On-site Repulsion Research Articles

Single-electron transport in a three-ion magnetic molecule modulated by a transverse field

We study single-electron transport in a three-ion molecule with strong uniaxial anisotropy and in the presence of a transverse magnetic field. Two magnetic ions are connected to each other through a third, nonmagnetic ion. The magnetic ions are coupled to ideal metallic leads and a back gate voltage is applied to the molecule, forming a field-effect transistor. The microscopic Hamiltonian describing this system includes inter-ion hopping, on-site repulsions and magnetic anisotropies. For a range of values of the parameters of the Hamiltonian, we obtain an energy spectrum similar to that of single-molecule magnets in the giant spin approximation where the two states with maximum spin projection along the uniaxial anisotropy axis are well separated from other states. In addition, upon applying an external in-plane magnetic field, the energy gap between the ground and first excited states of the molecule oscillates, going to zero at certain special values of the field, analogous to the diabolical points resulting from Berry phase interference in the giant spin model. Thus, our microscopic model provides the same phenomenological behavior expected from the giant spin model of a single-molecule magnet but with direct access to the internal structure of the molecule, thus making it more appropriate for realistic electronic transport studies. To illustrate this point, the nonlinear electronic transport in the sequential tunneling regime is evaluated for values of the field near these degeneracy points. We show that the existence of these points has a clear signature in the I–V characteristics of the molecule, most notably the modulation of excitation lines in the differential conductance.

Superconductivity from weak repulsion in hexagonal lattice systems

We analyze the pairing instabilities for fermions on hexagonal lattices (both honeycomb and triangular ones) in a wide range of fermionic densities. We argue that for a generic doping in this range, superconductivity at weak coupling is of Kohn-Luttinger type, and, due to the presence of electronic interactions beyond on-site repulsion, is a threshold phenomenon, with superconductivity emerging only if the attraction generated by the Kohn-Luttinger mechanism exceeds the bare repulsion in some channel. For disconnected Fermi pockets, we predict that Kohn-Luttinger superconductivity, if it occurs, is likely to be $f$-wave. While the Kohn-Luttinger analysis is adequate over most of the doping range, a more sophisticated analysis is needed near Van Hove doping. We treat Van Hove doping using a parquet renormalization group, the equations for which we derive and analyze. Near this doping level, superconductivity is a universal phenomenon, arising from any choice of bare repulsive interactions. The strongest pairing instability is into a chiral $d-$wave state ($d+id$). At a truly weak coupling, the strongest competitor is a spin-density-wave instability, however, $d-$wave superconductivity still wins. Moreover, the feedback of the spin density fluctuations into the Cooper channel significantly enhances the critical temperature over the estimates of the Kohn Luttinger theory. We analyze renormalization group equations at stronger couplings and find that the main competitor to $d-$wave supoerconductivity away from weak coupling is actually ferromagnetism. We also discuss the effect of the edge fermions and show that they are unimportant in the asymptotic weak coupling limit, but may give rise to, e.g., a charge-density-wave order at moderate coupling strengths.

Variational optimization of the 2DM: approaching three-index accuracy using extended cluster constraints

The reduced density matrix is variationally optimized for the two-dimensional Hubbard model. Exploiting all symmetries present in the system, we have been able to study $6\times6$ lattices at various fillings and different values for the on-site repulsion, using the highly accurate but computationally expensive three-index conditions. To reduce the computational cost we study the performance of imposing the three-index constraints on local clusters of $2\times2$ and $3\times3$ sites. We subsequently derive new constraints which extend these cluster constraints to incorporate the open-system nature of a cluster on a larger lattice. The feasibility of implementing these new constraints is demonstrated by performing a proof-of-principle calculation on the $6\times6$ lattice. It is shown that a large portion of the three-index result can be recovered using these extended cluster constraints, at a fraction of the computational cost.

Ferromagnetism and Borromean Binding in Three-Fermion Clusters

A three-particle spin-12 fermion problem with on-site repulsion and nearest-neighbor attraction is solved on the two-dimensional square lattice by discretizing a Schrödinger equation in momentum space. Energies of bound complexes (trions) and their binding conditions are obtained. For total spin S=1/2, a wide region of trion instability toward decaying into a stable singlet pair plus a free fermion is identified. The instability is attributed to the formation of a wave function node upon addition of the third fermion. In the S=3/2 sector, trions are found to form in the absence of bound pairs indicating Borromean binding. In the strong coupling limit the system transitions from an S=1/2 ground state to a ferromagnetic S=3/2 ground state in agreement with the Nagaoka theorem for a four-site plaquette.

