Magnetic phase diagram of an extended Hubbard model at half filling: Possible application for strongly correlated iron pnictides

We study the magnetic phase diagram within an extended half-filled Hubbard model, focusing on the roles of the next-nearest-neighbor (NNN) and the next-next-nearest-neighbor (3rd NN) hoppings in the magnetic configurations. We find that due to the spin frustration from the long range hopping and the competition between long-range hopping and Coulomb correlation, the striped antiferromagnetic (AFM) phase is stable when the NNN hopping is dominant, while the bicollinear AFM phase is robust when the 3rd NN hopping is considerably large. The triple points are found in various magnetic phase diagrams. Possible applications of the present theory on intermediately correlated LaFeAsO and strongly correlated FeTe are discussed.     

三带Hubbard模型中环形电流相的量子蒙特卡罗模拟

运用约束路径量子蒙特卡罗方法,对二维、三带Hubbard模型中的环形电流相进行数值模拟。在数值模拟过程中定义了表征环流相的不同算符及其关联函数,并且选用合理的模型Hamiltonian量中的参数。通过模拟发现,对应于闭合环形的关联函数在相同距离上要比其他所有没有闭合的关联函数大得多,因此证明在三带Hubbard模型中存在环形电流相。     

Quantum coherence and ground-state phase transition in a four-chain Bose–Hubbard model

We study the quantum coherence and ground-state phase transition of a four-chain Bose–Hubbard model with the long-range interaction. In a special four-chain Bose–Hubbard model,i.e., each chain only has one optical potential, four types of the ground-state phases are discovered. The effects of the disorder, the on-site interaction and the long-range interaction on the quantum coherence are studied. For the system without the long-range interaction, the quantum coherence changes from one periodic oscillation to two periodic oscillations as the onsite interaction increases. By considering the long-range interaction, the quantum coherence goes back to one periodic oscillation again. The on-site interaction itself suppresses the quantum coherence, both the on-site interaction and long-range interaction together enhance the quantum coherence with the weak disorder. If the disorder strength is increased beyond a critical value,they start to suppress the quantum coherence. In a regular four-chain Bose–Hubbard model, i.e.,each chain has many optical potentials, the ground-state phase transitions are obtained by using the cluster Gutzwiller mean-field method. Exotic ground-state phases are found, i.e., superfluid phase, integer Mott insulator phase, supersolid phase and loophole insulator phase. The combination of the loophole insulator phase and the supersolid phase expands the lobes with the half-integer filling per site for the small ratio β = t_■/t_⊥.     

On the flux phase conjecture at half-filling: An improved proof

We present a simplification of Lieb's proof of the flux phase conjecture for interacting fermion systems—such as the Hubbard model—at half-filling on a general class of graphs. The main ingredient is a procedure which transforms a class of fermionic Hamiltonians into reflection-positive form. The method can also be applied to other problems, which we briefly illustrate with two examples concerning thet–V model and an extended Falicov-Kimball model.     

Phase diagram of the three-dimensional Hubbard model at half filling

We investigate the phase diagram of the three-dimensional Hubbard model at half filling using quantum Monte Carlo (QMC) simulations. The antiferromagnetic Néel temperature is determined from the specific heat maximum in combination with finite-size scaling of the magnetic structure factor. Our results interpolate smoothly between the asymptotic solutions for weak and strong coupling, respectively, in contrast to previous QMC simulations. The location of the metal-insulator transition in the paramagnetic phase above is determined using the electronic compressibility as criterion. Received 11 April 2000 and Revised in final form 29 June 2000     

Quantum transport through anisotropic molecular magnets: Hubbard Green function approach

We extend the Green function approach to quantum transport through an anisotropic molecular magnet system with the help of Hubbard operators. Based on the single molecular magnet model, we reformulate the large spin and the total Hamiltonian in the language of Hubbard operators and obtain analytical expressions of the retarded Green function in sequential tunneling and Kondo regimes. In addition to this, we show the connection of our method to the master equation method in sequential regime and discuss a simple isotropic case in Kondo regime, in which we find a three-peak Kondo structure, a feature characterizing the isotropic exchange interaction between the localized electron and large spin.     

