The SU(N) Hubbard model is a natural extension of the SU(2) model. However, even the N=3 case remains poorly understood. We report a substantially new ground-state phase diagram of the square lattice SU(3) Fermi-Hubbard model. Using a backflow ansatz, we identify strong signatures of a Mott transition and a subsequent magnetic transition, and the suppression of a previously predicted magnetic phase. We study the hole-doped model, identifying a transition from magnetic to paramagnetic behavior in the strong-coupling regime. Our findings offer a qualitatively new ground state picture. More broadly, our work suggests a path to study general SU(N) Hubbard models with arbitrary filling and geometry.
The magnetic properties of the t-t' Hubbard Model in the two dimensional square lattice are studied within an unrestricted Hartree-Fock approximation in real space. The interplay between antiferromagnetism, ferromagnetism, phase separation and inhomogeneous magnetic textures is studied. It is shown that, at sufficiently large values of t'/t, a rich fenomenology is to be expected between the antiferromagnetic phase at half filling and the ferromagnetic phase a lower fillings.
We analyze the competition of magnetism and superconductivity in the two-dimensional Hubbard model with a moderate interaction strength, including the possibility of incommensurate spiral magnetic order. Using an unbiased renormalization group approach, we compute magnetic and superconducting order parameters in the ground state. In addition to previously established regions of Neel order coexisting with d-wave superconductivity, the calculations reveal further coexistence regions where superconductivity is accompanied by incommensurate magnetic order.
In order to study an interplay of disorder, correlation, and spin imbalance on antiferromagnetism, we systematically explore the ground state of one-dimensional spin-imbalanced Anderson-Hubbard model by using the density-matrix renormalization group method. We find that disorders localize the antiferromagnetic spin density wave induced by imbalanced fermions and the increase of the disorder magnitude shrinks the areas of the localized antiferromagnetized regions. Moreover, the antiferromagnetism finally disappears above a large disorder. These behaviors are observable in atomic Fermi gases loa…
We discuss the ground state magnetic phase diagram of the Hubbard model off half filling within the dynamical mean-field theory. The effective single-impurity Anderson model is solved by Wilson's numerical renormalization group calculations, adapted to symmetry broken phases. We find a phase separated, antiferromagnetic state up to a critical doping for small and intermediate values of U, but could not stabilise a Neel state for large U and finite doping. At very large U, the phase diagram exhibits an island with a ferromagnetic ground state. Spectral properties in the ordered phases are discu…
We propose a new treatment of the Hubbard model that is based both on the coherent-potential approximation (CPA) and the virtual-crystal approximation (VCA). It is well known that the equilibrium found using the one-particle CPA Green's functions does not predict an ordered magnetic ground state, while Stoner's mean-field treatment, which is equivalent to the VCA on the Hubbard model, does so for a wide range of parameters. A hybrid treatment, the tau-CPA, is developed, in which a particle is assumed to be scattered from an array of static opposite spins for a time tau related to the inverse o…
By means of dynamical mean-field theory allowing for complete account of SU(2) rotational symmetry of interactions between spin-1/2 particles, we observe a strong effect of suppression of ferromagnetic order in the multiorbital Fermi-Hubbard model in comparison with a widely used restriction to density-density interactions. In the case of orbital degeneracy, we show that the suppression effect is the strongest in the two-orbital model (with effective spin $S_{\rm eff}=1$) and significantly decreases when considering three orbitals ($S_{\rm eff}=3/2$), thus magnetic ordering can effectively rev…
We study a two-dimensional Hubbard-Holstein model with phonons treated in the adiabatic limit. A Hartree-Fock decomposition is employed for the Hubbard term. A range of electronic densities are discussed with special emphasis on the quarter-filling ($n=0.5$). We argue that the quarter-filled system is relevant for the electronic properties observed at the interface between LaAlO$_3$ and SrTiO$_3$, where half-electron per unit cell is transferred to the TiO$_2$ layer as a consequence of the polar discontinuity at the interface. In addition to presenting the overall phase diagrams, we identify a…
Magnetic properties of two and three-dimensional clusters of quantum dots are studied with exact diagonalization of a generalized Hubbard model. We study the weak coupling limit, where the electrons interact only within a quantum dot and consider cases where the second or third harmonic oscillator shell is partially filled. The results show that in the case of half-filled shell the magnetism is determined by the antiferromagnetic Heisenberg model with spin 1/2, 1 or 3/2, depending on the number of electrons in the open shell. For other fillings the system in most cases favors a large total spi…
We examine the nature of the transition to the antiferromagnetically ordered state in the half-filled three-dimensional Hubbard model using the dual-fermion multiscale approach. Consistent with analytics, in the weak-coupling regime we find that spin-flip excitations across the Fermi surface are important, and that the strong coupling regime is described by Heisenberg physics. In the intermediate interaction, strong correlation regime we find aspects of both local and non-local correlations. We analyze the critical exponents of the transition in the strong coupling regime and find them to be c…
The t-t' Hubbard model for the Fermi level near the Van Hove singularity is considered within the renormalization group and parquet approaches. The interplay of ferromagnetic, antiferromagnetic, and superconducting channels is investigated, and the phase diagram of the model is constructed. In comparison with previous approaches, the account of ferromagnetic fluctuations suppresses superconducting pairing and, vice versa, the influence of the Cooper channel decreases the Curie temperature, so that the Stoner criterion is inapplicable even qualitatively.
