On-site Repulsion Research Articles

Structure-dependent metal–insulator transition in one-dimensional Hubbard superlattice**Project supported by the National Natural Science Foundation of China (Grant Nos. 50573059 and 10874132).

We investigate the charge and spin gaps, and the spin structure in half-filled one-dimensional Hubbard superlattices with one repulsive site and L0 free sites per unit cell. For odd L0, it is correlated metal at the particle–hole symmetric point, and then turns into band insulator beyond this point. For even L0, the system has a Mott insulator phase around the particle–hole symmetric point and undergoes a metal–insulator transition with on-site repulsion U increasing. For large U, there exists a multiperiodic spin structure, which results from the ferromagnetic (antiferromagnetic) correlation between the nearest neighboring repulsive sites for odd (even) L0.

Trimer superfluid and supersolid on two-dimensional optical lattices

By the photoassociation method, the trimer superfluid phase disappears in the one dimensional state-dependent optical lattice if the ratio of the three-body interaction $W$ to the trimer tunneling $J$is kept at $W/J=12$ [Phys Rev A. {\bf 90}, 033622(2014)]. To search for a trimer superfluid and trimer supersolid, we load the cold atom into two-dimensional lattices, whose coordinate number $z$ and kinetic energy $-zJ$ are respectively larger and lower than those of a one dimensional lattice. Herein, we study the Bose-Hubbard model, which has an additional trimer tunneling term, a three-body interaction and a next-nearest repulsion. The on-site trimer and trimer superfluid exist if the on-site two-body repulsion and three-body repulsion are smaller than some thresholds. With atom-tunneling terms, the phase transitions from trimer superfluid phase to both atom superfluid and atom supersolid phases are first order. With $W/J=12$, in a one dimensional lattice, the trimer superfluid phase does not exist at all. In contrast, the trimer superfluid phase, exists in the lower density regions $0 \textless \rho \textless2$ on the square lattice if $J$ is not very large. The trimer superfluid phase emerges in a wider range $0 \textless \rho \textless3$ in the triangular lattice, or in the cubic lattice ($z=6$). When the three-body interaction is turned on, a trimer supersolid phase emerges due to the classical degeneracy between the quasi trimer solid and the trimer solid being broken by the quantum fluctuation. The phase transitions from the trimer supersolid phase to quasi trimer solid are first order and the phase transition from the trimer supersolid phase to trimer solid is continuous. Our results, obtained by mean-field and quantum Monte Carlo methods, will be helpful in realizing the trimer superfluid and supersolid by cold atom experiments.

How can multielectron transfer be realized? A case study with keggin-type polyoxometalates in acetonitrile.

Theoretical consideration and computational simulation have been performed on the voltammetric properties of Keggin polyoxometalates (POMs), and the conversion from successive one-electron transfer in unacidified media to four-electron transfer (through two-electron transfer) in acidified media has been discussed. Perfect simulation of the cyclic voltammograms of POMs could be achieved using the standard formal potentials and the protonation constants, systematically evaluated by the equations, in which “simple (intrinsic)” and “synergistic (extrinsic)” electron-withdrawing effects of the μ4-oxygen were taken into consideration. In the proposed model, the formal potential of the one-electron redox waves for the ith reduction step is presented by Ei°(z0, s) = Ei** + 0.51(z0 – i + 1) + 1.067s (i = 1, 2, 3, 4; E1** = E2** = 0.577 V; E3** = E4** = 0.377 V), where z0 is the initial ionic charge of a Keggin POM and s is the mean bond valence of the μ4-O–W bonds in the POM. The values of Ei**s are related to the energy levels of the two lowest unoccupied molecular orbitals (LUMOs) of a hypothetical Keggin POM with null charge and null bond valence. Then it was revealed that the LUMOs have small on-site repulsion, which may be an important factor that makes multielectron transfer feasible. These findings would give a big clue in developing novel redox materials exhibiting multielectron transfers.

