We introduced the inter-site electron-electron correlation to the Hubbard III approximation. This correlation was excluded in the Hubbard III approximation and also in the equivalent coherent potential approximation. Including it brings two spin dependent effects: the bandwidth correction and the bandshift correction, which both stimulate the ferromagnetic ground state. The bandshift correction factor causes an exchange splitting between the spin-up and spin-down spectrum, and its role is similar to the exchange interaction in the classic Stoner model. The spin dependent bandwidth correction lowers the kinetic energy of electrons by decreasing the majority spin bandwidth for some electron occupations with respect to the minority spin bandwidth. In certain conditions it can lead to ferromagnetic alignment. A gain in the kinetic energy achieved in this way is the opposite extreme to the effect of a gain in potential energy due to exchange splitting. The bandshift factor is a dominant force behind the ferromagnetism. The influence of the bandwidth factor is too weak to create ferromagnetism and the only result is the correction to the classic coherent potential approximation in favor of ferromagnetism.
We investigated kinetic properties of correlated pairing states in strongly correlated phase of the Hubbard model in two space dimensions. We employ an optimization variational Monte Carlo method, where we use the improved wave function $ψ_λ= e^{-λK}ψ_G$ for the Gutzwiller wave function $ψ_G$ with $K$ being the kinetic part of the Hamiltonian. The Gutzwiller-BCS state is stabilized as the potential energy driven superconductivity because the Coulomb interaction energy is lowered while the kinetic energy increases in this state. In contrast, we show that in the $ψ_λ$-BCS wave function $ψ_{λ-BCS…
Crossover from weakly to strongly correlated regions in the two-dimensional Hubbard model -- Off-diagonal wave function Monte Carlo studies of Hubbard model II --
We have performed a variational Monte Carlo simulation to study the ground state of a two-dimensional Hubbard model on a square lattice in the strong coupling region. The energy gain of possible inhomogeneous electron states are computed as a function of $U$ when the hole density $ε=1/8$ and next nearest-neighbor hopping $t'/t=-0.30$. The bond-centered ferromagnetic diagonal stripe state is stabilized in the strong coupling region ($U/t\geq$16), which is due to the gain of both kinetic energy and on-site Coulomb interaction energy due to the holon moving over the ferromagnetic domain and the g…
Backflow correlations in the Hubbard model: an efficient tool for the metal-insulator transition and the large-U limit
我们发现，回流相关的变分波函数的哈伯德模型大大提高了以前的结果所给出的斯莱特-杰斯特罗状态，通常认为在这种情况下。我们提供的证据表明，在这种方法中，有可能有一个令人满意的连接与强耦合制度。此外，我们表明，哈伯德模型的晶格，回流的相关性基本上是短的范围内，诱导空（holons）和双占据的网站（doublons）之间的有效吸引力。在挫折的存在下，我们报告的证据表明，金属莫特绝缘体过渡的标志是一个不连续的双重占用，连同类似的不连续的动力学项，不改变的数目的holons和doublons，而其他动力学项是连续的过渡。最后，我们显示的电荷间隙的估计，通过粒子-空穴激发{ \it la Feynman}在基态波函数。
利用自洽的Hartree-Fock近似研究了扩展的$t$ - $t'$哈伯德模型中各种条纹相的相对稳定性。人们发现，一个负的比例的次近邻跳跃$t'/t<0$驱逐反铁磁畴的空穴，并加强条纹秩序。因此，半填充的条纹不仅容纳空穴，而且重新分布空穴，从而获得动能，并且这些条纹在适合于YBa $_2$ Cu $_3$ O $_{6+δ}$的$t'/t\simeq -0.3$的区域中接管。
The thermalization of isolated quantum many-body systems is deeply related to fundamental questions of quantum information theory. While integrable or many-body localized systems display non-ergodic behavior due to extensively many conserved quantities, recent theoretical studies have identified a rich variety of more exotic phenomena in between these two extreme limits. The tilted one-dimensional Fermi-Hubbard model, which is readily accessible in experiments with ultracold atoms, emerged as an intriguing playground to study non-ergodic behavior in a clean disorder-free system. While non-ergo…
Certain classes of strongly correlated systems promise high thermopower efficiency, but a full understanding of correlation effects on the Seebeck coefficient is lacking. This is partly due to limitations of Boltzmann-type approaches. One needs a formula for the thermopower that allows separate investigations of the kinetic and potential energy contributions to the evolution with temperature and doping of the thermopower. Here we address this issue by deriving for Hubbard-like interactions a formula for the thermopower that separates the potential from the kinetic energy contribution and facil…
Local spin fluctuations provide the glue for orbital-singlet spin-triplet pairing in the doped Mott insulating regime of multi-orbital Hubbard models. At large Hubbard repulsion $U$, the pairing susceptibility is nevertheless very low, because the pairing interaction cannot overcome the suppression of charge fluctuations. Using nonequilibrium dynamical mean field simulations of the two-orbital Hubbard model, we show that out of equilibrium the pairing susceptibility in this large-$U$ regime can be strongly enhanced by creating a photo-induced population of the relevant charge states, and that …