We use synchrotron x-ray diffraction and electrical transport under pressure to probe both the magnetism and the structure of single crystal NiS2 across its Mott-Hubbard transition. In the insulator, the low-temperature antiferromagnetic order results from superexchange among correlated electrons and couples to a (1/2, 1/2, 1/2) superlattice distortion. Applying pressure suppresses the insulating state, but enhances the magnetism as the superexchange increases with decreasing lattice constant. By comparing our results under pressure to previous studies of doped crystals we show that this depen…
We study magnetic, transport and thermodynamic properties of the half-filled two-dimensional ($2D$) Hubbard model with layered distributed repulsive interactions using unbiased finite temperature quantum Monte Carlo simulations. Antiferromagnetic long-ranged correlations at $T=0$ are confirmed by means of the magnetic structure factor and the onset of short-ranged ones is at a minimum temperature which can be obtained by peaks in susceptibility and specific heat following an RPA prediction. We also show that transport is affected in the large interaction limit and is enhanced in the non-repuls…
We briefly overview the importance of Hubbard and Anderson-lattice models as applied to explanation of high-temperature and heavy-fermion superconductivity. Application of the models during the last two decades provided an explanation of the paired states in correlated fermion systems and thus extended essentially their earlier usage to the description of itinerant magnetism, fluctuating valence, and the metal-insulator transition. In second part, we also present some of the new results concerning the unconventional superconductivity and obtained very recently in our group. A comparison with e…
We show that evolution of magnetic properties in FeS under pressure cannot be explained only in terms of a spin state transition. While uniform compression does show substantial suppression of the local magnetic moment and increase of the weights of configurations with low spin, analysis of the local spin-spin correlation function demonstrates increase of the spin itinerancy. This is related to a strong modification of the electronic structure under pressure: in the high-pressure phase FeS is in the Fermi-liquid state, while decrease of the pressure moves the system to an orbital-selective reg…
The interplay between magnetic and superconducting states on a square lattice is studied using the extended Hubbard model, which takes into account the attraction of electrons located at nearest neighbor sites. Ferro-, antiferro-, and spiral magnetic states with all possible sets of spiral wave vectors, as well as singlet superconducting states with s-wave and d-wave pairing order parameters, are considered. Formation of a state with the intermediate s+id-symmetry and phase separation between different phases are allowed. The results of the Hartree-Fock and slave boson approximations are compa…
I investigate band and Mott insulating states in a two-band Hubbard model, with the aim of understanding the differences between the idealised one-orbital model and the more realistic multi-band case. Using a projection ansatz I show that additional orbitals suppress the metal-insulator transition, leading to a critical coupling of approximately eight times the bare band-width. I also demonstrate the effects of orbital ordering, which hinder Mott-Hubbard states and open a band gap. Since multi-band correlations are common in real materials, this work suggests that the existence of very strongl…
In quantum magnetism, the virtual exchange of particles mediates an interaction between spins. Here, we show that an inelastic Hubbard interaction fundamentally alters the magnetism of the Hubbard model due to dissipation in spin-exchange processes, leading to sign reversal of magnetic correlations in dissipative quantum dynamics. This mechanism is applicable to both fermionic and bosonic Mott insulators, and can naturally be realized with ultracold atoms undergoing two-body inelastic collisions. The dynamical reversal of magnetic correlations can be detected by using a double-well optical lat…
We find the eigenvalues $E_α $ and eigenvectors $|E_α>$ of the extended Hubbard dimer and we represent each part $E_α |E_α> < E_α |$ of the dimer Hamiltonian $(α=1,2,...,16)$in the second quantizations with the use of the Hubbard and spin operators. This procedure gives a review of all competitive, intrinsic interactions, deeply hidden in the orginal form of the considered Hamiltonian. Among competitive interactions we can find ferromagnetic and antiferromagnetic interactions (also in the form appearing in the $t-J$ model), hopping of the Cooper pairs between different dimer lattice sites (sim…