Bose-Hubbard model with occupation-parity couplings

We study a Bose-Hubbard model having on-site repulsion, nearest-neighbor tunneling, and ferromagneticlike coupling between occupation parities of nearest-neighbor sites. For a uniform system in any dimension at zero tunneling, we obtain an exact phase diagram characterized by Mott-insulator (MI) and pair liquid phases and regions of phase separation of two MIs. For a general trapped system in one and two dimensions with finite tunneling, we perform quantum Monte Carlo and Gutzwiller mean-field calculations, both of which show the evolution of the system, as the parity coupling increases, from a superfluid to wedding-cake-structure MIs with their occupations jumping by 2. We also identify an exotic pair superfluid at relatively large tunneling strength. Our model ought to effectively describe recent findings in imbalanced Fermi gases in two-dimensional optical lattices and also potentially apply to an anisotropic version of bilinear-biquadratic spin systems.

Magnetic exchange force microscopy from first principles: application to the antiferromagnetic NiO(001) surface

We present an accurate ab initio description of the magnetic exchange force microscopy (MExFM). As a prototypical system, the antiferromagnetic NiO(001) surface probed with a Fe tip is investigated. The tip–surface interaction is described on two levels. Short-range chemical and exchange forces between the tip apex and the surface atoms are described in the framework of spin-polarized density functional theory while long-range van der Waals forces are considered within a mesoscopic tip model. For the Ni atoms in the NiO surface as well as the Fe atoms of the tip apex, an on-site repulsion U in the transition-metal 3d shells is included. In order to understand the tip–surface interaction, we investigate the changes in the electronic structure of tip and surface versus distance. The resulting frequency shifts and MExFM images are in good qualitative agreement with experimental data.

P轨道占位库仑排斥对Mg<sub>2</sub>Sn电学性质的影响

利用基于密度泛函理论的广义梯度近似方法计算了Mg2Sn的能带结构、能态密度、差分电荷密度和介电函数。为了考虑Sn中5p轨道的强电子关联效应，我们采用GGA + U的方法计算Mg2Sn的电学性质。当有效U值为0 eV时，Mg2Sn带隙为负，与实验值相差较大。当有效U值为1.88eV时，间接带隙为0.30 eV，与实验值吻合较好。差分电荷密度的计算表明Mg2Sn中Sn-Sn键相对于Sn-Mg键有着较强的共价性，符合实际情况，介电函数的计算结果也与实验结果基本一致。这些证实p轨道占位库仑排斥对Mg2Sn的电学性质有着较大的影响。The band structure, density of states, electron density difference and dielectric function of Mg2Sn are investigated systematically by using the generalized gradient approximation based on density functional theory. To describe the strong electron correlation in the Sn 5p states, the GGA plus on-site repulsion method (GGA+U) is used in the electrical properties calculation of Mg2Sn. It is found that the band gap is negative with the effective U value of 0 eV, which is quite different from the experimental result. As the effective U value of 1.88 eV is considered, the compound is a semi-conductor with an indirect band gap of 0.30 eV, which agrees with the previous experimental ob-servation satisfactorily. The calculations of electron density difference show that the covalent bond between Sn-Sn is stronger than the covalent bond between Sn-Mg, which is accordant with the practical situation. The calculation of dielectric function agrees well with the experimental result, too. The important influence of the p-orbital on-site Coulumb repulsion for the electronic properties of Mg2Sn is confirmed.

Determinant quantum Monte Carlo study of exciton condensation in the bilayer Hubbard model

We studied the possibility of exciton condensation in a strongly correlated bilayer extended Hubbard model using Determinant Quantum Monte Carlo. To model both the onsite repulsion U and the interlayer interaction V we introduced a novel update scheme extending the standard Sherman-Morrison update. We observe that the sign problem increases dramatically with the inclusion of the interlayer interaction V, which prohibits at this stage a unequivocal conclusion regarding the presence of exciton condensation. However, enhancement of the interlayer tunneling results suggest that the strongest exciton condensation tendency lies around 10-20 % p/n-doping. Magnetic properties and conductivity turn out to be relatively independent of the interlayer interaction.

