this case the Mott transition occurs at the Hubbard repulsion U c ≈ 6.96t, where t is the hopping constant. The calculated spectral functions, density of states and momentum distribution are compared with results of Monte Carlo simulations. A satisfactory agreement was found for U > U c and for temperatures, at which magnetic ordering and spin correlations are suppressed. For U < U c and lower temperatures the theory describes qualitatively correctly positions and widths of spectral continua, variations of spectral shapes and occupation numbers with changing wave vector and repulsion. The locations of spectral maxima turn out to be close to the positions of δ-function peaks in the Hubbard-I approximation.