Size and shape of Mott regions for fermionic atoms in a two-dimensional optical lattice

We investigate the harmonic-trap control of the size and shape of Mott regions in the Fermi-Hubbard model on a square optical lattice. The use of Lanczos diagonalization on clusters with twisted boundary conditions, followed by an average over 50--80 samples, drastically reduces finite-size effects in some ground-state properties; calculations in the grand-canonical ensemble together with a local-density approximation allow us to simulate the radial density distribution. We have found that as the trap closes, the atomic cloud goes from a metallic state to a Mott core and to a Mott ring; the coverage of Mott atoms reaches a maximum at the core-ring transition. A ``phase diagram'' in terms of an effective density and of the on-site repulsion is proposed as a guide to maximize the Mott coverage. We also predict that the usual experimentally accessible quantities, the global compressibility and the average double occupancy (rather, its density derivative), display detectable signatures of the core-ring transition. Some spin-correlation functions are also calculated and predict the existence N\'eel-like ordering within Mott cores and rings.

Fractional quantum Hall states of dipolar gases in Chern bands

We study fermions and hard-core bosons with long-range dipolar interactions at fractional fillings in a topological checkerboard lattice with short-range hoppings up to next-next-nearest neighbors [T. Neupert, L. Santos, C. Chamon, and C. Mudry, Phys. Rev. Lett. 106, 236804 (2011)]. We consider the case that the dipoles are aligned in the perpendicular direction by an external field without the complication of anisotropic interaction. Using exact diagonalization, we find clear signatures of fractional quantum Hall (FQH) states at filling factors 1/3 and 1/5 for fermions (1/2 and 1/4 for bosons) in the lowest Chern band with a robust spectrum gap at moderate dipolar interaction strength. The robustness of these FQH states against a long-range interaction tail and band flatness is investigated. When the dipolar interaction decreases, the fermionic FQH states turn into normal states, and the bosonic 1/4 FQH state turns into a superfluid state. The bosonic 1/2 FQH state survives even in the absence of the dipolar interaction, but vanishes when the hard core becomes a soft core with a critical on-site repulsion. In the thin torus limit, the static density structure factors indicate that the FQH state turns into a commensurate charge density wave state.

Evolution of dimerized phase in a one-dimensional correlated electron system

The one-dimensional half-filled correlated electron system with on-site (U), nearest-neighbor (V) and pair hopping (Y) repulsions is studied analytically at weak coupling, combined the Abelian bosonization with renormalization group methods. The corresponding ground-state phase diagram consists of three insulating phases, a charge-density-wave (CDW) phase for U − 2V 2Y, and a bond-charge-density-wave (BOW) phase for | U − 2V | < 2Y. The pair hopping, which breaks an accident symmetry and splits the frustrating line U − 2V = 0, provides a possibility for the dimerized BOW phase between the CDW and SDW phases. In the phenomenological parameter regime, the superconducting (SC) and bond-spin-density-wave (BSDW) phases are briefly discussed.

Valence fluctuations in a lattice of magnetic molecules: Application to iron(II) phtalocyanine molecules on Au(111)

We study theoretically a square lattice of the organometallic Kondo adsorbate iron(II) phtalocyanine (FePc) deposited on top of Au(111), motivated by recent scanning tunneling microscopy experiments. We describe the system by means of an effective Hubbard-Anderson model, where each molecule has degenerate effective d-orbitals with xz and yz symmetry, which we solve for arbitrary occupation and arbitrary on-site repulsion U. To that end, we introduce a generalized slave-boson mean-field approximation (SBMFA) which correctly describes both the non-interacting limit (NIL) U = 0 and the strongly interacting limit , where our formalism reproduces the correct value of the Kondo temperature for an isolated FePc molecule. Our results indicate that while the isolated molecule can be described by an SU(4) Anderson model in the Kondo regime, the case of the square lattice corresponds to the intermediate-valence regime, with a total occupation of nearly 1.65 holes in the FePc molecular orbitals. Our results have important implications for the physical interpretation of the experiment.