Phase diagram and pair Tomonaga-Luttinger liquid in a Bose-Hubbard model with flat bands

To explore superfluidity in flat-band systems, we consider a Bose-Hubbard model on a cross-linked ladder with $\pi$ flux, which has a flat band with a gap between the other band for noninteracting particles, where we study the effect of the on-site repulsion nonperturbatively. For low densities, we find exact degenerate ground states, each of which is a Wigner solid with nonoverlapping Wannier states on the flat band. At higher densities, the many-body system, when projected onto the lower flat band, can be mapped to a spin-chain model. This mapping enables us to reveal the existence of a Tomonaga-Luttinger liquid comprising it pairs of bosons. Interestingly, the high- and low- density regions have an overlap, where the two phases coexist.

Energetics of Water Oxidation Catalyzed by Cobalt Oxide Nanoparticles: Assessing the Accuracy of DFT and DFT+U Approaches against Coupled Cluster Methods.

Some of the most promising catalysts for water oxidation rely on crystalline and amorphous cobalt oxide nanoparticles. Density functional theory (DFT) calculations are routinely used to study the electronic and atomic structures of these materials as well as the thermodynamics and mechanisms of the electrochemical oxygen evolution reaction. The accuracy of these theoretical predictions has never been compared to high-level quantum chemistry methods. We perform coupled cluster (CC) quantum chemistry calculations on model cobalt oxide surface sites and use them to benchmark the accuracy of the most popular exchange and correlation functionals. Hybrid B3LYP and PBE0 functionals lead to fair agreement with the CC energies, while standard gradient-corrected functionals show important discrepancies. The inclusion of on-site electronic repulsion (DFT+U) substantially improves the calculated electronic and structural properties, but no value of the U parameter reproduces the CC results. We discuss the implications of these findings for amorphous cobalt phosphate nanoparticles, showing that the reactivity of these catalysts is not altered by surface phosphate groups.

Spin-orbital frustration in molybdenum pyrochloresA2Mo2O7(A=rare earth)

Electronic and magnetic properties of molybdenum pyrochlores A2Mo2O7 are studied by the fully relativistic density-functional theory plus on-site repulsion (U) method, with focusing on the spin-glass insulating material Y2Mo2O7. We find that the system exhibits peculiar competition in energy between different magnetic states in the large-U insulating region. The magnetic competition cannot be explained by the conventional picture based on the geometrical frustration of isotropic Heisenberg antiferromagnetic exchange interactions. Through an analysis by using a generalized spin model, we find that the effective spin interactions are distinct from the simple Heisenberg form and strongly anisotropic in spin space. We also reveal that they give rise to keen competition between antiferromagnetic and ferromagnetic states. The complex form of the magnetic interactions indicates a crucial role of the orbital degree of freedom. Analyzing a three-orbital Hubbard model, we clarify that the magnetic competition is tightly connected with orbital frustration in the 4d2 electronic configuration through the spin-orbital interplay. The results challenge the conventional picture of the spin-glass behavior that attributes the origin to the geometrical frustration of purely antiferromagnetic exchange interactions.

Spin-resolved chiral condensate as a spin-unpolarizedν=0quantum Hall state in graphene

Motivated by the recent experiments indicating a spin-unpolarized $\ensuremath{\nu}=0$ quantum Hall state in graphene, we theoretically investigate the ground state based on the many-body problem projected onto the $n=0$ Landau level. For an effective model with the on-site Coulomb repulsion and antiferromagnetic exchange couplings, we show that the ground state is a doubly degenerate spin-resolved chiral condensate in which all the zero-energy states with up spin are condensed into one chirality, while those with down spin to the other. This can be exactly shown for an Ising-type exchange interaction. The charge gap due to the on-site repulsion in the ground state is shown to grow linearly with the magnetic field, in qualitative agreement with the experiments.

