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 tructure 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.     

Ground state phases of the half-filled one-dimensional extended hubbard model

Using quantum Monte Carlo simulations, results of a strong-coupling expansion, and Luttinger liquid theory, we determine quantitatively the ground state phase diagram of the one-dimensional extended Hubbard model with on-site and nearest-neighbor repulsions U and V. We show that spin frustration stabilizes a bond-ordered (dimerized) state for U approximately V/2 up to U/t approximately 9, where t is the nearest-neighbor hopping. The transition from the dimerized state to the staggered charge-density-wave state for large V/U is continuous for U < or approximately 5.5 and first order for higher U.     

Phase diagram of the one-dimensional half-filled extended Hubbard model

We determine the ground-state phase diagram of the one-dimensional half-filled Hubbard model with on-site (nearest-neighbor) repulsive interaction U (V) and nearest-neighbor hopping t using the density-matrix renormalization group technique. Based on the results of the excitation gaps, Luttinger-liquid exponents, and bond-order-wave (BOW) order parameter, we confirm that the BOW phase appears in a substantial region between the charge-density-wave (CDW) and spin-density-wave phases. Each phase boundary is determined by multiple means and it allows us to make a cross-check on the validity of our estimations. We also find that the BOW-CDW transition changes from continuous to first order at the tricritical point (U(t),V(t)) approximately (5.89 t,3.10 t) and the BOW phase shrinks to zero at the critical end point (U(c),V(c)) approximately (9.25 t,4.76 t).     

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.     

Bond-located phases driven by exchange interaction in the one-dimensional t-U-V-J model

The one-dimensional half-filled extended Hubbard model with on-site repulsion (U) and nearest-neighbor interactions including Coulomb repulsion (V) and exchange (J) is studied in the weak-coupling regime. We present a theoretical argument for the occurrence of bond-located phases. The bond-charge-density-wave (BCDW) is realized for J>0 and bond-spin-density-wave (BSDW) occurs for J<0.     

Increasing d-wave superconductivity by on-site repulsion

We study, through the variational Monte Carlo technique, an extended Hubbard model away from half filled band density which contains two competing nearest-neighbor interactions: a superexchange J favoring d-wave superconductivity and a repulsion V opposing it. We find that the on-site repulsion U effectively enhances the strength of J while suppressing that of V, thus favoring superconductivity. This result shows that attractions which do not involve charge fluctuations are very well equipped against strong electron-electron repulsion so much to get advantage from it.     

Ground-state phase diagram of a half-filled one-dimensional extended hubbard model

The density-matrix renormalization group is used to study the phase diagram of the one-dimensional half-filled Hubbard model with on-site (U) and nearest-neighbor (V) repulsion and hopping t. A critical line V(c)(U) approximately U/2 separates a Mott insulating phase from a charge-density-wave phase. The formation of bound charge excitations for V>2t changes the phase transition from continuous to first-order at a tricritical point U(t) approximately 3.7t, V(t)=2t. A frustrating effective antiferromagnetic spin coupling induces a bond-order-wave phase on the critical line V(c)(U) for U(t)相似文献   

New type of charge and magnetic order in the ferromagnetic kondo lattice

We study numerically the one dimensional ferromagnetic Kondo lattice, a model widely used to describe nickel and manganese perovskites. By including a nearest-neighbor Coulomb interaction ( V) and a superexchange interaction between the localized moments ( K), we obtain the phase diagram in parameter space for several dopings at T = 0. Because of the competition between double and superexchange, we find a region where the formation of magnetic polarons induces a charge-ordered state which survives also for V = 0. This mechanism should be taken into account in theories of charge ordering involving spin degrees of freedom.     

Phase diagram of the one-dimensional extended Hubbard model at half filling

We reexamine the ground-state phase diagram of the one-dimensional half-filled Hubbard model with on-site and nearest-neighbor repulsive interactions. We calculate second-order corrections to coupling constants in the weak-coupling renormalization-group approach ( g-ology) to show that the bond-charge-density-wave (BCDW) phase exists for weak couplings in between the charge-density-wave (CDW) and spin-density-wave (SDW) phases. We find that the umklapp scattering of parallel-spin electrons destabilizes the BCDW state and gives rise to a bicritical point where the CDW-BCDW and SDW-BCDW continuous-transition lines merge into the CDW-SDW first-order transition line.     

