On-site Repulsion Research Articles

Bad Metallic Transport in a Modified Hubbard Model

Strongly correlated metals often display anomalous transport, including T-linear resistivity above the Mott-Ioffe-Regel limit. We introduce a tractable microscopic model for bad metals, by restoring in the well-known Hubbard model-with hopping t and on-site repulsion U-a "screened Coulomb" interaction between charge densities that decays exponentially with spatial separation. This interaction lifts the extensive degeneracy in the spectrum of the t=0 Hubbard model, allowing us to fully characterize the small t electric, thermal, and thermoelectric transport in our strongly correlated model. Throughout the phase diagram we observe T-linear resistivity above the Mott-Ioffe-Regel limit, together with strong violation of the Wiedemann-Franz law and a large thermopower that can undergo sign change.

Coulomb problem in iron-based superconductors

We discuss the role of strong Coulomb interactions in iron-based superconductors (FeSCs). The presumed $s^{\pm}$ character of these superconductors means that the condensate is not symmetry protected against Coulomb repulsion. Remarkably, the transition temperatures and the excitation gap are quite robust across the large family of iron based superconductors, despite drastic changes in Fermi surface geometry. The Coulomb problem is to understand how these superconductors avoid the strong onsite Coulomb interaction at the iron atoms, while maintaining a robust transition temperature. Within the dominant space of $t_{2g}$ orbitals, on-site repulsion in the FeSCs enforces two linearly independent components of the condensate to vanish. This raises the possibility that iron-based superconductors might adapt their condensate to the Coulomb constraints by rotating the pairing state within the large manifold of entangled, extended s-wave gap functions with different orbital and momentum space structure. We examine this "orbital and k-space flexibility" (OKF) mechanism using both Landau theory and microscopic calculations within a multi-orbital t-J model. Based on our results, we conclude that OKF necessitates a large condensate degeneracy. One interesting possibility raised by our results, is that a resolution to the Coulomb problem in FeSC might require a reconsideration of triplet pairing.

The One-Dimensional Hubbard Model in the Limit of u ≫ t

We revisit the one-dimensional Hubbard model in the case of strong correlations, i.e. for on-site repulsion constant strongly greater than hopping constant u ≫ t, and assume that each atom has only a single relevant orbital. We present in detail the example of half-filled system with four atoms. We reconfirm that when the sites are almost independent atoms, i.e. in the atomic limit, the spin-spin coupling term appears, every site carries exactly one electron and hopping is suppressed. We compare the results with one-dimensional Heisenberg Hamiltonian using the translational and unitary symmetries, and separation of the spin and pseudo-spin degrees of freedom.

Emergence of topological Mott insulators in proximity of quadratic band touching points

Recently, the field of strongly correlated electrons has begun an intense search for a correlation induced topological insulating phase. An example is the quadratic band touching point which arises in a checkerboard lattice at half-filling, and in the presence of interactions gives rise to topological Mott insulators. In this work, we perform a mean-field theory computation to show that such a system shows instability to topological insulating phases even away from half-filling (chemical potential $\mu = 0 $). The interaction parameters consist of on-site repulsion ($ U $), nearest-neighbour repulsion ($ V $), and a next-nearest-neighbour correlated hopping ($ t_\text{c} $). The $t_\text{c}$ interaction originates from strong Coulomb repulsion. By tuning the values of these parameters, we obtain a desired topological phase that spans the area around $(V = 0 , \mu = 0)$, extending to regions with $(V>0,\mu=0)$ and $(V>0,\mu>0)$. This extends the realm of current experimental efforts to find these topological phases.

One-dimensional Hubbard-Holstein model with finite-range electron-phonon coupling

The Hubbard-Holstein model describes fermions on a discrete lattice, with on-site repulsion between fermions and a coupling to phonons that are localized on sites. Generally, at half-filling, increasing the coupling $g$ to the phonons drives the system towards a Peierls charge density wave state whereas increasing the electron-electron interaction $U$ drives the fermions into a Mott antiferromagnet. At low $g$ and $U$, or when doped, the system is metallic. In one-dimension, using quantum Monte Carlo simulations, we study the case where fermions have a long range coupling to phonons, with characteristic range $\xi$, interpolating between the Holstein and Fr\"ohlich limits. Without electron-electron interaction, the fermions adopt a Peierls state when the coupling to the phonons is strong enough. This state is destabilized by a small coupling range $\xi$, and leads to a collapse of the fermions, and, consequently, phase separation. Increasing interaction $U$ will drive any of these three phases (metallic, Peierls, phase separation) into a Mott insulator phase. The phase separation region is once again present in the $U \ne 0$ case, even for small values of the coupling range.