Pair supersolid with atom-pair hopping on the state-dependent triangular lattice

We systematically study an extended Bose-Hubbard model with atom hopping and atom-pair hopping in the presence of a three-body constraint on the triangular lattice. By means of large-scale Quantum Monte Carlo simulations, the ground-state phase diagram are studied. We find a continuous transition between the atomic superfluid phase and the pair superfluid when the ratio of the atomic hopping and the atom-pair hopping is adapted. We then focus on the interplay among the atom-pair hopping, the on-site repulsion and the nearest-neighbor repulsion. With on-site repulsion present, we observe first order transitions between the Mott Insulators and pair superfluid driven by the pair hopping. With the nearest-neighbor repulsion turning on, three typical solid phases with 2/3, 1 and 4/3-filling emerge at small atom-pair hopping region. A stable pair supersolid phase is found at small on-site repulsion. This is due to the three-body constraint and the pair hopping, which essentially make the model a quasi hardcore boson system. Thus the pair supersolid state emerges basing on the order-by-disorder mechanism, by which hardcore bosons avoid classical frustration on the triangular lattice. The transition between the pair supersolid and the pair superfluid is first order, except for the particle-hole symmetric point. We compare the results with those obtained by means of mean-field analysis.

Bose–Hubbard models with photon pairing in circuit-QED

In this work, we study a family of bosonic lattice models that combine an on-site repulsion term with a nearest-neighbour pairing term, Like the original Bose–Hubbard model, the nearest-neighbour term is responsible for the mobility of bosons and it competes with the local interaction, inducing two-mode squeezing. However, unlike a trivial hopping, the counter-rotating terms form a pairing that cannot be studied with a simple mean-field theory and does not present a quantum phase transition in phase space. Instead, we show that there is a cross-over from a pure insulator to long-range correlations that start up as soon as the two-mode squeezing is switched on. We also show how this model can be naturally implemented using coupled microwave resonators and superconducting qubits.

Zero finite-temperature charge stiffness within the half-filled 1D Hubbard model

Even though the one-dimensional (1D) Hubbard model is solvable by the Bethe ansatz, at half-filling its finite-temperature T>0 transport properties remain poorly understood. In this paper we combine that solution with symmetry to show that within that prominent T=0 1D insulator the charge stiffness D(T) vanishes for T>0 and finite values of the on-site repulsion U in the thermodynamic limit. This result is exact and clarifies a long-standing open problem. It rules out that at half-filling the model is an ideal conductor in the thermodynamic limit. Whether at finite T and U>0 it is an ideal insulator or a normal resistor remains an open question. That at half-filling the charge stiffness is finite at U=0 and vanishes for U>0 is found to result from a general transition from a conductor to an insulator or resistor occurring at U=Uc=0 for all finite temperatures T>0. (At T=0 such a transition is the quantum metal to Mott–Hubbard-insulator transition.) The interplay of the η-spin SU(2) symmetry with the hidden U(1) symmetry beyond SO(4) is found to play a central role in the unusual finite-temperature charge transport properties of the 1D half-filled Hubbard model.

The Kohn-Luttinger mechanism and phase diagram of the superconducting state in the Shubin-Vonsovsky model

Using the Shubin-Vonsovsky model in the weak-coupling regime W > U > V (W is the bandwidth, U is the Hubbard onsite repulsion, and V is the Coulomb interaction at neighboring sites) based on the Kohn-Luttinger mechanism, we determined the regions of the existence of the superconducting phases with the d xy , p, s, and $d_{x^2 - y^2 } $ symmetry types of the order parameter. It is shown that the effective interaction in the Cooper channel considerably depends not only on single-site but also on intersite Coulomb correlations. This is demonstrated by the example of the qualitative change and complication of the phase diagram of the superconducting state. The superconducting (SC) phase induction mechanism is determined taking into account polarization contributions in the second-order perturbation theory in the Coulomb interaction. The results obtained for the angular dependence of the superconducting gap in different channels are compared with angule-resolved photoemission spectroscopy (ARPES) results. The influence of long-range hops in the phase diagram and critical superconducting transition temperature in different channels is analyzed. The conditions for the appearance of the Kohn-Luttinger superconductivity with the $d_{x^2 - y^2 } $ symmetry and high critical temperatures T c ∼ 100 K near the half-filling are determined.