The Bose–Hubbard model with squeezed dissipation

The stationary properties of the Bose–Hubbard model under squeezed dissipation are investigated. The dissipative model does not possess a symmetry but conserves parity. We find that always holds, so no symmetry breaking occurs. Without the onsite repulsion, the linear case is known to be critical. At the critical point the system freezes to an EPR state with infinite two mode entanglement. We show here that the correlations are rapidly destroyed whenever the repulsion is switched on. As we increase the latter, the system approaches a thermal state with an effective temperature defined in terms of the squeezing parameter in the dissipators. We characterize this transition by means of a Gutzwiller ansatz and the Gaussian Hartree–Fock–Bogoliubov approximation.

Impurity-induced magnetic moments on the graphene-lattice Hubbard model: An inhomogeneous cluster dynamical mean-field theory study

Defect-induced magnetic moments are at the center of the research effort on spintronic applications of graphene. Here, we study the problem of a nonmagnetic impurity in graphene with a new theoretical method, inhomogeneous cluster dynamical mean-field theory (I-CDMFT), which takes into account interaction-induced short-range correlations while allowing long-range inhomogeneities. The system is described by a Hubbard model on the honeycomb lattice. The impurity is modeled by a local potential. For a large enough potential, interactions induce local antiferromagnetic correlations around the impurity and a net total spin $\frac{1}{2}$ appears, in agreement with Lieb's theorem. Bound states caused by the impurity are visible in the local density of states (LDOS) and have their energies shifted by interactions in a spin-dependent way, leading to the antiferromagnetic correlations. Our results take into account dynamical correlations; nevertheless they qualitatively agree with previous mean-field and density functional theory (DFT) studies. Moreover, they provide a relation between impurity potential and on-site repulsion $U$ that could in principle be used to determine experimentally the value of $U$.

Enhancement of spin polarization induced by Coulomb on-site repulsion between localized pz electrons in graphene embedded with line defects.

It is well known that the effect of Coulomb on-site repulsion can significantly alter the physical properties of the systems that contain localized d and/or f electrons. However, little attention has been paid to the Coulomb on-site repulsion between localized p electrons. In this study, we demonstrated that Coulomb on-site repulsion between localized pz electrons also plays an important role in graphene embedded with line defects. It is shown that the magnetism of the system largely depends on the choice of the effective Coulomb on-site parameter Ueff. Ueff at the edges of the defect enhances the exchange splitting, which increases the magnetic moment and stabilizes a ferromagnetic state of the system. In contrast, Ueff at the center of the defect weakens the spin polarization of the system. The behavior of the magnetism is explained with the Stoner criterion and the charge accumulation at the edges of the defect. Based on the linear response approach, we estimate reasonable values of Ueff to be 2.55 eV (2.3 eV) at the center (edges) of the defects. More importantly, using a DFT+U+J method, we find that exchange interactions between localized p electrons also play an important role in the spin polarization of the system. These results imply that Coulomb on-site repulsion is necessary to describe the strong interaction between localized pz electrons of carbon related materials.

Exact Solutions of an Extended Bose-Hubbard Model with E 2 Symmetry

An extended Bose-Hubbard (BH) model with number-dependent multi-site and infinite-range hopping is proposed, which, similar to the original BH model, describes a phase transition between the delocalized superfluid (SF) phase and localized Mott insulator (MI) phase. It is shown that this extended model with local Euclidean E 2 symmetry is exactly solvable when on-site local potentials are included, while the model without local potentials is quasi-exactly solvable, which means only a part of the excited states including the ground state being exactly solvable. As applications of the exact solution for the ground state, phase diagram of the model in 1D without local potential and on-site disorder for filling factor ρ = 1 with M = 6, M = 10, and M = 14 sites are obtained. The ground state probabilities to detect n particles on a single site, P n , for n = 0, 1, 2 as functions of the control parameter U/t in these cases are also calculated. It is shown that the critical point in P n and in the entanglement measure is away from that of the SF-MI transition determined in the phase analysis. It is also shown that the model-independent entanglement measure is related with P n , which, therefore, may be practically useful because P n is measurable experimentally. The ground state expectation value of local particle numbers, the ground state local particle number fluctuations, the ground state probabilities to detect n particles on every site, and the entanglement measure have also been studied in the model for N = M = 4 with the two-body onsite repulsion and a local confining harmonic potential. The connection between these quantities and the entanglement observed previously is verified.

