We formulate a pseudofermion functional renormalization group (PFFRG) scheme to address frustrated quantum magnetism in three dimensions. In a scenario where many numerical approaches fail due to sign problem or small system size, three-dimensional (3D) PFFRG allows for a quantitative investigation of the quantum spin problem and its observables. We illustrate 3D PFFRG for the simple cubic $J_1$-$J_2$-$J_3$ quantum Heisenberg antiferromagnet, and benchmark it against other approaches, if available.
We report tests of various density functionals for ferromagnetic, Fe, Co and Ni with a focus on characterizing the behavior of the so-called strongly constrained and appropriately normed (SCAN) functional. It is found that SCAN is closer in behavior to functionals that yield localized behavior, such as hybrid functionals, than other semilocal functionals that are tested. The results are understood in terms of a tendency to differentiate orbitals, favoring integer occupation, which is necessary for a correct description of atomic systems, but inappropriate for the open shell metallic ferromagne…
Interplay between magnetism, superconductivity, and orbital order in a 5-pocket model for iron-based superconductors - a parquet renormalization group study
Poisoning of magnetism in silicon doped with Re, caused by a charge transfer from interstitials to substitutionals, by means of the self-interaction corrected density-functional approach
We extend the density functional perturbation theory formalism to the case of non-collinear magnetism. The main problem comes with the exchange-correlation (XC) potential derivatives, which are the only ones that are affected by the non-collinearity of the system. Most of the present XC functionals are constructed at the collinear level, such that the off-diagonal (containing magnetization densities along $x$ and $y$ directions) derivatives cannot be calculated simply in the non-collinear framework. To solve this problem, we consider here possibilities to transform the non-collinear XC derivat…
Magnetism of the Fe$^{2+}$ and Ce$^{3+}$ sublattices in Ce$_{2}$O$_{2}$FeSe$_{2}$: a combined neutron powder diffraction, inelastic neutron scattering and density functional study
在30 K以上的122铁硒化物材料中发现超导性需要了解潜在的磁相互作用。我们提出了磁性和半导体Ce $_{2}$ O $_{2}$ FeSe $_{2}$组成的边连接的铁硒四面体链的实验和理论研究相结合。结合中子衍射和非弹性散射的研究和密度泛函计算证实了最近邻的铁-硒-铁相互作用的铁磁性质的ZrCuSiAs相关的铁硒氧化物Ce $_{2}$ O $_{2}$ FeSe $_{2}$。非弹性测量提供了最近邻的Fe-Fe和Fe-Ce相互作用的强度的估计。这与密度泛函理论计算结果一致，表明Ce $_{2}$ O $_{2}$ FeSe $_{2}$的Fe-Se片层中的相关性很弱. Fe原位排斥$U_{Fe}$与所报道的砷氧化物和K $_{1-x}$ Fe $_{2-y}$ Se $_{2}$相当，它们是铁基超导体的母体。
Two-dimensional moire superlattices have recently emerged as a fertile ground for creating novel electronic phases of matter with unprecedented control. Despite intensive efforts, theoretical investigation of correlated moire systems has been challenged by the large number of atoms in a superlattice unit cell and the inherent difficulty of treating electron correlation. The physics of correlated moire systems is governed by low-energy electrons in a coarse-grained long-wavelength potential, unlike the singular Coulomb potential of atomically-spaced ions in natural solids. Motivated by the sepa…
A scaling theory of the Kondo lattices with frustrated exchange interactions is developed, criterium of antiferromagnetic ordering and quantum-disordered state being investigated. The calculations taking into account magnon and incoherent spin dynamics are performed. Depending on the bare model parameters, one or two quantum phase transitions into non-magnetic spin-liquid and Kondo Fermi-liquid ground states can occur with increasing the bare coupling constant. Whereas the renormalization of the magnetic moment in the ordered phase can reach orders of magnitude, spin fluctuation frequency and …
The recent observation of superconductivity in infinite-layer nickelates has brought intense debate on the established knowledge of unconventional superconductivity based on the cuprates. Despite many similarities, the nickelates differ from the cuprates in many characteristics, the most notable one among which is the magnetism. Instead of a canonical antiferromagnetic Mott insulator as the undoped cuprates, from which the superconductivity is generally believed to arise upon doping, the undoped nickelates show no sign of magnetic ordering in experiments. Through a combined density functional …
We investigate, using a first-principles density-functional methodology, the nature of magnetism in monolayer $1T$-phase of tantalum disulfide ($1T$-TaS$_2$ ). Magnetism in the insulating phase of TaS$_2$ is a longstanding puzzle and has led to a variety of theoretical proposals including notably the realization of a two-dimensional quantum-spin-liquid phase. By means of non-collinear spin calculations, we derive $\textit{ab initio}$ spin Hamiltonians including two-spin bilinear Heisenberg exchange, as well as biquadratic and four-spin ring-exchange couplings. We find that both quadratic and q…
The magnetism of the double perovskite compounds \SLFCOx\ ($x$ = 0, 1, 2) are contrasted using magnetization, neutron diffraction and electron paramagnetic resonance with the support from density functional theory calculations. \LFCO\ is identified as a long-range ordered antiferromagnet displaying a near-room temperature transition at $T_N$ = 270~K, accompanied by a low temperature structural phase transition at $T_S$ = 200~K. The structural phase transformation at $T_S$ occurs from $R\overline{3}c$ at 300~K to $Pnma$ at 200~K. The density functional theory calculations support an insulating …
We show that the N-patch functional renormalization group (pFRG), a theoretical method commonly applied for correlated electron systems, is unable to implement consistently the matrix element interference arising from strong momentum dependence in the Bloch state contents or the interaction vertices. We show that such a deficit could lead to results incompatible with checkable limits of weak and strong coupling. We propose that the pFRG could be improved by a better account of momentum conservation.
