Slave-boson Method Research Articles

Band crossover and magnetic phase diagram of the high- Tc superconducting compound Ba2CuO4−δ

We present the influences of electronic and magnetic correlations and doping evolution on the groundstate properties of recently discovered superconductor Ba$_{2}$CuO$_{4-\delta}$ by utilizing the Kotliar-Ruckenstein slave boson method. Starting with an effective two-orbital Hubbard model (Scalapino {\it et al.} Phys. Rev. {\bf B 99}, 224515 (2019)), we demonstrate that with increasing doping concentration, the paramagnetic (PM) system evolves from two-band character to single-band ones around the electron filling n=2.5, with the band nature of the $d_{3z^{2}-r^{2}}$ and $d_{x^{2}-y^{2}}$ orbitals to the $d_{x^{2}-y^{2}}$ orbital, slightly affected when the electronic correlation U varies from 2 to 4 eV. Considering the magnetic correlations, the system displays one antiferromagnetically metallic (AFM) phase in $2<n<2.16$ and a PM phase in $n>2.16$ at U=2 eV, or two AFM phases in $2<n<2.57$ and $2.76<n<3$, and a PM phase in $2.57<n<2.76$ respectively, at U=4 eV. Our results show that near realistic superconducting state around n=2.6 the intermediate correlated Ba$_{2}$CuO$_{3,2}$ should be single band character, and the s-wave superconducting pairing strength becomes significant when U$>$2 eV, and crosses over to d-wave when U$>$2.2 eV.

RTGW2020: An efficient implementation of the multi-orbital Gutzwiller method with general local interactions

In the present paper, we propose an efficient numerical scheme for Gutzwiller method for multi-band Hubbard models with general onsite Coulomb interaction. Following the basic idea of Deng et al. (2009) [26] and extensions by Lanata et al. (2012) [28], the ground state is variationally determined through optimizing the total energy with respect to the variational single particle density matrix (n0), which is called “outer loop”. In the corresponding “inner loop” where n0 is fixed, the non-interacting wave function and the parameters contained in the Gutzwiller projector are determined by a two-step iterative approach. All derivatives of the implementation process have been analytically derived, which allows us to apply some advanced minimization or root-searching algorithms for both the inner and outer loops leading to the highly efficient convergence. In addition, an atomic diagonalization method taking the point group symmetry into account has been developed for the customized design of the Gutzwiller projector, making it convenient to explore many interesting orders at a lower cost of computation. As benchmarks, several different types of correlated models have been studied utilizing the proposed method, which are in perfect agreement with the previous results by DMFT and multi-orbital slave-boson mean field method. Compared with the linear mixing method, Newton's method with analytical derivatives shows much faster convergence for the inner loop. As for the outer loop, the minimization using analytical derivatives also shows much better stability and efficiency compared with that using numerical derivatives.