Magnetism of theFe2+andCe3+sublattices inCe2O2FeSe2: A combined neutron powder diffraction, inelastic neutron scattering, and density functional study

The discovery of superconductivity in the 122 iron selenide materials above 30 K necessitates an understanding of the underlying magnetic interactions. We present a combined experimental and theoretical investigation of magnetic and semiconducting ${\mathrm{Ce}}_{2}{\mathrm{O}}_{2}{\mathrm{FeSe}}_{2}$ composed of chains of edge-linked iron selenide tetrahedra. The combined neutron diffraction and inelastic scattering study and density functional calculations confirm the ferromagnetic nature of nearest-neighbor Fe-Se-Fe interactions in the ZrCuSiAs-related iron oxyselenide ${\mathrm{Ce}}_{2}{\mathrm{O}}_{2}{\mathrm{FeSe}}_{2}$. Inelastic measurements provide an estimate of the strength of nearest-neighbor Fe-Fe and Fe-Ce interactions. These are consistent with density functional theory calculations, which reveal that correlations in the Fe-Se sheets of ${\mathrm{Ce}}_{2}{\mathrm{O}}_{2}{\mathrm{FeSe}}_{2}$ are weak. The Fe on-site repulsion ${U}_{Fe}$ is comparable to that reported for oxyarsenides and ${\mathrm{K}}_{1\ensuremath{-}x}{\mathrm{Fe}}_{2\ensuremath{-}y}{\mathrm{Se}}_{2}$, which are parents to iron-based superconductors.

Benchmarking the DFT+U Method for Thermochemical Calculations of Uranium Molecular Compounds and Solids

Ability to perform a feasible and reliable computation of thermochemical properties of chemically complex actinide-bearing materials would be of great importance for nuclear engineering. Unfortunately, density functional theory (DFT), which on many instances is the only affordable ab initio method, often fails for actinides. Among various shortcomings, it leads to the wrong estimate of enthalpies of reactions between actinide-bearing compounds, putting the applicability of the DFT approach to the modeling of thermochemical properties of actinide-bearing materials into question. Here we test the performance of DFT+U method--a computationally affordable extension of DFT that explicitly accounts for the correlations between f-electrons - for prediction of the thermochemical properties of simple uranium-bearing molecular compounds and solids. We demonstrate that the DFT+U approach significantly improves the description of reaction enthalpies for the uranium-bearing gas-phase molecular compounds and solids and the deviations from the experimental values are comparable to those obtained with much more computationally demanding methods. Good results are obtained with the Hubbard U parameter values derived using the linear response method of Cococcioni and de Gironcoli. We found that the value of Coulomb on-site repulsion, represented by the Hubbard U parameter, strongly depends on the oxidation state of uranium atom. Last, but not least, we demonstrate that the thermochemistry data can be successfully used to estimate the value of the Hubbard U parameter needed for DFT+U calculations.

Quantum bright solitons in the Bose-Hubbard model with site-dependent repulsive interactions

We introduce a one-dimensional (1D) spatially inhomogeneous Bose-Hubbard model (BHM) with the strength of the onsite repulsive interactions growing, with the discrete coordinate $z_{j}$, as $|z_{j}|^{\alpha }$ with $\alpha >0$. Recently, the analysis of the mean-field (MF) counterpart of this system has demonstrated self-trapping of robust unstaggered discrete solitons, under condition $\alpha >1$. Using the numerically implemented method of the density matrix renormalization group (DMRG), we demonstrate that, in a certain range of interaction, the BHM also self-traps, in the ground state, into a soliton-like configuration, at $\alpha >1$, and remains weakly localized at $\alpha <1$. An essential quantum feature is a residual density in the background surrounding the soliton-like peak in the BHM ground state, while in the MF limit the finite-density background is absent. Very strong onsite repulsion eventually destroys soliton-like states, and, for integer densities, the system enters the Mott phase with a spatially uniform density

