We investigate the quasiparticle dynamics in the two-orbital Hubbard model on the square lattice at quarter filling by means of the cellular dynamical mean field theory. We show that the Fermi-liquid state is stabilized up to the large Hubbard interactions in the symmetric case without the Hund's coupling, and find the heavy quasiparticles around the metal-insulator boundary. It is elucidated that the Hund's coupling enhances the antiferro-orbital correlations, which give rise to the pseudo gap behavior in the single-particle excitations. We also find the nonmonotonic temperature dependence in the quasiparticle dynamics for intermediate strength of the Hund's coupling, and clarify that it is caused by the competition between the Fermi-liquid formation and the antiferro-orbital fluctuations.
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…
We develop a diagrammatic method for the evaluation of general multi-band Gutzwiller wave functions in finite dimensions. Our approach provides a systematic improvement of the widely used Gutzwiller approximation. As a first application we investigate itinerant ferromagnetism and correlation-induced deformations of the Fermi surface for a two-band Hubbard model on a square lattice.
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 …
We perform exact numeric calculations for the two-orbital Hubbard model on the four-site cluster. In the limit of large on-site coupling the model becomes equivalent to the spin $S=1$ Heisenberg model. By comparing energy spectra of these two models, we quantified the range of interaction parameters for which the Heisenberg model satisfactorily reproduces the two-orbital Hubbard model. Then we examined how the spectrum evolves when we are outside of this region, focusing especially on checking of how it is modified when various ways of interatomic hoppings of electrons between different orbita…
We investigate the half-filled two-orbital Hubbard model with the crystalline electric field using dynamical mean-field theory combined with the continuous-time quantum Monte Carlo simulations. We systematically study how the interplay of the intra- and interorbital Coulomb interations together with the Hund coupling realizes the diagonal and off-diagonal ordered states. It is found that the antiferroorbital ordered state is realized in the Hubbard model, in addition to the antiferromagnetically ordered and excitonic states. The competition between the antiferroorbital ordered and excitonic st…
We study non-local correlations in a three-orbital Hubbard model defined on an extended one-dimensional chain using determinant quantum Monte Carlo and density matrix renormalization group methods. We focus on a parameter with robust Hund's coupling, which produces an orbital selective Mott phase (OSMP) at intermediate values of the Hubbard U, as well as an orbitally ordered ferromagnetic insulating state at stronger coupling. An examination of the orbital and spin-correlation functions indicates that the orbital ordering occurs before the onset of magnetic correlations in this parameter regim…
Inspired by recent discovery of correlated insulating states in twisted bilayer graphene (TBG), we study a two-orbital Hubbard model on the honeycomb lattice with two electrons per unit cell. Based on the real-space density matrix renormalization group (DMRG) simulation, we identify a metal-insulator transition around $U_c/t=2.5\sim3$. In the vicinity of $U_c$, we find strong spin/orbital density wave fluctuations at commensurate wavevectors, accompanied by weaker incommensurate charge density wave (CDW) fluctuations. The spin/orbital density wave fluctuations are enhanced with increasing syst…
We solve the orbitally degenerate two-band Hubbard model within dynamical mean field theory and map out the instabilities to various symmetry-broken phases based on an analysis of the corresponding lattice susceptibilities. Phase diagrams as a function of the Hund coupling parameter J are obtained both for the model with rotationally invariant interaction and for the model with Ising-type anisotropy. For negative J, an intra-orbital spin-singlet superconducting phase appears at low temperatures, while the normal state properties are characterized by an orbital freezing phenomenon. This is the …
We study the interplay between the electron-phonon (e-ph) and on-site electron-electron (e-e) interactions in a three-orbital Hubbard-Holstein model on an extended one-dimensional lattice using determinant quantum Monte Carlo. For weak e-e and e-ph interactions, we observe a competition between an orbital-selective Mott phase (OSMP) and a (multicomponent) charge-density-wave (CDW) insulating phase, with an intermediate metallic phase located between them. For large e-e and e-ph couplings, the OSMP and CDW phases persist, while the metallic phase develops short-range orbital correlations and be…
One of the most challenging problems in solid state systems is the microscopic analysis of electronic correlations. A paramount minimal model that encodes correlation effects is the Hubbard Hamiltonian, which -- albeit its simplicity -- is exactly solvable only in a few limiting cases and approximate many-body methods are required for its solution. In this review we present an overview on the non-perturbative Two-Particle Self-Consistent method (TPSC) which was originally introduced to describe the electronic properties of the single-band Hubbard model. We introduce here a detailed derivation …
We report ten ground states arising from strong correlations in the single-orbital Hubbard model on the decorated honeycomb lattice; including Dirac metals, flat-band ferromagnets, real-space Mott insulators, dimer and trimer Mott insulators, and a spin-$1$ Mott insulator. The rich phase diagram arises from structures within the unit cell. Hence, such states are absent on simpler lattices. We argue that such insulating phases are prevalent on decorated lattices. These are found in many materials and common in coordination polymers, providing a playground to explore this physics.