Instability of Nagaoka State and Quantum Phase Transition via Kinetic Frustration Control
Emory University（埃默里大学）；California State University, Northridge（北岭加州州立大学）；Institute of Quantum Information and Matter（量子信息与物质研究所）；California Institute of Technology（加州理工学院）；Department of Physics, Florida State University（佛罗里达州立大学物理系）；National High Magnetic Field Laboratory（国家高磁场实验室）
We present the first-ever multi-scale dynamical simulation of the temperature-controlled Mott metal-insulator transition in the Hubbard model. By integrating advanced electronic structure method and an efficient Gutzwiller/slave-boson solver into molecular dynamics simulations, we demonstrate that the transformation from a correlated metal to the Mott insulating phase proceeds via the nucleation and growth of the Mott droplets. Moreover, the time evolution of the Mott volume fraction is found to follow a universal transformation kinetics. We show that after an initial incubation period, the ea…
Using a dual representation of lattice fermion models that is based on spin-charge transformation and fermionisation of the original description, I derive an algorithm for diagrammatic Monte Carlo simulation of strongly correlated systems. This scheme allows eliminating large expansion parameters, as well as large corrections to the density matrix that generally prevent diagrammatic methods from being efficient in this regime. As an example, I compute the filling factor for the Hubbard model at infinite onsite repulsion and compare the results to controllable data obtained from Numerical Linke…
Mott transition in the Hubbard model on the hyper-kagome lattice
基于最近对Na $_4$ Ir $_3$ O $_8$化合物的实验研究，我们采用动力学集团近似（DCA）方法（$N_c$ =12）结合连续时间量子蒙特卡罗（CT QMC）方法研究了“超kagome晶格”上的哈伯德模型.当Hubbard相互作用$U/W$（$W$是带宽）超过$T$ =0.1时的值1.2时，系统经历Mott转变，并且由于磁关联和电子的动能之间的竞争（由于几何阻挫）而显示重入行为。我们观察到一个“临界减速”的双人入住，这表明一个连续的过渡的证据。最近邻和次最近邻自旋-自旋关联表明，在我们的数值工具可以访问的温度范围内的弱耦合制度和反铁磁（AF）莫特绝缘体在强耦合制度的顺磁金属态。
Influence of the inter-orbital interaction and kinetic terms on superconductivity: a simple two-orbital Hubbard model
SISSA, International School for Advanced Studies（国际高等研究院）；Institute for Condensed Matter Physics and Complex Systems, DISAT, Politecnico di Torino（都灵理工大学DISAT凝聚态物理与复杂系统研究所）；Dipartimento di Fisica, Università di Trieste（的里雅斯特大学物理系）
Kinetic Magnetism at the Interface Between Mott and Band Insulators
我们发现，高密度的二维电子气和本地化的电子在相邻的莫特绝缘体的相互作用导致独特的莫特/带绝缘体界面的动力学磁性。我们的研究是基于一个双层哈伯德模型在$U=\infty$与电势差之间的两层。我们结合分析结果与DMRG模拟表明，磁性，特别是铁磁性，大大提高了相对的两个子系统的接近。这些结果可能与最近的实验表明在$R$ TiO $_3$ /SrTiO $_3$异质结构的磁性有关。
Functional renormalization group without functional integrals: implementing Hilbert space projections for strongly correlated electrons via Hubbard X-operators
The Hubbard and Su-Schrieffer-Heeger Hamiltonians (SSH) are iconic models for understanding the qualitative effects of electron-electron and electron-phonon interactions respectively. In the two-dimensional square lattice Hubbard model at half filling, the on-site Coulomb repulsion, $U$, between up and down electrons induces antiferromagnetic (AF) order and a Mott insulating phase. On the other hand, for the SSH model, there is an AF phase when the electron-phonon coupling $λ$ is less than a critical value $λ_c$ and a bond order wave when $λ> λ_c$. In this work, we perform numerical studies on…
We study the interplay of strong electron correlations and intra-triangle spin exchange at two-thirds filling of the single-orbital Hubbard model on the decorated honeycomb lattice using rotationally invariant slave bosons. We find that the spin exchange tunes between a spin-$1$ Mott insulator, a metal, and a spin-$0$ Mott insulator when the exchange is antiferromagnetic. The Mott insulators occur from effective intra-triangle multi-orbital interactions and are adiabatically connected to the ground state of an isolated triangle. An antiferromagnetic spin exchange, as determined by the Goodenou…
We investigate the ground-state phase diagram of the two-dimensional Hubbard model based on the optimization variational Monte Carlo method. We use a wave function that is an off-diagonal type given as $ψ=\exp(-λK)P_Gψ_0$, where $ψ_0$ is a one-particle state, $P_G$ is the Gutzwiller operator, $K$ is the kinetic operator, and $λ$ is a variational parameter. The many-body effect plays an important role as an origin of spin correlation and superconductivity in correlated electron systems. We examine the competition between the antiferromagnetic state and superconducting state by varying the Coulo…