Boson Subsidiary Solver (BoSS) v1.1

How best to model systems of interacting electrons in an accurate and computationally efficient manner is an outstanding problem in theoretical and computational materials science. For materials where strong electronic interactions are primarily of a localized character and act within a subspace of localized quantum states on separate atomic sites (e.g., in transition metal and rare-earth compounds), their electronic behaviors are typically described by the Hubbard model and its extensions. In this work, we describe BoSS (Boson Subsidiary Solver), a software implementation of the subsidiary-boson (also known as slave-boson or auxiliary-boson) method appropriate for describing a variety of extended Hubbard models, namely p−d models that include both the interacting atomic sites (“d” states) and non-interacting or ligand sites (“p” states). We provide a theoretical background, a description of the equations solved by BoSS, an overview of the algorithms used, the key input/output and control variables of the software program, and tutorial examples of its use featuring band renormalization in SrVO3, Ni 3d multiplet structure in LaNiO3, and the relation between the formation of magnetic moments and insulating behavior in SmNiO3. BoSS interfaces directly with popular electronic structure codes: it can read the output of the Wannier90 software package [1,2] which postprocesses results from workhorse electronic structure software such as Quantum Espresso [3] or VASP [4]. Program summaryProgram title: Boson Subsidiary Solver (BoSS)CPC Library link to program files:https://doi.org/10.17632/3bwx6prn2w.1Developer's repository link:bitbucket.org/yalebosscode/bossCode Ocean capsule:https://codeocean.com/capsule/9605047Licensing provisions: Creative Commons by 4.0Programming language: MATLAB [5]Nature of problem: The BoSS approach, a type of subsidiary-boson method (also called slave-boson or auxiliary-boson method), provides approximate solutions to interacting electron problems described by Hubbard models in a computationally efficient manner. Hubbard models are widely used to describe materials systems with strongly localized electron-electron interactions. The interacting fermion problem is mapped onto two separate, but easier, coupled quantum problems: non-interacting fermions moving on a lattice (spinons) via tunneling between nearby atomic orbitals, and interacting subsidiary bosons that live on individual atomic sites. A self-consistent description of the two degrees of freedom requires matching of mean particle numbers (spinons and bosons) on each site as well as the renormalization of tunneling events for one set of particles due to the fluctuations of the other set of particles. The method can be used to describe the interacting electronic ground state of a particular electronic configuration, or more generally it can find the minimum energy electronic configuration by searching over various symmetry broken phases (e.g., magnetic configurations, configurations with unequal occupation of nominally equivalent atomic orbitals, etc.)Solution method: The spinon and subsidiary-boson problems are each represented as Hermitian eigenvalue problems where the lowest energy (eigenvalue) state is sought. The present implementation uses dense matrix digaonalization for the spinon problem and can use either dense or sparse matrix diagonalization for the boson problem. Particle number matching between the two descriptions is achieved by adjustment of Lagrange multipliers which represent potential energies for the bosons: their appropriate values are found by applying Newton's method to match spinon and boson occupancies. Self-consistency is achieved by simple fixed point iteration (solving spinon, then subsidiary, then spinon, etc.) Minimization of the energy uses gradient descent with adjustable step size.Additional comments including restrictions and unusual features: Most users will prepare the input data for BoSS by running band structure calculations on a material, e.g., density functional theory (DFT) using available software packages such as Quantum Espresso [3] or VASP [4]. Post processing of these calculations to create a spatially localized basis set provides the input to BoSS: most users will create the localized description by using software that transforms the electronic description into a Wannier function basis such as Wannier90 [1] which BoSS interfaces with by default. However, one can bypass this approach and create BoSS input files manually to describe specific localized electron models. Referenceshttp://bitbucket.org/yalebosscode/bosshttp://www.wannier.org/https://www.quantum-espresso.org/https://www.mathworks.com/products/matlab.htmlhttps://www.vasp.at/

Breakdown of charge homogeneity in the two-dimensional Hubbard model: Slave-boson study of magnetic order

We study the two-dimensional one-band Hubbard model on the square lattice through the spin rotation invariant Kotliar-Ruckenstein slave-boson method, with an emphasis on the electron-doped regime. The phase diagram determined within mean field approximation reveals three different magnetically ordered phases separated by first-order transitions, and a wide instability region as indicated by a negative compressibility. We show that this conundrum of the unstable mean field domain is resolved by spatially mixed phases of neighboring stable states. We also find charge density wave type instabilities in the antiferromagnetically ordered (AFM) state at wave vectors commensurate with the doping. The corresponding charge and spin density response functions are calculated from a Gaussian fluctuations formalism about a magnetic saddle point, for which we provide a detailed derivation. Further, we present density and spin excitation spectra in the AFM phase, allowing for a quantitative calculation of the spin wave parameters, the gap in the longitudinal spin excitation spectrum, and the density excitations in the upper Hubbard band.

Hybridization effect on the x-ray absorption spectra for actinide materials: Application to PuB4

Studying the local moment and 5$f$-electron occupations sheds insight into the electronic behavior in actinide materials. X-ray absorption spectroscopy (XAS) has been a powerful tool to reveal the valence electronic structure when assisted with theoretical calculations. However, the analysis currently taken in the community on the branching ratio of the XAS spectra generally does not account for the hybridization effects between local $f$-orbitals and conduction states. In this paper, we discuss an approach which employs the DFT+Gutzwiller rotationally-invariant slave boson (DFT+GRISB) method to obtain a local Hamiltonian for the single-impurity Anderson model (SIAM), and calculates the XAS spectra by the exact diagonalization (ED) method. A customized numerical routine was implemented for the ED XAS part of the calculation. By applying this technique to the recently discovered 5$f$-electron topological Kondo insulator PuB$_4$, we determined the signature of 5$f$-electronic correlation effects in the theoretical X-ray spectra. We found that the Pu 5$f$-6$d$ hybridization effect provides an extra channel to mix the $j=5/2$ and $7/2$ orbitals in the 5$f$ valence. As a consequence, the resulting electron occupation number and spin-orbit coupling strength deviate from the intermediate coupling regime.