Dipolar molecules in optical lattices

We study the extended Bose-Hubbard model describing an ultracold gas of dipolar molecules in an optical lattice, taking into account all on-site and nearest-neighbor interactions, including occupation-dependent tunneling and pair tunneling terms. Using exact diagonalization and the multiscale entanglement renormalization ansatz, we show that these terms can destroy insulating phases and lead to novel quantum phases. These considerable changes of the phase diagram have to be taken into account in upcoming experiments with dipolar molecules.     

<Emphasis Type="Italic">T</Emphasis> = 0 phase diagram of the 1<Emphasis Type="Italic">D</Emphasis> Hubbard model with magnetic interactions in the narrow band limit

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.     

Metal-insulator transition in the quarter-filled frustrated checkerboard lattice

We study the electronic structure and correlations in the geometrically frustrated two dimensional checkerboard lattice. In the large U limit considered here we start from an extended Hubbard model of spinless fermions at half-filling. We investigate the model within two distinct Greens function approaches: In the first approach a single-site representation decoupling scheme is used that includes the effect of nearest neighbor charge fluctuations. In the second approach a cluster representation leading to a multiorbital model is investigated which includes intra-cluster correlations more rigorously and those between clusters on a mean field basis. It is demonstrated that with increasing nearest-neighbor Coulomb interaction V both approaches lead to a metal-insulator transition with an associated Mott-Hubbard like gap caused by V. Within the single site approach we also explore the possibility of charge order. Furthermore we investigate the evolution of the quasiparticle bands as funtion of V.     

Spin density wave in oxypnictide superconductors in a three-band model

The spin density wave and its temperature dependence in oxypnictide are studied in a three-band model. The spin susceptibilities with various interactions are calculated in the random phase approximation (PPA). It is found that the spin susceptibility peaks around the M point show a spin density wave (SDW) with momentum (0, π) and a clear stripe-like spin configuration. The intra-band Coulomb repulsion enhances remarkably the SDW but the Hund’s coupling weakens it. It is shown that a new resonance appears at higher temperatures at the Γ point indicating the formation of a paramagnetic phase. There is a clear transition from the SDW phase to the paramagnetic phase.     

Ab-initio calculations of interactions between Cu adatoms on Cu(1 1 0): Sensitivity of strong multi-site interactions to adatom relaxations

We have parameterized the various interactions between Cu adatoms on Cu(1 1 0) using density-functional theory based ab-initio calculations. Our results indicate that in addition to pair interactions, 3-adatom and 4-adatom interactions of significant strengths are present in this system. This further stresses the importance of multi-site interactions in constructing a complete lattice–gas picture. Even though adding these multi-site interactions leads to good convergence in interaction energies, we find that some multi-site interactions are very sensitive to adatom relaxations. This makes the application of a simple lattice–gas picture inadequate for such surfaces. We also parameterize adatom interactions on this surface using the recently developed connector model. The connector model parameterization is as efficient as the parameterization using lattice–gas model. Further, we present diffusion barriers for nearest-neighbor (NN) and next-nearest-neighbor (NNN) hops on this surface.     

Effect of spin fluctuations on the superconducting phase of Hubbard fermions in the t-t′-t″-J* model