Quantum critical Hall exponents

We investigate a finite size “double scaling” hypothesis using data from an experiment on a quantum Hall system with short range disorder ,  and . For Hall bars of width w at temperature T   the scaling form is w^−μT^−κ$w^{-\mu }{T}^{-\kappa }$, where the critical exponent μ≈0.23$\mu \approx 0.23$ we extract from the data is comparable to the multi-fractal exponent _α0−2${\alpha }_0-2$ obtained from the Chalker–Coddington (CC) model [4]. We also use the data to find the approximate location (in the resistivity plane) of seven quantum critical points, all of which closely agree with the predictions derived long ago from the modular symmetry of a toroidal σ-model with m matter fields [5]. The value _ν8=2.60513…${\nu }_8=2.60513\dots$ of the localisation exponent obtained from the m=8$m=8$ model is in excellent agreement with the best available numerical value _νnum=2.607±0.004${\nu }_{\mathrm{num}}=2.607\pm 0.004$ derived from the CC-model [6]. Existing experimental data appear to favour the m=9$m=9$ model, suggesting that the quantum Hall system is not in the same universality class as the CC-model. We discuss the reason this may not be the case, and propose experimental tests to distinguish between the two possibilities.     

Quantum phase diagram of the half filled Hubbard model with bond-charge interaction

Using quantum field theory and bosonization, we determine the quantum phase diagram of the one-dimensional Hubbard model with bond-charge interaction X in addition to the usual Coulomb repulsion U at half-filling, for small values of the interactions. We show that it is essential to take into account formally irrelevant terms of order X  . They generate relevant terms proportional to X²$X^2$ in the flow of the renormalization group (RG). These terms are calculated using operator product expansions. The model shows three phases separated by a charge transition at U=Uc$U=U_c$ and a spin transition at U=Us>Uc$U=U_s>U_c$. For U<Uc$U<U_c$ singlet superconducting correlations dominate, while for U>Us$U>U_s$, the system is in the spin-density wave phase as in the usual Hubbard model. For intermediate values Uc<U<Us$U_c<U<U_s$, the system is in a spontaneously dimerized bond-ordered wave phase, which is absent in the ordinary Hubbard model with X=0$X=0$. We obtain that the charge transition remains at Uc=0$U_c=0$ for X≠0$X\ne 0$. Solving the RG equations for the spin sector, we provide an analytical expression for Us(X)$U_s(X)$. The results, with only one adjustable parameter, are in excellent agreement with numerical ones for X<t/2$X<t/2$ where t is the hopping.     

Simulations of the Hubbard model

We discuss results of simulations of the Hubbard model of interacting electrons on a lattice. We start with a brief discussion of methodology and point out some of the outstanding problems. We then discuss results of simulations of the model in three, two, and one dimension, particularly in connection with its magnetic and superconducting properties. We conclude with a brief discussion of future directions.     

Resonance state in the 2D attractive Hubbard model

The systematic change of a resonance state with high momenta is studied with increasing particle density in the 2D attractive Hubbard model. Within the conserving self-consistent T-matrix approximation, we present the spectral functions for the one and two particle Green's functions as well as the self-energy. In the small density limit, the resonant state becomes stable and the result from the self-consistent calculations shows a good agreement with that from a simple analytical calculation. As particle density is increased, the resonance state acquires a short lifetime due to the increasing decay into two free particles.     

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.     

Thermoelectric power of high-T c superconductors using extended Hubbard model

The thermoelectric power (TEP) for a one dimensional lattice has been studied by using the extended Hubbard model in the limitU≠∞, whereU is the on-site Coulomb interaction. A new expression for TEP, derived in this study, has been found to successfully reproduce the experimental results of the insulating samples of different hole- and electron-doped high temperature superconducting systems.     

半满Hubbard模型的新处理方法

从标准Hubbard模型出发,对半满狭带强关联系统,在讨论自旋为δ的电子运动时,忽略自旋为-δ的电子在格点间的跳跃,得到不对称哈密顿量,并运用平均场近似求得相应准粒子谱．在绝对零度时,与Green函数近似解作了比较;在有限温度时,讨论了从绝缘体到金属相变的可能．     

Magnetism in the single-band Hubbard model

A self-consistent spectral density approach (SDA) is applied to the Hubbard model to investigate the possibility of spontaneous ferro- and antiferromagnetism. The starting point is a two-pole ansatz for the single-electron spectral density, the free parameter of which can be interpreted as energies and spectral weights of respective quasiparticle excitations. They are determined by fitting exactly calculated spectral moments. The resulting self-energy consists of a local and a non-local part. The higher correlation functions entering the spin-dependent local part can be expressed as functionals of the single-electron spectral density. Under certain conditions for the decisive model parameters (Coulomb interaction U, Bloch bandwidth W, band occupation n, temperature T) the local part of the self-energy gives rise to a spin-dependent band shift, thus allowing for spontaneous band magnetism. As a function of temperature, second-order phase transitions are found away from half-filling, but close to half-filling, the system exhibits a tendency towards first-order transitions. The non-local self-energy part is determined by use of proper two-particle spectral densities. Its main influence concerns a (possibly spin-dependent) narrowing of the quasiparticle bands with the tendency to stabilize magnetic solutions. The non-local self-energy part disappears in the limit of infinite dimensions. We present a full evaluation of the Hubbard model in terms of quasiparticle densities of states, quasiparticle dispersions, magnetic phase diagram, critical temperatures (T_c, T_N) as well as spin and particle correlation functions. Special attention is focused on the non-locality of the electronic self-energy, for which some rigorous limiting cases are worked out.     