Slave-boson analysis of the two-dimensional Hubbard model

We present a comprehensive study of the 2D one-band Hubbard model applying the spin rotation invariant slave-boson method. We utilize a spiral magnetic mean field and fluctuations around a paramagnetic mean field to determine the magnetic phase diagram and find the two approaches to be in good agreement. Apart from the commensurate phases characterized by ordering wave vectors $\boldsymbol Q = (\pi, \pi), (0, \pi)$, and $(0, 0)$ we find incommensurate phases where the ordering wave vectors $\boldsymbol Q = (Q, Q)$, and $(Q, \pi)$ vary continuously with filling, interaction strength or temperature. The mean field quantities magnetization and effective mass are found to change discontinuously at the phase boundaries separating the $(Q, Q)$ and $(Q, \pi)$ phases, indicating a first order transition. The band structure and Fermi surface is shown in selected cases. The dynamic spin and charge susceptibilities as well as the structure factors are calculated and discussed, including the emergence of collective modes of the zero sound and Mott insulator type. The dynamical conductivity is calculated in dependence of doping, interaction strength and temperature. Finally, a temperature-interaction strength phase diagram is established.

Magnetic and topological transitions in three-dimensional topological Kondo insulator☆☆Supported by the National Natural Science Foundation of China under Grant Nos 11764010, 11504061, 11564008, 11704084, and 11704166, the Natural Science Foundation of Guangxi Province under Grant Nos 2017GXNSFAA198169 and 2017GXNSFBA198115, and the SPC-Lab Research Fund under Grant No XKFZ201605.

Using an extended slave-boson method, we draw a global phase diagram summarizing both magnetic phases and paramagnetic (PM) topological insulators (TIs) in a three-dimensional topological Kondo insulator (TKI). By including electron hopping (EH) up to the third neighbors, we identify four strong TI (STI) phases and two weak TI (WTI) phases. Then, the PM phase diagrams characterizing topological transitions between these TIs are depicted as functions of EH, f-electron energy level, and hybridization constant. We also find an insulator–metal transition from an STI phase that has surface Fermi rings and spin textures in qualitative agreement with the TKI candidate SmB6. In the weak hybridization regime, antiferromagnetic (AF) order naturally arises in the phase diagrams. Depending on how the magnetic boundary crosses the PM topological transition lines, AF phases are classified into the AF topological insulator (AFTI) and the non-topological AF insulator, according to their indices. In two small regions of parameter space, two distinct topological transition processes between AF phases occur, leading to two types of AFTIs showing distinguishable surface dispersions around their Dirac points.

Quench of paramagnetic orbital selective Mott phase and appearance of antiferromagnetic orbital selective slater phase in multiorbital correlated systems

We present the modulation of magnetic order on the orbital selective Mott phases (OSMP) and the metal-insulator transitions (MIT) of multi-orbital Hubbard models by employing the rotationally invariant slave-boson methods. We show that at half filling, the well-known paramagnetic (PM) OSMP is completely covered by an antiferromagnetic (AFM) Slater insulator, and the PM Mott phase by an AFM Mott insulator when electron correlation strength varies from intermediate to strong both in two- and three-orbitals Hubbard systems. Away from half-filling, we find that a partial-polarized AFM orbital-selective Slater phase appears in the intermediate correlation regime, and an almost full-polarized AFM OSMP fully covers the paramagnetic OSMP. In addition, the ferromagnetic phase in the three-orbital case is more robust than that in the two-orbital case. These results demonstrate that the modulation of magnetic correlation to the quasiparticle spectra leads to much rich and more interesting MIT scenario in multiorbital correlated systems.

Phase diagrams of the Kane-Mele-Hubbard model in the presence of an external magnetic field

We studied the Kane-Mele-Hubbard model at half filling with Zeeman magnetic field using rotationally invariant slave boson method. The competition between external magnetic field and spin orbital coupling at large Hubbard U is explored. It is found that different canted antiferromagnetic phases exist in the presence of longitudinal and transverse magnetic fields. With longitudinal external magnetic field and strong electron correlation, the z component of the local moment is preferred by the finite spin-orbital coupling.

Slave Boson Theory of Orbital Differentiation with Crystal Field Effects: Application to UO_{2}.

We derive an exact operatorial reformulation of the rotational invariant slave boson method, and we apply it to describe the orbital differentiation in strongly correlated electron systems starting from first principles. The approach enables us to treat strong electron correlations, spin-orbit coupling, and crystal field splittings on the same footing by exploiting the gauge invariance of the mean-field equations. We apply our theory to the archetypical nuclear fuel UO_{2} and show that the ground state of this system displays a pronounced orbital differentiation within the 5f manifold, with Mott-localized Γ_{8} and extended Γ_{7} electrons.