Band-Edge Quasiparticles from Electron-Phonon Coupling and Resistivity Saturation.

We address the problem of resistivity saturation observed in materials such as the A-15 compounds. To do so, we calculate the resistivity for the Hubbard-Holstein model in infinite spatial dimensions to second order in on-site repulsion U≤D and to first order in (dimensionless) electron-phonon coupling strength λ≤0.5, where D is the half bandwidth. We identify a unique mechanism to obtain two parallel quantum conducting channels: low-energy and band-edge high-energy quasi-particles. We identify the source of the hitherto unremarked high-energy quasiparticles as a positive slope in the frequency dependence of the real part of the electron self-energy. In the presence of phonons, the self-energy grows linearly with the temperature at high T, causing the resistivity to saturate. As U is increased, the saturation temperature is pushed to higher values, offering a mechanism by which electron correlations destroy saturation.

Eigenstate Distribution Fluctuation of a Quenched Disordered Bose–Hubbard System in Thermal-to-Localized Transitions**Supported by the National Natural Science Foundation of China under Grant No 11504021, and the Fundamental Research Funds for Central Universities of China under Grant No FRF-TP-17-023A2.

We study the thermalization of a quenched disordered Bose–Hubbard system. By considering the eigenstate distribution fluctuation, we show that the thermal to many-body localized transition is always connected to a minimum of this distribution fluctuation. We also observe a Mott-localized regime, where the system fails to thermalize due to the strong on-site repulsion. Lastly, we show how to detect this eigenstate distribution fluctuation in a cold atom system, which is equivalent to measure the Loschmidt echo of the system. Our work suggests a way to measure the thermal-to-localized transitions in experiments, especially for a large system.

Superconductivity arising from layer differentiation in multilayer cuprates

In order to theoretically identify the factors governing superconductivity in multi-layer cuprates, a three-layer Hubbard model is studied with the two-particle self-consistent (TPSC) approach so as to incorporate electron correlations. The linearized Eliashberg equation is then solved for the gap function in a matrix form to resolve the role of outer CuO$_2$ planes (OPs) and inner plane (IP). We show that OPs dominate IP in the $d_{x^{2}-y^{2}}$-wave superconductivity, while IP dominates in the antiferromagnetism. This comes from an electron correlation effect in that the correlation makes the doping rates different between OPs and IP (i.e., a self-doping effect), which occurs in intermediate and strong correlation regimes. Namely, the antiferromagnetic fluctuations in IP are stronger due to a stronger electron correlation, which simultaneously reduces the quasiparticle density of states in IP with a suppressed $d_{x^{2}-y^{2}}$-wave superconductivity. Intriguingly, while the off-diagonal (inter-layer) elements in the gap function matrix are tiny, {\it inter-layer pair scattering} processes are in fact at work in enhancing the superconducting transition temperature $T_{\text{c}}$ through the inter-layer Green's functions. This actually causes the trilayer system to have higher $T_{\text{c}}$ than the single-layer in a weak- and intermediate-coupling regimes. This picture holds for a range of the on-site Hubbard repulsion $U$ that contains those estimated for the cuprates. The present result is qualitatively consistent with nuclear magnetic resonance experiments in multi-layer cuprates superconductors.