有限温度下一维Hubbard模型的化学势泛函理论研究

通过数值方法求解了有限温度下一维均匀Hubbard模型的热力学Bethe-ansatz方程组,得到了在给定温度和相互作用强度情况下,比热c、磁化率χ和压缩比κ随化学势μ的变化图像.基于有限温度下一维均匀Hubbard模型的精确解,利用化学势(μ)-泛函理论研究了一维谐振势下的非均匀Hubbard模型,给出了金属态和Mott绝缘态下不同温度情况时局域粒子密度n_i和局域压缩比_κi随格点的变化情况.     

Zero finite-temperature charge stiffness within the half-filled 1D Hubbard model

Even though the one-dimensional (1D) Hubbard model is solvable by the Bethe ansatz, at half-filling its finite-temperature T>0$T>0$ transport properties remain poorly understood. In this paper we combine that solution with symmetry to show that within that prominent T=0$T=0$ 1D insulator the charge stiffness D(T)$D\left(T\right)$ vanishes for T>0$T>0$ and finite values of the on-site repulsion U$U$ in the thermodynamic limit. This result is exact and clarifies a long-standing open problem. It rules out that at half-filling the model is an ideal conductor in the thermodynamic limit. Whether at finite T$T$ and U>0$U>0$ it is an ideal insulator or a normal resistor remains an open question. That at half-filling the charge stiffness is finite at U=0$U=0$ and vanishes for U>0$U>0$ is found to result from a general transition from a conductor to an insulator or resistor occurring at U=U_c=0$U=U_c=0$ for all finite temperatures T>0$T>0$. (At T=0$T=0$ such a transition is the quantum metal to Mott-Hubbard-insulator transition.) The interplay of the η$\eta$-spin SU(2)$SU\left(2\right)$ symmetry with the hidden U(1)$U\left(1\right)$ symmetry beyond SO(4)$SO\left(4\right)$ is found to play a central role in the unusual finite-temperature charge transport properties of the 1D half-filled Hubbard model.     

Generalized Hartree-Fock theory and the Hubbard model

The familiar unrestricted Hartree-Fock variational principles is generalized to include quasi-free states. As we show, these are in one-to-one correspondence with the one-particle density matrices and these, in turn, provide a convenient formulation of a generalized Hartree-Fock variational principle, which includes the BCS theory as a special case. While this generalization is not new, it is not well known and we begin by elucidating it. The Hubbard model, with its particle-hole symmetry, is well suited to exploring this theory because BCS states for the attractive model turn into usual HF states for the repulsive model. We rigorously determine the true, unrestricted minimizers for zero and for nonzero temperature in several cases, notably the half-filled band. For the cases treated here, we can exactly determine all broken and unbroken spatial and gauge symmetries of the Hamiltonian.Dedicated to Philippe Choquard on his 65th birthday.     

Mott transition in the asymmetric Hubbard model at half-filling within dynamical mean-field theory

The asymmetric Hubbard model with hopping integrals dependent on an electron spin (particle sort) is studied using an approximate analytic method within the dynamical mean-field theory. The equations of motion for Hubbard operators followed by projecting and different-time decoupling are used for solving the single-site problem. Particle spectra are investigated at half-filling within various approximations (Hubbard-I, alloy-analogy and a generalization of the Hubbard-III approximation). At half-filling these approximations can describe only continuous gap opening in the spectrum. The approach is used to describe the system between two limit cases (the Falicov-Kimball model and the standard Hubbard model) with continuous transition where U_c is dependent on the value of hopping parameters of different particles.     

Quantum phase transition and von Neumann entropy of quasiperiodic Hubbard chains

The half-filled Hubbard chains with the Fibonacci and Harper modulating site potentials are studied in a selfconsistent mean-field approximation. A new order parameter is introduced to describe a charge density order. We also calculate the von Neumann entropy of the ground state. The results show that the von Neumann entropy can identify a CDW/SDW （charge density wave/spin density wave） transition for quasiperiodic models.