The ground-state magnetic phase diagram is investigated within the single-band Hubbard model for square and different cubic lattices. The results of employing the generalized non-correlated mean-field (Hartree-Fock) approximation and generalized slave-boson approach by Kotliar and Ruckenstein with correlation effects included are compared. We take into account commensurate ferromagnetic, antiferromagnetic, and incommensurate (spiral) magnetic phases, as well as phase separation into magnetic phases of different types, which was often lacking in previous investigations. It is found that the spi…
The nature of metal-insulator and magnetic transitions is still a subject under intense debate in condensed matter physics. Amongst the many possible mechanisms, the interplay between electronic correlations and spin-orbit couplings is an issue of a great deal of interest, in particular when dealing with quasi-2D compounds. In view of this, here we use a Hartree-Fock approach to investigate how the Rashba spin-orbit coupling, $V_\text{SO}$, affects the magnetic ordering provided by a Hubbard interaction, $U$, on a square lattice. At half-filling, we have found a sequence of transitions for inc…
Noncollinear magnetic states in clusters are studied by using the single-band Hubbard Hamiltonian. The unrestricted Hartree-Fock (UHF) approximation is considered without imposing any symmetry constraints neither to the size or orientation of the local magnetic moments $<\vec S_l>$ nor to the local charge densities $<n_l>$. A variety of qualitatively different selfconsistent solutions is obtained as a function of cluster size, structure, number of valence electrons $ν$ and Coulomb interaction strength $U/t$. This includes inhomogeneous density distributions, paramagnetic solutions, magnetic so…
The ground--state magnetic phase diagram is investigated for the two-- and three--dimensional $t$--$t'$ Hubbard model. We take into account commensurate ferro--, antiferromagnetic, and incommensurate (spiral) magnetic phases, as well as phase separation into magnetic phases of different types, which was often missed in previous investigations. We trace the influence of correlation effects on the stability of both spiral and collinear magnetic order by comparing the results of employing both the generalized non-correlated mean--field (Hartree--Fock) approximation and generalized slave boson app…
Sr2IrO4 has been suggested as a Mott insulator from a single J_eff=1/2 band, similar to the cuprates. However this picture is complicated by the measured large magnetic anisotropy and ferromagnetism. Based on a careful mapping to the J_eff=1/2 (pseudospin-1/2) space, we propose that the low energy electronic structure of Sr2IrO4 can indeed be described by a SU(2) invariant pseudospin-1/2 Hubbard model very similar to that of the cuprates, but with a "twisted" coupling to external magnetic field (a g-tensor with a staggered antisymmetric component). This perspective naturally explains the magne…
Motivated by the recent angle-resolved photoemission spectroscopy (ARPES) on FeSe and iron pnictide families of iron-based superconductors, we have studied the orbital nematic order and its interplay with antiferromagnetism within the two-orbital Hubbard model. We used random phase approximation (RPA) to calculate the dependence of the orbital and magnetic susceptibilities on the strength of interactions and electron density (doping). To account for strong electron correlations not captured by RPA, we further employed non-perturbative variational cluster approximation (VCA) capable of capturin…
The variational cluster approximation is used to study the isotropic triangular-lattice Hubbard model at half filling, taking into account the nearest-neighbor ($t_1$) and next-nearest-neighbor ($t_2$) hopping parameters for magnetic frustrations. We determine the ground-state phase diagram of the model. In the strong correlation regime, the 120$^\circ$ Néel and stripe ordered phases appear, and a nonmagnetic insulating phase emerges in between. In the intermediate correlation regime, the nonmagnetic insulating phase expands to a wider parameter region, which goes into a paramagnetic metallic …
The electronic and magnetic properties of Ba$_5$AlIr$_2$O$_{11}$ containing Ir-Ir dimers are investigated using the GGA and GGA+SOC calculations. We found that strong suppression of the magnetic moment in this compound recently found in [J. Terzic {\it et al.}, Phys. Rev. B {\bf 91}, 235147 (2015)] is not due to charge-ordering, but is related to the joint effect of the spin-orbit interaction and strong covalency, resulting in the formation of metal-metal bonds. They conspire and act against the intra-atomic Hund's rule exchange interaction to reduce total magnetic moment of the dimer. We argu…
