Stripe-like and bubble-like patterns spontaneously form in numerous physical, chemical, and biological systems when competing long-range and short-range interactions banish uniformity. Stripe-like and the related nematic morphology are also under intense scrutiny in various strongly correlated electron systems. In contrast, the electronic bubble morphology is rare. Some of the most intriguing electron bubbles develop in the two-dimensional electron gas subjected to a perpendicular magnetic field. However, in contrast to bubbles forming in classical systems such as the Turing activator-inhibitor reaction or Langmuir films, bubbles in electron gases owe their existence to elementary quantum mechanics: they are stabilized as wavefunctions of individual electrons overlap. Here we report a rich pattern of multi-electron bubble phases in a high Landau level and we conclude that this richness is due to the nodal structure of the orbital component of the electronic wavefunction.
Wavefunctions constructed from electron-pair states can accurately model strong electron correlation effects and are promising approaches especially for larger many-body systems. In this article, we analyze the nature and the type of electron correlation effects that can be captured by wavefunctions restricted to electron-pair states. We focus on the Antisymmetric Product of 1-reference orbital Geminal (AP1roG) method combined with an orbital optimization protocol presented in [Phys. Rev. B, 89, 201106(R), 2014] whose performance is assessed against electronic structures obtained form DMRG ref…
We report formation of magnetic textures in the ferromagnetic (FM) phase of La$_{1-x}$Sr$_x$MnO$_3$ for $x =$ 0.125; these textures are magnetic bubbles, magnetic stripe domains, and forced FM states. In situ Lorentz microscopy (LM) observations show that magnetic bubbles exist in the FM insulating phase accompanying the formation of the charge$/$orbital ordering (CO$/$OO). Furthermore, stable magnetic bubbles still exist in an intermediate temperature region between the CO$/$OO ($T_{CO} =$ 155 K) and FM ($T_c =$ 190 K) transition temperatures. These magnetic bubbles are believed to originate …
The strong boundary normalized condition of wavefunction for fully occupied semicore 3d orbitals leads the linear response DFT+U on such metal oxide to have an insurmountable obstacle in Hubbard U determination. We treated the orbital self-energy and orbital relaxation as components of eigenvalues with respective orbital occupation number that follows the Fermi-Dirac distribution. By self-consistently solving the second partial deviation of total energy based on the most simple local density formalism with Hubbard U correction, we found the local density exchange-correlation potential function…
Anomalous Hall Effect in $t_{2g}$ Orbital Kagome Lattice due to Non-collinearity:Significance of Orbital Aharonov-Bohm Effect
通过引入d轨道自由度，提出了倾斜铁磁金属中自旋结构驱动反常霍尔效应（AHE）的新机制。我们发现，在非共线自旋结构和自旋轨道相互作用的存在下，传导电子由于复杂的d轨道波函数而获得Berry相。由这种轨道导出的Berry相驱动的AHE比由自旋手征诱导的AHE大得多，这自然解释了烧绿石Nd $_2$ Mo $_2$ O $_7$中自旋结构驱动的AHE的显著特征。由于所提出的AHE甚至可以发生在共面自旋序（$M_z=0$），它有望出现在其他有趣的几何挫折系统。
This paper presents a mathematical and numerical analysis of the flatband wavefunctions occurring in the chiral model of twisted bilayer graphene at the "magic" twist angles. We show that the chiral model possesses an exact intra-valley inversion symmetry. Writing the flatband wavefunction as a product of a lowest Landau level quantum Hall state and a spinor, we show that the components of the spinor are anti-quantum Hall wavefunctions related by the inversion symmetry operation introduced here. We then show numerically that as one moves from the lowest to higher magic angles, the spinor compo…
The natural orbital functional theory (NOFT) has emerged as an alternative formalism to both density functional (DF) and wavefunction methods. In NOFT, the electronic structure is described in terms of the natural orbitals (NOs) and their occupation numbers (ONs). The approximate NOFs have proven to be more accurate than those of the density for systems with a significant multiconfigurational character, on one side, and scale better with the number of basis functions than correlated wavefunction methods, on the other side. A challenging task in NOFT is to efficiently perform orbital optimizati…
Anomalous Hall Effect due to Non-collinearily in Pyrochlore Compounds: Role of Orbital Aharonov-Bohm Effect
为了阐明烧绿石化合物中自旋结构驱动的反常霍尔效应（AHE）的起源，我们构建了$t_{2g}$ -轨道kagome晶格模型，并分析了反常霍尔电导（AHC）.我们发现，一个传导电子获得一个Berry相位由于复杂的d-轨道波函数的存在下的自旋轨道相互作用。这种“轨道Aharonov-Bohm（AB）效应”产生了在非共线自旋结构存在下急剧变化的AHC。在铁磁化合物Nd $_2$ Mo $_2$ O $_7$和顺磁化合物Pr $_2$ Ir $_2$ O $_7$中，由轨道AB效应产生的AHC完全支配自旋手征机制，并成功地解释了自旋结构与AHC之间的实验关系。特别地，在Pr $_2$ Ir $_2$ O $_7$中观察到的“在没有磁化的情况下的有限AHC”可以通过假设Ir 5d电子的小磁序而用轨道机制来解释。