Chiral symmetry breaking and the quantum Hall effect in monolayer graphene

Monolayer graphene in a strong magnetic field exhibits quantum Hall states at filling fractions $\nu = 0$ and $\nu = \pm 1$ that are not explained within a picture of noninteracting electrons. We propose that these states arise from interaction-induced chiral symmetry-breaking orders. We argue that when the chemical potential is at the Dirac point, weak on-site repulsion supports an easy-plane antiferromagnet state, which simultaneously gives rise to ferromagnetism oriented parallel to the magnetic field direction, whereas for $|\nu|=1$ easy-axis antiferromagnet and charge-density-wave orders coexist. We perform self-consistent calculations of the magnetic field dependence of the activation gap for the $\nu = 0$ and $|\nu| = 1$ states and obtain excellent agreement with recent experimental results. Implications of our study for fractional Hall states in monolayer graphene are highlighted.

Ground-state phase diagram of the half-filled bilayer Hubbard model

Employing a combination of functional renormalization group calculations and projective determinantal quantum Monte Carlo simulations, we examine the Hubbard model on the square lattice bilayer at half filling. From this combined analysis, we obtain a comprehensive account on the ground state phase diagram with respect to the extent of the system's metallic and (antiferromagnetically ordered) Mott-insulating as well as band-insulating regions. By means of an unbiased functional renormalization group approach, we exhibit the antiferromagnetic Mott-insulating state as the relevant instability of the free metallic state, induced by any weak finite onsite repulsion. Upon performing a careful analysis of the quantum Monte Carlo data, we resolve the difficulty of identifying this antiferromagnetic ground state for finite interlayer hopping in the weak-coupling regime, where nonmonotonous finite-size corrections are shown to relate to the two-sheeted Fermi surface structure of the metallic phase. On the other hand, quantum Monte Carlo simulations are well suited to identify the transition between the Mott-insulating phase and the band insulator in the intermediate-to-strong coupling regime. Here, we compare our numerical findings to indications for the transition region obtained from the functional renormalization group procedure.

Resonating-Valence-Bond Liquid in Low Dimensions

The Hubbard model in $D$ dimensions, with the on-site repulsion $U$ and the transfer integral between nearest neighbors $-t/\sqrt{D}$, is studied on the basis of the Kondo-lattice theory. If $U/|t| \gg 1$, $|n - 1| \lesssim |t|/(DU)$, where $n$ is the number of electrons per unit cell, and $D$ is so small that $|J|/D \gg k_{\rm B}T_c$, where $J = -4t^2/U$ and $T_c$ is $0 {\rm K}$ for $D = 1$ and is the highest critical temperature among possible ones for $D \ge 2$, a low-$T$ phase where $T_c < T \ll |J|/(k_{\rm B}D)$ is a frustrated electron liquid. Since the liquid is stabilized by the Kondo effect in conjunction with the resonating-valence-bond (RVB) mechanism, it is simply the RVB electron liquid; in one dimension, it is also the Tomonaga-Luttinger liquid. The Kondo energy of the RVB liquid is $k_{\rm B}T_{\rm K} = O(|J|/D)$; its effective Fermi energy is $O(k_{\rm B}T_{\rm K})$. A midband appears on the chemical potential between the upper and lower Hubbard bands; the Hubbard gap is a pseudogap. As regards the density of states per unit cell of the midband, its bandwidth is $O(k_{\rm B}T_{\rm K})$ or $O(|J|/D)$, its peak height is $O(1/U)$, and its spectral weight is $O[t^2/(DU^2)]$. Since the midband almost disappears in the Heisenberg limit, the RVB electron liquid in the Heisenberg limit is simply the RVB spin liquid. The RVB electron and spin liquids adiabatically continue to each other. Since local moments form in a high-$T$ phase where $T \gtrsim T_{\rm K}$, the high-$T$ phase is simply the Mott insulator.

