Ferromagnetism in the single-band Hubbard model: An exact high-temperature expansion

The first ten terms of the high-temperature expansion of the susceptibility of the single-band Hubbard model in the strong correlation limit are obtained for arbitrary electron density. The series is analyzed by ratio methods and Padé approximants. A critical temperature is found for 0.2 0.8; for > 1 further terms in the series are required.Supported in part by the National Research Council of Canada.     

用重整化群流方程方法求解t-J模型元激发能谱

t-J模型是研究电子强关联作用和高T_c超导理论的重要模型之一.将重整化群方法应用于t-J模型，得出相应的流方程，再由流方程求解t-J模型的元激发能谱，并利用函数的对称性，解出t-J模型在零温条件下能谱的具体表达式，最后与常规的格林函数方法所得的结果作了比较. 关键词： 重整化群 t-J模型 流方程     

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.     

Flow equations for the ionic Hubbard model

Taking the site-diagonal terms of the ionic Hubbard model (IHM) in one and two spatial dimensions, as H₀, we employ Continuous Unitary Transformations (CUT) to obtain a “classical” effective Hamiltonian in which hopping term has been renormalized to zero. For this Hamiltonian spin gap and charge gap are calculated at half-filling and subject to periodic boundary conditions. Our calculations indicate two transition points. In fixed Δ, as U increases from zero, there is a region in which both spin gap and charge gap are positive and identical; characteristic of band insulators. Upon further increasing U, first transition occurs at U=Uc₁, where spin and charge gaps both vanish and remain zero up to U=Uc₂. A gap-less state in charge and spin sectors characterizes a metal. For U>Uc₂ spin gap remains zero and charge gap becomes positive. This third region corresponds to a Mott insulator in which charge excitations are gaped, while spin excitations remain gap-less.     

由流方程求解非零温条件下t-J模型能谱

t_J模型是研究电子强关联作用和高T_c超导理论的重要模型之一. 将重正化群流 方程方法应用于t_J模型，分别解出了t_J模型在非零温条件下费米子和玻色子元激发能谱的 解析式. 并将结果与采用格林函数方法求解的结果作了比较，两者基本一致.重正化群流方 程方法解出的结果是解析解，而格林函数方法求解的结果是数值解. 关键词： 重正化群 t－J模型 流方程     

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.     

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．     

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.     

Flow to strong coupling in the two-dimensional Hubbard model

We extend the analysis of the renormalization group flow in the two-dimensional Hubbard model close to half-filling using the recently developed temperature flow formalism. We investigate the interplay of d-density wave and Fermi surface deformation tendencies with those towards d-wave pairing and antiferromagnetism. For a ratio of next nearest to nearest neighbor hoppings, t'/t = - 0.25, and band fillings where the Fermi surface is inside the Umklapp surface, only the d-pairing susceptibility diverges at low temperatures. When the Fermi surface intersects the Umklapp surface close to the saddle points, d-wave pairing, d-density wave, antiferromagnetic and, to a weaker extent, d-wave Fermi surface deformation susceptibilities grow together when the interactions flow to strong coupling. We interpret these findings as indications for a non-trivial strongly coupled phase with short-ranged superconducting and antiferromagnetic correlations, in close analogy with the spin liquid ground state in the well-understood two-leg Hubbard ladder. Received 23 January 2002     

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.     

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.     

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.     

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.     

Ferromagnetism in the Hubbard model on the square lattice: Improved instability criterion for the Nagaoka state

The instability of the fully polarized ferromagnetic state (Nagaoka state) with respect to single spin flips is re-examined for the Hubbard model on the square lattice with a large family of variational wave functions which include correlation effects of the majority spins in the vicinity of the flipped spin. We find a critical hole density of δ_cr = 0.251 for U = ∞ and a critical coupling of U_cr = 77.7t. Both values improve previous variational results considerably.     

Ferromagnetism in the Hubbard model: Spin waves and instability of the Nagaoka state

We discuss two single spin flip variational wave functions describing spin wave excitations which were proposed earlier by Shastry, Krishnamurthy and Anderson (SKA) and by Basile and Elser (BE), respectively, in order to investigate the instability of the fully polarized ferromagnetic state (Nagaoka state) in the infinite U Hubbard model. We calculate the energy of these variational states for the square lattice and for multiple chains. At the zone boundary in the vicinity of the point (0, π) the spin wave energy is reduced substantially by the binding of the spin up hole to the flipped down spin. For the square lattice this leads to a critical hole density of δ_cr = 0.407 for the SKA spin wave and of δ_cr = 0.322 for the BE spin wave which implies remarkable improvements in comparison to the corresponding scattering states investigated previously.     

Decorated star-triangle relations and exact integrability of the one-dimensional Hubbard model

The exact integrability of the one-dimensional Hubbard model is demonstrated with the help of a novel set of triangle relations, the decorated star-triangle relations. The covering two-dimensional statistical mechanical model obeys the star-triangle or Yang-Baxter relation. A conjecture is presented for the eigenvalues of the transfer matrix.     

The one-dimensional Hubbard model for large or infiniteU

The magnetic properties of the one-dimensional Hubbard model with a hardcore interaction on a ring (periodic boundary conditions) are investigated. At finite temperatures it is shown to behave up to exponentially small corrections as a pure paramagnet. An explicit expression for the ground-state degeneracies is derived. The eigenstates of this model are used to perform a perlurbational treatment for large but finite interactions. In first order inU ¹ an effective Hamiltonian for the one-dimensional Hubbard model is derived. It is the Hamiltonian of the one-dimensional Hcisenberg model with antiferromagnetic couplings between nearest neighbor spins. An asymptotic expansion for the ground-state energy is given. The results are valid for arbitrary densities of electrons.