Unconventional superconducting phases for the two-dimensional extended Hubbard model on a square lattice

We study the phase diagram of the extended Hubbard model on a two-dimensional square lattice, including on-site (U) and nearest-neighbor (V) interactions, at weak couplings. We show that the charge-density-wave phase that is known to occur at half-filling when 4V > U gives way to a d_{xy} -wave superconducting instability away from half-filling, when the Fermi surface is not perfectly nested, and for sufficiently large repulsive and a range of on-site repulsive interaction. In addition, when nesting is further suppressed and in presence of a nearest-neighbor attraction, a triplet time-reversal breaking (p_x + ip_y)-wave pairing instability emerges, competing with the d_{x2+y2} pairing state that is known to dominate at fillings just slightly away from half. At even smaller fillings, where the Fermi surface no longer presents any nesting, the (p_x +ip_y)-wave superconducting phase dominates in the whole regime of on-site repulsions and nearest-neighbor attractions, while d_{xy}-pairing occurs in the presence of on-site attraction. Our results suggest that zero-energy Majorana fermions can be realized on a square lattice in the presence of a magnetic field. For a system of cold fermionic atoms on a two-dimensional square optical lattice, both an on-site repulsion and a nearest-neighbor attraction would be required, in addition to rotation of the system to create vortices. We discuss possible ways of experimentally engineering the required interaction terms in a cold atom system.

Magnetic properties and Mott transition in the square-lattice Hubbard model with frustration

The magnetic properties and Mott transition of the Hubbard model on the square lattice with frustration are studied at half-filling and zero temperature by the variational cluster approximation. When the on-site repulsion $U$ is large, magnetically disordered state is realized in highly frustrated region between the N\'eel and collinear phases, and no imcommensurate magnetic states are found there. As for the Mott transition, in addition to the Mott gap and double occupancy, which clarify the nature of the transition, the structure of the self-energy in the spectral representation is studied in detail below and above the Mott transition point. The spectral structure of the self-energy is almost featureless in the metallic phase, but clear single dispersion, leading to the Mott gap, appears in the Mott insulator phase.

Theory of the APECS spectra of antiferromagnetic transition metal oxides

Angular resolved Auger-Photoelectron Coincidence Spectra (APECS) show a dichroic effect called DEAR-APECS in the antiferromagnetic phase of transition metal oxides and reveal well-defined structures in the Auger line shapes which are not seen otherwise in such partially filled bands. We propose a theory of the XPS and M23M45M45 APECS line shapes. Experimental photoemission and Auger spectra of CoO and NiO are compared with computed profiles. The method takes strong correlation into account, based on the exact diagonalization of octahedral cluster models with different electron numbers, including the on-site repulsion on the central ion expressed in terms of Racah parameters. The hopping parameters are written as combinations of Slater–Coster ones. We compute the relevant Auger matrix elements. The Racah A parameter and the hopping parameters which are known from the literature are refined by fitting the XPS lines; this allows for a parameter-free evaluation of the Auger lines. The Auger line shapes are explained in detail for both compounds, labeling the final states by their total spin. In the case of Co the different spin components peak at separated spectral regions and one sees a transfer of intensity to the high-spin region by varying the photoelectron-Auger electron geometry. In the NiO case the peaks overlap much more but a similar transfer from singlet to triplet final states is nevertheless unambiguously observed, and the theory accounts well for the observed resonance energies. Finally, we highlight the main questions about the dichroic effect that are still unanswered and will require a considerable extension of the theory.

Wave-packet dynamics in the one-dimensional extended Hubbard model

Using the time-dependent density-matrix renormalization group, we study the time evolution of electronic wave packets in the one-dimensional extended Hubbard model with on-site and nearest-neighbor repulsion, $U$ and $V$, respectively. As expected, the wave packets separate into spin-only and charge-only excitations (spin-charge separation). Charge and spin velocities exhibit nonmonotonic dependence on $V$. For small and intermediate values of $V$, both velocities increase with $V$. However, the charge velocity exhibits a stronger dependence than that of the spin, leading to a more pronounced spin-charge separation. Charge fractionalization, on the other hand, is weakly affected by $V$. The results are explained in terms of Luttinger liquid theory in the weak-coupling limit and an effective model in the strong-coupling regime.