Phase transition of light in circuit-QED lattices coupled to nitrogen-vacancy centers in diamond

We propose a hybrid quantum architecture for engineering a photonic Mott insulator-superfluid phase transition in a two-dimensional (2D) square lattice of a superconducting transmission line resonator (TLR) coupled to a single nitrogen-vacancy (NV) center encircled by a persistent current qubit. The localization-delocalization transition results from the interplay between the on-site repulsion and the nonlocal tunneling. The phase boundary in the case of photon hopping with real-valued and complex-valued amplitudes can be obtained using the mean-field approach. Also, the quantum jump technique is employed to describe the phase diagram when the dissipative effects are considered. The unique feature of our architecture is the good tunability of effective on-site repulsion and photon-hopping rate, and the local statistical property of TLRs which can be analyzed readily using present microwave techniques. Our work opens new perspectives in quantum simulation of condensed-matter and many-body physics using a hybrid spin circuit-QED system. The experimental challenges are realizable using currently available technologies.

Variational description of the ground state of the repulsive two-dimensional Hubbard model in terms of nonorthogonal symmetry-projected Slater determinants

The few determinant (FED) methodology, introduced in our previous works for 1D lattices, is here adapted for the repulsive two-dimensional Hubbard model at half-filling and with finite doping fractions. Within this configuration mixing scheme, a given ground state with well defined spin and space group quantum numbers, is expanded in terms of a nonorthogonal symmetry-projected basis determined through chains of variation-after projection calculations. The results obtained for the ground state and correlation energies of half-filled and doped 4$\times$4, 6$\times$6, 8$\times$8, and 10$\times$10 lattices, as well as momentum distributions and spin-spin correlation functions in small lattices, compare well with those obtained using other state-of-the-art approximations. The structure of the intrinsic determinants resulting from the variational strategy is interpreted in terms of defects that encode information on the basic units of quantum fluctuations in the considered 2D systems. The varying nature of the underlying quantum fluctuations, reflected in a transition to a stripe regime for increasing onsite repulsions, is discussed using the intrinsic determinants belonging to a 16$\times$4 lattice with 56 electrons. Such a transition is further illustrated by computing spin-spin and charge-charge correlation functions with the corresponding multireference FED wave functions. In good agreement with previous studies, the analysis of the pairing correlation functions reveals a weak enhancement of the extended $s$-wave and d$_{x^2-y^2}$ pairing modes. Given the quality of results here reported together with those previously obtained for 1D lattices and the parallelization properties of the FED scheme, we believe that symmetry projection techniques are very well suited for building ground state wave functions of correlated electronic systems, regardless of their dimensionality.

Zeeman-field-induced nontrivial topology in a spin-orbit-coupled superconductor

The hope to realize Majorana fermions at the vortex core of a two-dimensional topological superconductor has led to a variety of proposals for devices which exhibit topological superconductivity. Many of these include superconductivity through the proximity effect and therefore require a layer of a conventional superconductor deposited on top of another system, which lends its topological properties. The necessity of the superconducting layer poses some technical complications and, in particular, makes it harder to probe the Majorana state. In this work we propose to replace the proximity effect pairing by an innate tendency for pairing, mediated by interactions. We use a model system with spin-orbit coupling and on-site repulsion and apply renormalization group to the interaction vertex. Without a Zeeman field this model exhibits pairing instabilities in different channels depending on the tuning of parameters. Once a Zeeman field is introduced the model favors topological superconductivity where the order parameter winds an odd number of times around the Fermi surface. This suggests that certain superconductors, with strong spin-orbit coupling, may go through a topological phase transition as a function of applied magnetic field.