Impenetrable SU(N) fermions in one-dimensional lattices

We study SU(N) fermions in the limit of infinite on-site repulsion between all species. We focus on states in which every pair of consecutive fermions carries a different spin flavor. Since the particle order cannot be changed (because of the infinite on-site repulsion) and contiguous fermions have a different spin flavor, we refer to the corresponding constrained model as the model of distinguishable quantum particles. We introduce an exact numerical method to calculate equilibrium one-body correlations of distinguishable quantum particles based on a mapping onto noninteracting spinless fermions. In contrast to most many-body systems in one dimension, which usually exhibit either power-law or exponential decay of off-diagonal one-body correlations with distance, distinguishable quantum particles exhibit a Gaussian decay of one-body correlations in the ground state, while finite-temperature correlations are well described by stretched exponential decay.

Fermi surface pockets in electron-doped iron superconductor by Lifshitz transition

The Fermi surface pockets that lie at the corner of the two-iron Brillouin zone in heavily electron-doped iron selenide superconductors are accounted for by an extended Hubbard model over the square lattice of iron atoms that includes the principal 3dxz and 3dyz orbitals. At half filling, and in the absence of intra-orbital next-nearest neighbor hopping, perfect nesting between electron-type and hole-type Fermi surfaces at the the center and at the corner of the one-iron Brillouin zone is revealed. It results in hidden magnetic order in the presence of magnetic frustration within mean field theory. An Eliashberg-type calculation that includes spin-fluctuation exchange finds that the Fermi surfaces undergo a Lifshitz transition to electron/hole Fermi surface pockets centered at the corner of the two-iron Brillouin zone as on-site repulsion grows strong. In agreement with angle-resolved photoemission spectroscopy on iron selenide high-temperature superconductors, only the two electron-type Fermi surface pockets remain after a rigid shift in energy of the renormalized band structure by strong enough electron doping. At the limit of strong on-site repulsion, a spin-wave analysis of the hidden-magnetic-order state finds a ‘floating ring’ of low-energy spin excitations centered at the checkerboard wavenumber . This prediction compares favorably with recent observations of low-energy spin resonances around (π, π) in intercalated iron selenide by inelastic neutron scattering.

Repulsion-attraction asymmetry in the Bose-Fermi-Hubbard model

It is shown that in the Bose-Fermi-Hubbard model, used for a description of the atomic boson-fermion mixture in the optical lattice, the fermion-hole symmetry allows one to establish a correspondence between cases of the on-site repulsion and attraction. Based on the phase diagrams, built with the help of a corresponding transformation of model parameters within the framework of the grand canonical ensemble, the conditions of the superfluid phase existence at the boson-fermion attraction are analyzed. The phase diagrams that illustrate the difference of behavior of the BF mixture in the cases of BF repulsion or attraction are obtained. A relation to the available experimental data is discussed.

Nonequivalent Spin Exchanges of the Hexagonal Spin Lattice Affecting the Low-Temperature Magnetic Properties of RInO3 (R = Gd, Tb, Dy): Importance of Spin-Orbit Coupling for Spin Exchanges between Rare-Earth Cations with Nonzero Orbital Moments.

Rare-earth indium oxides RInO3 (R = Gd, Tb, Dy) consist of spin-frustrated hexagonal spin lattices made up of rare-earth ions R3+, where R3+ = Gd3+ (f7, L = 0), Tb3+ (f8, L = 3), and Dy3+ (f9, L = 5). We carried out DFT calculations for RInO3, including on-site repulsion U with/without spin-orbit coupling (SOC), to explore if their low-temperature magnetic properties are related to the two nonequivalent nearest-neighbor (NN) spin exchanges of their hexagonal spin lattices. Our DFT + U + SOC calculations predict that the orbital moments of the Tb3+ and Dy3+ ions are smaller than their free-ion values by ∼2μB while the Tb3+ spins have an in-plane magnetic anisotropy, in agreement with the experiments. This suggests that the f orbitals of each R3+ (R = Tb, Dy) ion are engaged, though weakly, in bonding with the surrounding ligand atoms. The magnetic properties of GdInO3 with the zero orbital moment are adequately described by the spin exchanges extracted by DFT + U calculations. In describing the magnetic properties of TbInO3 and DyInO3 with nonzero orbital moments, however, the spin exchanges extracted by DFT + U + SOC calculations are necessary. The spin exchanges of RInO3 (R = Gd, Tb, Dy) are dominated by the two NN spin exchanges J1 and J2 of their hexagonal spin lattice, in which the honeycomb lattice of J2 forms spin-frustrated ( J1, J1, J2) triangles. The J2/ J1 ratios are calculated to be ∼3, ∼1.7, and ∼1 for GdInO3, TbInO3, and DyInO3, respectively. This suggests that the antiferromagnetic (AFM) ordering of GdInO3 below 1.8 K is most likely an AFM ordering of its honeycomb spin lattice and that TbInO3 would exhibit low-temperature magnetic properties similar to those of GdInO3 while DyInO3 would not.

