Dynamical Model and Path Integral Formalism for Hubbard Operators

In this paper, the possibility to construct apath integral formalism by using the Hubbard operatorsas field dynamical variables is investigated. By meansof arguments coming from the Faddeev-Jackiw symplectic Lagrangian formalism as well as from theHamiltonian Dirac method, it can be shown that it is notpossible to define a classical dynamics consistent withthe full algebra of the Hubbard X-operators. Moreover, from the Faddeev-Jackiw symplectic algorithm,and in order to satisfy the Hubbard X-operatorscommutation rules, it is possible to determine thenumber of constraints that must be included in aclassical dynamical model. Following this approach, it isclear how the constraint conditions that must beintroduced in the classical Lagrangian formulation areweaker than the constraint conditions imposed by the full Hubbard operators algebra. The consequenceof this fact is analyzed in the context of the pathintegral formalism. Finally, in the framework of theperturbative theory, the diagrammatic and the Feynman rules of the model are discussed.     

Estimations of the Free Energy for the Hubbard Model

A series of upper bounds and two lower bounds for the partition function of the Hubbard model have been derived. These bounds are expressible by certain properties of the Falicov-Kimball model. The upper bounds have been derived mainly by the use of the Golden-Thompson inequality and its generalizations, and the Hölder inequality. The lower bounds are based on the Bogoliubov-Peierls inequality. The numerical values of bounds have also been calculated for small systems.     

Magnetization Curve for One-Dimensional Hubbard Model in Critical Region

A power series expression of the exact solution of the one-dimensional (1D) Hubbard model in an external magnetic field is derived to study the an tiferromagnet-ferromagnet transition in the critical region. Aside from the magnetization curve, the critical field and susceptibility are analytically evaluated, and the results of these quantities in some limiting cases are discussed.     

Nagaoka Ferromagnetism in Two-Band Hubbard Model

In the present paper, we investigate the existence of ferromagnetism in a two-band Hubbard model, by applying a recently-introduced method by us to study ferromagnetism in metallic clusters. We prove rigorously that the ground state of this model is ferromagnetic if the intra-orbital Coulomb repulsion between electrons is infinitely strong and only one hole exists in the system. Our theorem improves a previous result. Furthermore, our method can also be applied to deal with the case of multiple holes.     

Segregation in the Asymmetric Hubbard Model

We study the “asymmetric” Hubbard model, where hoppings of electrons depend on their spin. For strong interactions and sufficiently asymmetric hoppings, it is proved that the ground state displays phase separation away from half-filling. This extends a recent result obtained with Freericks and Lieb for the Falicov–Kimball model. It is based on estimates for the sum of lowest eigenvalues of the discrete Laplacian in arbitrary domains.     

Superconductivity in the Two-Dimensional Hubbard Model

It is shown that the existence of d-wave superconductivity in the two-dimensional Hubbard model close to half-filling can be inferred from a renormalization group analysis at one-loop level.     

Charge Gap in One-Dimensional Extended Hubbard Model

By using the bosonization and renormalization group methods, we have studied the low energy physical properties in one-dimensional extended Hubbard model. The formation of charge and spin gaps is investigated at the half-filled electron band. An analytical expression for the charge gap in terms of the Coulomb repulsive interaction strength U and the nearest-neighbour interaction parameter V is obtained.     

Quantum Group Symmetry of the Hubbard Model

Quantum group symmetry is shown to exist for the Hubbard model. It is extendedto include infinitesimally deformed phonons. A simplified version of Alam'smodel is generalized to include phonons and is shown to have quantum groupsymmetry.     

Quantum Group Symmetry of the Hubbard Model

Quantum group symmetry is shown to exist for the Hubbard model. It is extendedto include infinitesimally deformed phonons. Also a simplified version of Alam'smodel is generalized to include phonons and is shown to have quantum groupsymmetry.     

Entanglement, Hubbard Model, and Symmetries

Entangled quantum states are an important component of quantum computing techniques such as quantum error-correction, dense coding, and quantum teleportation. We use the requirements for a state in the Hilbert space C ² C ² to be entangled to find when states evolving under the two-point Hubbard model become entangled. We also investigate the connection of entanglement and discrete symmetries of the two-point Hubbard model. Furthermore we discuss the inclusion of phonon coupling.     