Spin-dependent thermoelectric effects in a strongly correlated double quantum dot

We investigate spin-dependent thermoelectric transport through a system of two coupled quantum dots attached to reservoirs of spin-polarized electrons. Generally, we focus on the strongly correlated regime of transport. To this end, a slave-boson method for finite $U$ is employed. Our main goal is to show that, apart from complex low-temperature physics, such a basic multilevel system provides a possibility to examine various quantum interference effects, with particular emphasis put on the influence of such phenomena on thermoelectric transport. Apart from the influence of interference effects on spin-degenerate charge transport, we show how spin-dependent transport, induced by ferromagnetic leads, can be modified as well. Finally, we also consider the case where the spin-relaxation time in the ferromagnetic leads is relatively long, which leads to the so-called spin thermoelectric effects.

Numerical optimization algorithm for rotationally invariant multi-orbital slave-boson method

We develop a generalized numerical optimization algorithm for the rotationally invariant multi-orbital slave boson approach, which is applicable for arbitrary boundary constraints of high-dimensional objective function by combining several classical optimization techniques. After constructing the calculation architecture of rotationally invariant multi-orbital slave boson model, we apply this optimization algorithm to find the stable ground state and magnetic configuration of two-orbital Hubbard models. The numerical results are consistent with available solutions, confirming the correctness and accuracy of our present algorithm. Furthermore, we utilize it to explore the effects of the transverse Hund’s coupling terms on metal–insulator transition, orbital selective Mott phase and magnetism. These results show the quick convergency and robust stable character of our algorithm in searching the optimized solution of strongly correlated electron systems.

X-boson cumulant approach to the topological Kondo insulators

In this work we present a generalization of our previous work of the X-boson approach to the periodic Anderson model (PAM), adequate to study a novel class of intermetallic 4f and 5f orbitals materials: the topological Kondo insulators, whose paradigmatic material is the compound SmB6.For simplicity, we consider a version of the PAM on a 2D square lattice, adequate to describe Ce-based compounds in two dimensions. The starting point of the model is the 4f - Ce ions orbitals, with J = 5/2 multiplet, in the presence of spin-orbit coupling. Our technique works well for all of the parameters of the model and avoids the unwanted phase transitions of the slave boson mean field theory. We present a critical comparison of our results with those of the usual slave boson method, that has been intensively used to describe this class of materials. We also obtain a new valence first order transition which we attribute to the k⃗ dependence of the hybridization.

Magnetic and orbital instabilities in a lattice of SU(4) organometallic Kondo complexes

Motivated by experiments of scanning tunneling spectroscopy (STS) on self- assembled networks of iron(II)-phtalocyanine (FePc) molecules deposited on a clean Au(111) surface [FePc/Au(111)] and its explanation in terms of the extension of the impurity SU(4) Anderson model to the lattice in the Kondo regime, we study the competition between the Kondo effect and the magneto-orbital interactions occurring in FePc/Au(111). We explore the quantum phases and critical points of the model using a large-N slave-boson method in the mean-field approximation. The SU(4) symmetry in the impurity appears as a combination of the usual spin and an orbital pseudospin arising from the degenerate 3dxz and 3dyz orbitals in the Fe atom. In the case of the lattice, our results show that the additional orbital degrees of freedom crucially modify the low-temperature phase diagram, and induce new types of orbital interactions among the Fe atoms, which can potentially stabilize exotic quantum phases with magnetic and orbital order. The dominant instability corresponds to spin ferromagnetic and orbital antiferromagnetic order.

In-gap collective mode spectrum of the topological Kondo insulatorSmB6

Samarium hexaboride (SmB$_6$) is the first strongly correlated material with a recognized non-trivial band-structure topology. Its electron correlations are seen by inelastic neutron scattering as a coherent collective excitation at the energy of 14 meV. Here we calculate the spectrum of this mode using a perturbative slave boson method. Our starting point is the recently constructed Anderson model that properly captures the band-structure topology of SmB$_6$. Most self-consistent renormalization effects are captured by a few phenomenological parameters whose values are fitted to match the calculated and experimentally measured mode spectrum in the first Brillouin zone. A simple band-structure of low-energy quasiparticles in SmB$_6$ is also modeled through this fitting procedure, because the important renormalization effects due to Coulomb interactions are hard to calculate by ab-initio methods. Despite involving uncontrolled approximations, the slave boson calculation is capable of producing a fairly good quantitative match of the energy spectrum, and a qualitative match of the spectral weight throughout the first Brillouin zone. We find that the "fitted" band-structure required for this match indeed puts SmB$_6$ in the class of strong topological insulators. Our analysis thus provides a detailed physical picture of how the SmB$_6$ band topology arises from strong electron interactions, and paints the collective mode as magnetically active exciton.