The effect of spin-fluctuation scattering processes on the region of the superconducting phase in strongly correlated electrons (Hubbard fermions) is investigated by the diagram technique for Hubbard operators. Modified Gor’kov equations in the form of an infinitely large system of integral equations are derived taking into account contributions of anomalous components $ P_{0\sigma ,\bar \sigma 0} The effect of spin-fluctuation scattering processes on the region of the superconducting phase in strongly correlated electrons (Hubbard fermions) is investigated by the diagram technique for Hubbard operators. Modified Gor’kov equations in the form of an infinitely large system of integral equations are derived taking into account contributions of anomalous components of strength operator . It is shown that spinfluctuation scattering processes in the one-loop approximation for the t-t′-t″-J* model taking into account long-range hoppings and three-center interactions are reflected by normal (P _{0σ, 0σ}) and anomalous () components of the strength operator. Three-center interactions result in different renormalizations of the kernels of the integral equations for the superconducting d phase in the expressions for the self-energy and strength operators. In this approximation for the d-type symmetry of the order parameter for the superconducting phase, the system of integral equations is reduced to a system of nonhomogeneous equations for amplitudes. The resultant dependences of critical temperature on the electron concentrations show that joint effect of long-range hoppings, three-center interactions, and spin-fluctuation processes leads to strong renormalization of the superconducting phase region. Original Russian Text ? V.V. Val’kov, A.A. Golovnya, 2008, published in Zhurnal éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2008, Vol. 134, No. 6, pp. 1167–1180.     

Supersolids versus phase separation in two-dimensional lattice bosons

We study the nature of the ground state of the two-dimensional extended boson Hubbard model on a square lattice by quantum Monte Carlo methods. We demonstrate that strong but finite on-site interaction U along with a comparable nearest-neighbor repulsion V result in a thermodynamically stable supersolid ground state for densities larger than 1/2, in contrast to fillings less than 1/2 or for very large U, where the checkerboard supersolid is unstable towards phase separation. We discuss the relevance of our results to realizations of supersolids using cold bosonic atoms in optical lattices.     

Phase transitions detached from stationary points of the energy landscape

The stationary points of the potential energy function V are studied for the ?4 model on a two-dimensional square lattice with nearest-neighbor interactions. On the basis of analytical and numerical results, we explore the relation of stationary points to the occurrence of thermodynamic phase transitions. We find that the phase transition potential energy of the ?4 model does in general not coincide with the potential energy of any of the stationary points of V. This disproves earlier, allegedly rigorous, claims in the literature on necessary conditions for the existence of phase transitions. Moreover, we find evidence that the indices of stationary points scale extensively with the system size, and therefore the index density can be used to characterize features of the energy landscape in the infinite-system limit. We conclude that the finite-system stationary points provide one possible mechanism of how a phase transition can arise, but not the only one.     

Phase diagram of the extended hubbard model with pair hopping interaction

A one-dimensional model of interacting electrons with on-site U, nearest-neighbor V, and pair-hopping interaction W is studied at half-filling using the continuum limit field theory approach. The ground state phase diagram is obtained for a wide range of coupling constants. In addition to the insulating spin-density wave (SDW) and charge-density wave (CDW) phases for large U and V, respectively, we identify a bond-charge-density-wave (BCDW) phase W < 0, | U - 2V| < | 2W| and a bond-spin-density-wave (BSDW) for W > 0, | U - 2V| < W. The possibility of bond-located ordering results from the site-off-diagonal nature of the pair-hopping term and is a special feature of the half-filled band case. The BCDW phase corresponding to an enhanced Peierls instability in the system. The BdSDW is an unconventional insulating magnetic phase, characterized by a gapless spin excitation spectrum and a staggered magnetization located on bonds between sites. The general ground state phase diagram including insulating, metallic, and superconducting phases is discussed. A transition to the η-superconducting phase at | U - 2V| ≪ 2t?W is briefly discussed. Received 20 February 2002 / Received in final form 11 April 2002 Published online 19 July 2002     

First-Order Phase Transition in Potts Models with Finite-Range Interactions

We consider the Q-state Potts model on Z ^d , Q≥ 3, d≥ 2, with Kac ferromagnetic interactions and scaling parameter γ. We prove the existence of a first order phase transition for large but finite potential ranges. More precisely we prove that for γ small enough there is a value of the temperature at which coexist Q+1 Gibbs states. The proof is obtained by a perturbation around mean-field using Pirogov-Sinai theory. The result is valid in particular for d = 2, Q = 3, in contrast with the case of nearest-neighbor interactions for which available results indicate a second order phase transition. Putting both results together provides an example of a system which undergoes a transition from second to first order phase transition by changing only the finite range of the interaction.