While excitonic instabilities in multiorbital systems recently have come under scrutiny in a variety of transition-metal compounds, understanding emergence of these instabilities from strong electronic interactions has remained a challenge. Here, we present a sign-problem-free determinant quantum Monte Carlo study of excitonic density orders in a half-filled two-orbital Hubbard-Kanamori model with broken orbital degeneracy, which accounts for the role of Hund's coupling in transition-metal compounds. For strong inverted (negative) Hund's exchange, we find numerical evidence for the emergence o…
We study the interplay between the electron-electron (e-e) and the electron-phonon (e-ph) interactions in the two-orbital Hubbard-Holstein model at half filling using the dynamical mean field theory. We find that the e-ph interaction, even at weak couplings, strongly modifies the phase diagram of this model and introduces an orbital-selective Peierls insulating phase (OSPI) that is analogous to the widely studied orbital-selective Mott phase (OSMP). At small e-e and e-ph coupling, we find a competition between the OSMP and the OSPI, while at large couplings, a competition occurs between Mott a…
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…
We study the electronic spectral properties at zero temperature of the one-dimensional (1D) version of the degenerate two-orbital Kanamori Hubbard model (KHM), one of the well established frameworks to study transition metal compounds, using state-of-the-art numerical techniques based on the Density Matrix Renormalization Group. While the system is Mott insulating for the half-filled case, as expected for an interacting 1D system, we find interesting and rich structures in the single-particle density of states (DOS) for the hole-doped system. In particular, we find the existence of in-gap stat…
Local moment approach to multi-orbital Anderson and Hubbard models
变分局部矩法（V-LMA）是Logan { \it et al}等人提出的方法的改进，在这里介绍。从一开始就考虑了局部矩的存在，并通过变分原理通过最小化相应的基态能量来确定它们的值。我们的变分方法使我们能够处理费米和非费米液体系统的许多轨道以及绝缘体没有任何额外的假设。通过显式构造相应的Ward泛函，证明了V-LMA属于守恒逼近类。作为例子，V-LMA被用来解决多轨道单杂质安德森模型。该方法也被应用于求解多轨道哈伯德模型的动力学平均场方程。特别是，莫特-哈伯德金属-绝缘体过渡是在这种方法中解决。
We study the Hubbard model on a square lattice, using the dynamical vertex approximation and the parquet approximation. These methods allow us to describe the mutual interference of spin-fluctuations in the particle-hole channel and superconducting fluctuations in the cooperon channel in an unbiased way. For small dopings we find predominant commensurable antiferromagnetic spin- and d-wave superconducting fluctuations; for larger doping incommensurate antiferromagnetic spin fluctuations are concomitant to triplet s-wave superconducting fluctuations.
Motivated by experimental developments introducing the concept of spin-orbit separation, we study the real-space time evolution of an excitonic wave-packet using a two-orbital Hubbard model. The exciton is created by exciting an electron from a lower energy half-filled orbital to a higher energy empty orbital. We carry out the real-time dynamics of the resulting excitonic wave-packet, using the time-dependent density matrix renormalization group method. We find clear evidence of charge-spin and spin-orbit separation in real-space, by tracking the time evolution of local observables. We show th…
Resonant inelastic X-ray scattering (RIXS) detects various types of high- and low-energy elementary excitations in correlated solids, and this tool will play an increasingly important role in investigations of time-dependent phenomena in photo-excited systems. While theoretical frameworks for the computation of equilibrium RIXS spectra are well established, the development of appropriate methods for nonequilibrium simulations are an active research field. Here, we apply a recently developed nonequilibrium dynamical mean field theory (DMFT) based approach to compute the RIXS response of photo-e…
A repulsive Coulomb interaction between electrons in different orbitals in correlated materials can give rise to bound quasiparticle states. We study the non-hybridized two-orbital Hubbard model with intra (inter)-orbital interaction $U$ ($U_{12}$) and different band widths using an improved dynamical mean field theory numerical technique which leads to reliable spectra on the real energy axis directly at zero temperature. We find that a finite density of states at the Fermi energy in one band is correlated with the emergence of well defined quasiparticle states at excited energies $Δ=U-U_{12}…
Coulomb matrix elements are needed in all studies in solid-state theory that are based on Hubbard-type multi-orbital models. Due to symmetries, the matrix elements are not independent. We determine a set of independent Coulomb parameters for a $d$-shell and a $f$-shell and all point groups with up to $16$ elements ($O_h$, $O$, $T_d$, $T_h$, $D_{6h}$, and $D_{4h}$). Furthermore, we express all other matrix elements as a function of the independent Coulomb parameters. Apart from the solution of the general point-group problem we investigate in detail the spherical approximation and first-order c…