Effect of electron correlations on the formation of spiral magnetic states in the two-dimensional t-t′ Hubbard model

The formation of the spiral magnetic order in the ground state of the Hubbard model for a square lattice has been studied within the slave-boson method in a wide range of the parameters of the carrier density and Coulomb interaction. Next-nearest-neighbor electron hopping, as well as the magnetic phase separation, has been taken into account. It has been shown that the electron correlations lead to the suppression of the ferromagnetic and spiral phases in comparison with the Hartree—Fock approximation. The application of the results to the explanation of the experimental data, in particular, to the description of the magnetic state of the high-temperature superconductors of the cuprate-based systems has been discussed.

Global phase diagram of a doped Kitaev-Heisenberg model

The global phase diagram of a doped Kitaev-Heisenberg model is studied using an SU(2) slave-boson mean-field method. Near the Kitaev limit, p-wave superconducting states which break the time-reversal symmetry are stabilized as reported by You {\it et al.} [Phys. Rev. B {\bf 86}, 085145 (2012)] irrespective of the sign of the Kitaev interaction. By further doping, a d-wave superconducting state appears when the Kitaev interaction is antiferromagnetic, while another p-wave superconducting state appears when the Kitaev interaction is ferromagnetic. This p-wave superconducting state does not break the time-reversal symmetry as reported by Hyart {\it et al.} [Phys. Rev. B {\bf 85}, 140510 (2012)], and such a superconducting state also appears when the antiferromagnetic Kitaev interaction and the ferromagnetic Heisenberg interaction compete. This work, thus, demonstrates the clear difference between the antiferromagnetic Kitaev model and the ferromagnetic Kitaev model when carriers are doped while these models are equivalent in the undoped limit, and how novel superconducting states emerge when the Kitaev interaction and the Heisenberg interaction compete.

Topological view on magnetic adatoms in graphene

We study theoretically the physical properties of a magnetic impurity in graphene. Within the Anderson model for a very strong Coulomb interaction on the impurity, we start from the Slave-Boson method and introduce a topological picture consisting of a degree of a map and a winding number (WN) to analyze the phase shift and the occupation on the impurity. The occupation is linked to WN. For a generic normal metal we find a fractional WN. In contrast, the winding is accelerated by the relativistic dispersion of graphene at half-filling leading to an integer occupation. We show that the renormalization parameter that shifts the impurity level is insufficient to invert the sign of the energy level. Consequently, the state at half-filling is stable unless a gate voltage is tuned such that the Fermi level touches the edge of the broadened impurity level. Only in this case the zero field susceptibility is finite and shows a pronounced peak structure with the gate voltage.

Considerable nonlocal electronic correlations in strongly dopedNaxCoO2

The puzzling electronic correlation effects in the sodium cobaltate system are studied by means of the combination of density functional theory and the rotationally invariant slave boson (RISB) method in a cellular-cluster approach. Realistic non-local correlations are hence described in the short-range regime for finite Coulomb interactions on the underlying frustrated triangular lattice. A local Hubbard U is sufficient to model the gross in-plane magnetic behavior with doping x, namely antiferromagnetic correlations at intermediate doping and the onset of ferromagnetic order above x>3/4 with a mixed phase for 0.62<x<3/4. Important insight is thereby provided by the occupations of local cluster multiplets retrieved from the RISB framework. The extended modeling of the x$\ge$2/3 doping regime with an additional inter-site Coulomb repulsion V on an experimentally verified effective kagom\'e lattice allows to account for relevant charge-ordering physics. Therewith a fluctuating charge-density-wave state with small quasiparticle weight and a maximum in-plane magnetic susceptibility may be identified at x$\sim$3/4, just where the magnetic ordering sets in.

Electronic correlations in vanadium chalcogenides:BaV Se3 versusBaV S3

Albeit structurally and electronically very similar, at low temperature the quasi-one-dimensional vanadiumsulfide BaV S3 shows a metal-to-insulator transition via the appearance of a charge-density-wave state, whileBaV Se3 apparently remains metallic down to zero temperature. This different behavior upon cooling isstudied by means of density functional theory and its combination with the dynamicalmean-field theory and the rotationally invariant slave-boson method. We reveal several subtledifferences between these chalcogenides that provide indications for the deviant behavior ofBaV Se3 at low temperature. In this regard, a smaller HubbardU in line with an increased relevance of the Hund’s exchangeJ plays a vital role.