We present a numerical scheme for the Hubbard model that throws light on the rather esoteric nature of the Upper and Lower Hubbard bands that have been invoked often in literature. We present a self consistent solution of the ladder diagram equations for the Hubbard model, and show that these provide, at least in the limit of low densities of particles, a vivid picture of the Hubbard split bands. We also address the currently topical problem of decay of the doublon states that are measured in optical trap studies, using the ladder scheme and also by an exact two particle calculation of a relevant Greens function.
We have studied the doping-driven orbital-selective Mott transition in multi-band Hubbard models with equal band width in the presence of crystal field splitting. Crystal field splitting lifts one of the bands while leaving the others degenerate. We use single-site dynamical mean-field theory combined with continuous time quantum Monte Carlo impurity solver to calculate a phase diagram as a function of total electron filling $N$ and crystal field splitting $Δ$. We find a large region of orbital-selective Mott phase in the phase diagram when the doping is large enough. Further analysis indicate…
Ferromagnetism in the t-t' Hubbard model: interplay of lattice, band dispersion, and interaction effects studied within a Goldstone-mode preserving scheme
研究了哈伯德模型中sc、bcc和fcc晶格上的铁磁性，采用了系统的逆简并（$1/{\cal N}$）展开，该展开包含了自能和顶点修正，使得自旋旋转对称性和Goldstone模得到了明确的保留.一阶量子修正的磁振子能量进行评估的几种情况下，提供了一个全面的图片的晶格，带色散的相互作用和相互作用对铁磁状态的稳定性相对于长波长和短波长的波动。我们的研究结果支持这样一种观点，即对于有限$t'$的面心立方晶格，只要DOS足够不对称且在带边附近有强峰，铁磁性是哈伯德模型在中强耦合下的一个普遍特征.对于短波长模式，特征能量标度$ω^* \sim T_c$（磁振子DOS峰值能量）的行为与DMFT内的$T_c$与$n$行为非常一致，无论是关于密度的稳定范围（$0.20 < n < 0.85$）还是最佳密度$n=0.65$。然而，我们的发现消失的自旋刚度附近的最佳密度突出的作用，长波长的波动，进一步减少了稳定的密度范围。
In this work we study the two-orbital Hubbard model on a square lattice in the presence of hybridization between nearest-neighbor orbitals and a crystal-field splitting. We use a highly reliable numerical technique based on the density matrix renormalization group to solve the dynamical mean field theory self-consistent impurity problem. We find that the orbital mixing always leads to a finite local density states at the Fermi energy in both orbitals when at least one band is metallic. When one band is doped, and the chemical potential lies between the Hubbard bands in the other band, the cohe…
Here the line shape of the up- and down-spin one-particle spectral functions at and in the (k,energy)-plane's vicinity of their cusp singularities is studied for the Mott-Hubbard insulator described by the 1D Hubbard model with one fermion per site at zero and finite magnetic fields. At zero field they can be accessed in terms of electrons by photoemission experiments. At finite field, such functions and corresponding interplay of correlations and magnetic-field effects refer to an involved non-perturbative many-particle problem that is poorly understood. The Mott-Hubbard gap that separates th…
We investigate the Hubbard Hamiltonian on ladders where the number of sites per rung alternates between two and three. These geometries are bipartite, with a non-equal number of sites on the two sublattices. Thus they share a key feature of the Hubbard model in a class of lattices which Lieb has shown analytically to exhibit long-range ferrimagnetic order, while being amenable to powerful numeric approaches developed for quasi-one-dimensional geometries. The Density Matrix Renormalization Group (DMRG) method is used to obtain the ground state properties, e.g. excitation gaps, charge and spin d…
Correlation functions and low-energy excitations are investigated in the asymmetric two-leg ladder consisting of a Hubbard chain and a noninteracting tight-binding (Fermi) chain using the density matrix renormalization group method. The behavior of charge, spin and pairing correlations is discussed for the four phases found at half filling, namely, Luttinger liquid, Kondo-Mott insulator, spin-gapped Mott insulator and correlated band insulator. Quasi-long-range antiferromagnetic spin correlations are found in the Hubbard leg in the Luttinger liquid phase only. Pair-density-wave correlations ar…
We study the weak-coupling limit of the $t-t^\prime-U$ Hubbard model on a two-dimensional square lattice using a direct perturbative approach. Aided by symbolic computational tools, we compute the longitudinal density-density correlation functions in the $χ_{\uparrow \uparrow}$ and $χ_{\uparrow \downarrow}$ basis from which we can obtain the dynamical spin and charge susceptibilities at arbitrary doping and temperature. We find that for non-zero $t^\prime$, the zero frequency commensurate $\mathbf{q} = (π, π)$ spin and charge excitations are each strongest at different densities and we observe…
The topological nature of the Mott-Hubbard state in strongly correlated systems is treated. These systems are described in terms of spin-charge separation, i.e. spinon-holon deconfinement in the gauge field. Analogies with the quantum Hall effect and Landau quantization are considered, the presence of the Chern-Simons term being important for proper description of the Hubbard splitting. Occurrence of topological frustrations with doping in an effective two-band model is demonstrated. The role of orbital degrees of freedom and possible occurrence of orbital currents are discussed.
We numerically investigate 1D Bose-Hubbard chains with onsite disorder by means of exact diagonalization. A primary focus of our work is on characterizing Fock-space localization in this model from the single-particle perspective. For this purpose, we compute the one-particle density matrix (OPDM) in many-body eigenstates. We show that the natural orbitals (the eigenstates of the OPDM) are extended in the ergodic phase and real-space localized when one enters into the MBL phase. Furthermore, the distributions of occupations of the natural orbitals can be used as measures of Fock-space localiza…
Ferromagnetism in the one-dimensional Hubbard model with orbital degeneracy: From low to high electron density
用密度矩阵重整化群方法研究了双简并原子轨道的一维哈伯德模型的铁磁性，得到了基态相图。结果表明，当相互作用足够强时，铁磁性从低到高（0< n < 1.75）电子密度是稳定的。准长程序的三重态超导电性与铁磁有序共存的强Hund耦合区，其中轨道间相互作用U '-J是吸引的。在四分之一填充（n=1），绝缘铁磁态出现伴随着轨道准长程序。对于低密度（n<1），由于电子的虚跳跃引起的铁磁交换相互作用，铁磁性发生，与四分之一填充系统相同。这来自于强耦合极限中电荷和自旋-轨道自由度的分离。这种铁磁性对于能带结构的变化是脆弱的。对于高密度（n>1），铁磁相的相图类似于在无限维中获得的相图。在这种情况下，双交换机制是可操作的，以稳定的铁磁秩序和这种长程序是强大的对带色散的变化。在1.68<n<1.75的密度区出现部分极化态，在半填充区（n=2）的正下方出现相分离。
We employ the numerical linked-cluster expansion to study finite-temperature properties of the uniform cubic lattice Hubbard model in the thermodynamic limit for a wide range of interaction strengths and densities. We carry out the expansion to the 9th order and find that the convergence of the series extends to lower temperatures as the strength of the interaction increases, giving us access to regions of the parameter space that are difficult to reach by most other numerical methods. We study the precise trends in the specific heat, the double occupancy, and magnetic correlations at temperat…