Emergent magnetism and spin liquids in an extended Hubbard description of moiré bilayers
University of California, Santa Barbara（加州大学圣塔芭芭拉分校）；University of Cologne（科隆大学）；Kavli Institute for Theoretical Physics, University of California, Santa Barbara（加州大学圣塔芭芭拉分校卡弗里理论物理研究所）；French American Center for Theoretical Science, CNRS, KITP, Santa Barbara（法国美国理论科学中心，CNRS，KITP，圣塔芭芭拉）；Canadian Institute for Advanced Research（加拿大高级研究院）；Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory（斯坦福材料能源科学研究所，SLAC国家加速器实验室）
We analyze a variety of integration schemes for the momentum space functional renormalization group calculation with the goal of finding an optimized scheme. Using the square lattice $t-t'$ Hubbard model as a testbed we define and benchmark the quality. Most notably we define an error estimate of the solution for the ordinary differential equation circumventing the issues introduced by the divergences at the end of the FRG flow. Using this measure to control for accuracy we find a threefold reduction in number of required integration steps achievable by choice of integrator. We herewith publis…
Functional renormalization group approach to the singlet-triplet transition in quantum dots
利用泛函重整化群方法研究了具有两个不同轨道的量子点在Hund耦合作用下的零偏压输运性质。通过调节轨道态的能量分离，量子点可以被驱动通过单重态-三重态跃迁。我们的方法，Karrasch { \em et al}的方法的基础上，我们适用于自旋相关的相互作用，恢复的量子点输运性质的关键特性，很少的数值工作。我们目前的结果在附近的过渡和比较我们的结果与以前的数值重整化群的结果和预测的微扰重整化群的电导。
Fe$_{3-x}$GeTe$_2$ is a layered van der Waals magnetic material with a relatively high ordering temperature and large anisotropy. While most studies have concluded the interlayer ordering to be ferromagnetic, there have also been reports of interlayer antiferromagnetism in Fe$_{3-x}$GeTe$_2$. Here, we investigate the interlayer magnetic ordering by neutron diffraction experiments, scanning tunneling microscopy (STM) and spin-polarized STM measurements, density functional theory plus U calculations and STM simulations. We conclude that the layers of Fe$_{3-x}$GeTe$_2$ are coupled ferromagnetica…
We show an application of the functional-renormalization-group aided density functional theory to the homogeneous electron gas with arbitrary spin polarization, which gives the energy density functional in the local spin density approximation. The correlation energy per particle is calculated at arbitrary Wigner-Seitz radius $ r_{\rm s} $ and spin polarization $ ζ$. In the high-density region, our result shows good agreement with Monte Carlo (MC) data. The agreement with MC data is better in the case of small spin polarization, while the discrepancy increases as the spin polarization increases…
We show an $\textit{ab initio}$ construction of the energy density functional (EDF) for electron systems using the functional renormalization group. The correlation energies of the homogeneous electron gas given in our framework reproduce the exact behavior at high density and agree with the Monte-Carlo data in a wide range of densities. Our analytic technique enables us to get the correlation energies efficiently for various densities, which realizes the determination of EDF in the local density approximation (LDA) without any fitting for physically relevant densities. Applied to the Kohn-Sha…