The wavefunction method provides us with a useful tool to describe electron correlations in solids at the ground state. In this paper we review the recent development of the momentum-dependent local ansatz wavefunction (MLA). It is constructed by taking into account two-particle excited states projected onto the local orbitals, and the momentum-dependent amplitudes of these states are chosen as variational parameters. The MLA describes accurately correlated electron states from the weak to the intermediate Coulomb interaction regime in infinite dimensions, and works well even in the strongly c…
In this work, we introduce three algorithmic improvements to reduce the cost and improve the scaling of orbital space variational Monte Carlo (VMC). First, we show that by appropriately screening the one- and two-electron integrals of the Hamiltonian one can improve the efficiency of the algorithm by several orders of magnitude. This improved efficiency comes with the added benefit that the resulting algorithm scales as the second power of the system size $O(N^2)$, down from the fourth power $O(N^4)$. Using numerical results, we demonstrate that the practical scaling obtained is in fact $O(N^{…
The transferred hyperfine interaction between nuclear and electron spins in an heavy fermion material depends on the hybridization between the $f$-electron orbitals and those surrounding a distant nucleus. In CeMIn$_5$ (M=Rh, Ir, Co), both the hyperfine coupling to the two indium sites as well as the crystalline electric field at the Ce are strongly dependent on the transition metal. We measure a series of CeRh$_{1-x}$Ir$_x$In$_5$ crystals and find that the hyperfine coupling reflects the orbital anisotropy of the ground state Ce 4$f$ wavefunction. These findings provide direct proof that the …
The accurate electronic structure calculation for strongly correlated chemical systems requires an adequate description for both static and dynamic electron correlation, and is a persistent challenge for quantum chemistry. In order to account for static and dynamic electron correlations accurately and efficiently, in this work we propose a new method by integrating the density matrix renormalization group (DMRG) method and multi-reference second-order Epstein-Nesbet perturbation theory (ENPT2) with a selected configuration interaction (SCI) approximation. Compared with previous DMRG-based dyna…
The electronic structure of the nitrogenase metal cofactors is central to nitrogen fixation. However, the P-cluster and iron molybdenum cofactor, each containing eight irons, have resisted detailed characterization of their electronic properties. Through exhaustive many-electron wavefunction simulations enabled by new theoretical methods, we report on the low-energy electronic states of the P-cluster in three oxidation states. The energy scales of orbital and spin excitations overlap, yielding a dense spectrum with features we trace to the underlying atomic states and recouplings. The clusters…
The discovery of superconductivity in hole-doped infinite-layer NdNiO$_2$ -- a transition metal (TM) oxide that is both isostructural and isoelectronic to cuprate superconductors -- has lead to renewed enthusiasm in the hope of understanding the origin of unconventional superconductivity. Here, we investigate the electron-removal states in infinite-layered Ni$^{1+}$ oxide, NdNiO$_2$, which mimics hole-doping, with the state-of-the-art many-body multireference quantum chemistry methods. From the analysis of the many-body wavefunction, we find that the hole-doped $d^8$ ground state of NdNiO$_2$ …
Fanpy is a free and open-source Python library for developing and testing multideterminant wavefunctions and related ab initio methods in electronic structure theory. The main use of Fanpy is to quickly prototype new methods by making it easier to transfer the mathematical conception of a new wavefunction ansätze to a working implementation. Fanpy uses the framework of our recently introduced Flexible Ansatz for N-electron Configuration Interaction (FANCI), where multideterminant wavefunctions are represented by their overlaps with Slater determinants of orthonormal spin-orbitals. In the simpl…
We propose a novel four-coloring model which describes "frustrated superfluidity" of $p$-band bosons in the diamond optical lattice. The superfluid phases of the condensate wavefunctions on the diamond-lattice bonds are mapped to four distinct colors at low temperatures. The fact that a macroscopic number of states satisfy the constraints that four differently colored bonds meet at the same site leads to an extensive degeneracy in the superfluid ground state at the classical level. We demonstrate that the phase of the superfluid wavefunction as well as the orbital angular momentum correlations…