Collective diffusion of dense adsorbate at surfaces of arbitrary geometry

A convenient variational formula for collective diffusion of many particles adsorbed at lattices of arbitrary geometry is formulated. The approach allows us to find the expressions for the diffusion coefficient for any value of the system’s coverage. It is assumed that particles interact via on-site repulsion excluding double site occupancy. It is shown that the method can be applied to various systems of different geometry. Examples of real systems such as GaAs with specific energetic landscapes are also presented. Diffusion of Ga adatoms on GaAs(0 0 1) surface reconstructed in two different symmetries is studied. It is shown how increasing Ga coverage changes the character of diffusion from isotropic 2D into highly anisotropic, almost 1D. It is shown how important the role of the inter-particle correlations is, which influences the value of the collective diffusion coefficient at higher coverages.

Absence of ballistic charge transport in the half-filled 1D Hubbard model

Whether in the thermodynamic limit of lattice length L→∞, hole concentration mηz=−2Sηz/L=1−ne→0, nonzero temperature T>0, and U/t>0 the charge stiffness of the 1D Hubbard model with first neighbor transfer integral t and on-site repulsion U is finite or vanishes and thus whether there is or there is no ballistic charge transport, respectively, remains an unsolved and controversial issue, as different approaches yield contradictory results. (Here Sηz=−(L−Ne)/2 is the η-spin projection and ne=Ne/L the electronic density.) In this paper we provide an upper bound on the charge stiffness and show that (similarly as at zero temperature), for T>0 and U/t>0 it vanishes for mηz→0 within the canonical ensemble in the thermodynamic limit L→∞. Moreover, we show that at high temperature T→∞ the charge stiffness vanishes as well within the grand-canonical ensemble for L→∞ and chemical potential μ→μu where (μ−μu)≥0 and 2μu is the Mott–Hubbard gap. The lack of charge ballistic transport indicates that charge transport at finite temperatures is dominated by a diffusive contribution. Our scheme uses a suitable exact representation of the electrons in terms of rotated electrons for which the numbers of singly occupied and doubly occupied lattice sites are good quantum numbers for U/t>0. In contrast to often less controllable numerical studies, the use of such a representation reveals the carriers that couple to the charge probes and provides useful physical information on the microscopic processes behind the exotic charge transport properties of the 1D electronic correlated system under study.

Nonlinear Pauli susceptibilities in Sr3Ru2O7 and universal features of itinerant metamagnetism

We report, for the first time, measurements of the third order, $\chi_3$ and fifth order, $\chi_5$, susceptibilities in an itinerant oxide metamagnet, Sr$_3$Ru$_2$O$_7$ for magnetic fields both parallel and perpendicular to the c-axis. These susceptibilities exhibit maxima in their temperature dependence such that $T_1 \approx 2T_3 \approx 4T_5$ where the $T_i$ are the position in temperature where a peak in the $i$-th order susceptibility occurs. These features taken together with the scaling of the critical field with the temperature $T_1$ observed in a diverse variety of itinerant metamagnets find a natural explanation in a single band model with one Van Hove singularity (VHS) and onsite repulsion $U$. The separation of the VHS from the Fermi energy $\Delta$, sets a single energy scale, which is the primary driver for the observed features of itinerant metamagnetism at low temperatures.