Pseudogaps in the 2D Hubbard Model

We study the pseudogaps in the spectra of the 2D Hubbard model using both finite-size and dynamical cluster approximation (DCA) quantum Monte Carlo calculations. At half-filling, a charge pseudogap, accompanied by non-Fermi-liquid behavior in the self-energy, is shown to persist in the thermodynamic limit. The DCA (finite-size) method systematically underestimates (overestimates) the width of the pseudogap. A spin pseudogap is not seen at half-filling. At finite doping, a divergent d-wave pair susceptibility is observed.     

Block Entanglement in the Single-Hole Hubbard Model

We investigate the distribution of the entanglement of the one-dimensional single-hole Hubbard model （HM） and study the relationship between the entanglement and quantum phase transition in the model. The von Neumann entropy of a block with neighbouring spins L for a single-hole HM is calculated using the densitymatrix renormalization group. The distributions of the entanglement entropy in the ground state, as a function of block length, show a dramatic effect, i.e. effectively decoupling with the centres, no matter how the Coulomb interaction u 〉0 or u 〈0. Contrarily, for the Coulomb interaction u = 0 or close to zero, the entanglement entropy in the single-hole model reaches a saturation value for a certain block size. For a fixed size L = 40, the ground state entanglement entropy measure, as a function of u1 shows a peak corresponding to the critical quantum phase transition.     

The Critical Properties of One—Dimensional Extended Hubbard Model

In the framework of nonperturbative quantum field theory,the critical phenomena of one-dimensional extended Hubbard model (EHM) at half-filling are discussed from weak to intermediate interactions.After the EHM being mapped into two decoupled sine-Gordon models,the ground state phase diagram of the system is derived in an explicit way.It is confirmed that the coexisting phases appear in different interaction regimes which cannot be found by conventional theoretical methods.The diagram shows that there are seven different phase regions in the ground state,which seems not to be the same as previous discussions,especially the boundary between the phase separation and condensed phase regions.The phase transition properties of the model between various phase regions are studied in detail.     

Fermion Coherent State Studies of One-Dimensional Hubbard Model

We present a comparative study of the ground state of the one-dimensional Hubbard model. We first use a new fermion coherent state method in the framework of Fermi liquid theory by introducing a hole operator and considering the interactions of two pairs electrons and holes. We construct the ground state of the Hubbard model as ｜〉=[f＋∑^tφk1σ1hk2σ2ck3σ3hk4σ4 ∏exp（ρck1σ1 hk2σ2）]｜〉0,where φ and ρ are the coupling constants. Our results are then compared to those of varlational methods, density functional theory based on the exact solvable Bethe ansatz solutions, variational Monto-Carlo method （VMC） as well as to the exact result of the infinite system. We find satisfactory agreement between the fermion coherent state scheme and the VMC data, and provide a new picture to deal with the strongly correlated system.     

Finite-Temperature Optical Conductivity of the Two-Dimensional Hubbard Model

The finite-temperature optical conductivity of the two-dimensional Hubbard model is studied by means of the grand canonical quantum Monte Carlo method. Results are reported for the half-filled and nonhalf-filled band. The formation and variation of Hubbard gap are observed. For the half-filled band case, our results support that there exists a high-temperature insulator-metal transition.     

A Possible Pairing Mechanism in Two-Band Hubbard Model

A theoretical scheme for describing the quasiparticle-pair superconductivity in doped CuO₂ system is suggested based on the model put forward by Emery and Reiter. The doped O holes and associated two neighboring Cu-spins form spin-1/2 quasiparticles. Through the magnetic interaction with the spin background, the quasiparticles interact with each other and lead to pair condensation which is responsible for the superconductivity.     

Quantum Integrability of 1D Ionic Hubbard Model

The quantum integrability of the 1D ionic Hubbard model (IHM) is established using two independent numerical methods, namely i) energy level spacing statistics and ii) occupation profile of one-particle density matrix (OPDM) eigen-values. Both methods suggest that the 1D IHM is integrable. The calculations of energy level statistics reproduce the known results for the standard Hubbard model. Upon turning on the the ionic term, the energy level spacing distribution of this model continues to obey the Poissonian distribution. Occupation patterns as extracted from OPDM indicate that quasi-particles are sharpened upon increasing the ionic potential. This is evidenced by a larger jump in the occupation number distribution.