The dynamics of a polariton dimer in a disordered coupled array of cavities

We investigate the effect of disorder in the laser intensity on the dynamics of dark-state polaritons in an array of 20 cavities, each containing an ensemble of four-level atoms that is described by a Bose-Hubbard Hamiltonian. We examine the evolution of the polariton number in the cavities starting from a state with either one or two polaritons in one of the cavities. For the case of a single polariton without disorder in the laser intensity, we calculate the wavefunction of the polariton and find that it disperses away from the initial cavity with time. The addition of disorder results in minimal suppression of the dispersal of the wavefunction. In the case of two polaritons with an on-site repulsion to hopping strength ratio of 20, we find that the polaritons form a repulsively bound state or dimer. Without disorder the dimer wavefunction disperses similarly to the single polariton wavefunction but over a longer time period. The addition of sufficiently strong disorder results in localization of the polariton dimer. The localization length is found to be described by a power law with exponent -1.31. We also find that we can localise the dimer at any given time by switching on the disorder.

Diagrammatic Monte Carlo procedure for the spin-charge transformed Hubbard model

Using a dual representation of lattice fermion models that is based on spin-charge transformation and fermionisation of the original description, I derive an algorithm for diagrammatic Monte Carlo simulation of strongly correlated systems. This scheme allows eliminating large expansion parameters, as well as large corrections to the density matrix that generally prevent diagrammatic methods from being efficient in this regime. As an example, I compute the filling factor for the Hubbard model at infinite onsite repulsion and compare the results to controllable data obtained from Numerical Linked Cluster Expansion. I find excellent agreement between the two methods, as well as rapid convergence of the diagrammatic series. I also report results for the momentum distribution and kinetic energy of the electrons.

Superconductivity in correlated BEDT-TTF molecular conductors: Critical temperatures and gap symmetries

Starting from an {\it ab initio}-derived two-site dimer Hubbard hamiltonian on a triangular lattice, we calculate the superconducting gap functions and critical temperatures for representative $\kappa$-(BEDT-TTF)$_2$X superconductors by solving the linearized Eliashberg equation using the Two-Particle Self-Consistent approach (TPSC) extended to multi-site problems. Such an extension allows for the inclusion of molecule degrees of freedom in the description of these systems. We present both, benchmarking results for the half-filled dimer model as well as detailed investigations for the 3/4-filled molecule model. Remarkably, we find in the latter model that the phase boundary between the two most competing gap symmetries discussed in the context of these materials -d$_{xy}$ and the recently proposed eight-node gap s+d$_{x^2-y^2}$ symmetry- is located within the regime of realistic model parameters and is especially sensitive to the degree of in-plane anisotropy in the materials as well as to the value of the on-site Hubbard repulsion. We show that these results provide a more complete and accurate description of the superconducting properties of $\kappa$-(BEDT-TTF)$_2$X than previous Random Phase Approximation (RPA) calculations and, in particular, we discuss predicted critical temperatures in comparison to experiments. Finally, our findings suggest that it may be even easier to experimentally switch between the two pairing symmetries as previously anticipated by invoking pressure, chemical doping or disorder effects.

Ferromagnetism in the Hubbard Model with a Gapless Nearly-Flat Band

We present a version of the Hubbard model with a gapless nearly-flat lowest band which exhibits ferromagnetism in two or more dimensions. The model is defined on a lattice obtained by placing a site on each edge of the hypercubic lattice, and electron hopping is assumed to be only between nearest and next nearest neighbor sites. The lattice, where all the sites are identical, is simple, and the corresponding single-electron band structure, where two cosine-type bands touch without an energy gap, is also simple. We prove that the ground state of the model is unique and ferromagnetic at half-filling of the lower band, if the lower band is nearly flat and the strength of on-site repulsion is larger than a certain value which is independent of the lattice size. This is the first example of ferromagnetism in three dimensional non-singular models with a gapless band structure.

Magnetism of a four-center transition-metal cluster revisited

We propose a surprisingly efficient procedure to map a sophisticated treatment of electronic correlations to a few-parameter model Hamiltonian. By pushing first-principles coupled-cluster methods to the limit we get a lucid picture of the electronic excitations responsible for the magnetic interactions in a paradigm ${\mathrm{Ni}}_{4}$ cluster. Using an extended Hubbard model, we demonstrate that the magnetism in this system cannot be explained solely on the basis of spin models but additionally requires consideration of the indirect mechanism involving hopping and on-site repulsion. We present a protocol to extract the corresponding parameters from experiment or calculations.