Based on the Hubbard models, quantum magnetism of topologically-designed graphene nanoribbons (GNRs) is studied using exact numerical simulations. We first study a two-band Hubbard model describing the low-energy topological bands using density matrix renormalization group (DMRG) and determinant quantum Monte Carlo (DQMC) methods. It is found the spin correlations decay quickly with the distance, and the local moment is extrapolated to zero in the presence of symmetry-breaking terms. The results show that the two-band Hubbard chain is nonmagnetic, which is in contrast to the mean-field calcula…
We investigate the evolution of magnetic properties as a function of hydrogen doping in iron based superconductor LaFeAsO$_{1-x}$H$_x$ using the dynamical mean-field theory combined with the density-functional theory. We find that two independent consequences of the doping, the increase of the electron occupation and the structural modification, have the opposite effects on the strength of electron correlation and magnetism, resulting in the minimum of the calculated magnetic moment around the intermediate doping level as a function of $x$. Our result provides a natural explanation for the puz…
We study a two-band Hubbard model using the dynamical mean-field theory combined with the exact diagonalization method. At the electron density $n=2$, a transition from a band-insulator to a correlated semimetal occurs when the on-site Coulomb interaction $U$ is varied for a fixed value of the charge-transfer energy $Δ$. At low temperature, the correlated semimetal shows ferromagnetism or superconductivity. With increasing doping $|n-2|$, the ferromagnetic transition temperature rapidly decreases and finally becomes zero at a critical value of $n$. The second-order phase transition occurs at h…
We investigate the competition between charge-density-wave (CDW) states and a Coulomb interaction-driven topological Mott insulator (TMI) in the honeycomb extended Hubbard model. For the spinful model with on-site ($U$) and next-nearest-neighbor ($V_2$) Coulomb interactions at half filling, we find two peculiar six-sublattice charge-density-wave insulating states by using variational Monte Carlo simulations as well as the Hartree-Fock approximation. We observe that conventional ordered states always win with respect to the TMI. The ground state is given in the large-$V_2$ region by a CDW chara…
A self-consistent spectral density approach (SDA) is applied to the Hubbard model to investigate the possibility of spontaneous ferro- and antiferromagnetism. Starting point is a two-pole ansatz for the single-electron spectral density, the free parameter of which can be interpreted as energies and spectral weights of respective quasiparticle excitations. They are determined by fitting exactly calculated spectral moments. The resulting self-energy consists of a local and a non-local part. The higher correlation functions entering the spin-dependent local part can be expressed as functionals of…
The $S=1/2$ antiferromagnetic Heisenberg spin chain compound Sr$_2$CuO$_3$ doped with $1 \%$ and $2 \%$ of Ni impurities has been studied by means of $^{63}$Cu nuclear magnetic resonance. A strong decrease of the spin-lattice relaxation rate $T_1^{-1}$ at low temperatures points toward a spin gap, while a stretching exponent $λ< 1$ and a frequency dependence of $T_1^{-1}$ indicate that this spin gap varies spatially and should rather be characterized as a spin pseudogap. The magnitude of the spin pseudogap scales with doping level. Our results therefore evidence the finite-size character of th…
We study the time evolution of a half-filled Hubbard layer coupled to a magnon bath after a quench of the Hubbard interaction. Qualitatively different regimes, regarding the asymptotic long-time dynamics, are identified and characterized within the mean-field approximation. In the absence of the bath, the dynamics of the closed system is similar to that of a quenched BCS condensate. Though the presence of the bath introduces an additional relaxation mechanism, our numerical results and analytical arguments show that equilibration with the bath is not necessarily attained within the approximati…
We study the phase diagram of a square lattice Hubbard model with a perfect vacancy superstructure. The model can be also defined on a new bipartite lattice with each building blocks consisting of a minimal square. The non-interacting model is exactly solved and a mid-band gap opens at the Fermi energy in the weak inter-block hopping regime. Increasing the Coulomb interaction will develop the Néel antiferromagnetic order with varying block spin moments. The metal-insulator transition with $U_{\rm MI}$ smaller than the one without vacancies occurs above the magnetic instability $U_{\rm M}$. The…
We use the Gutzwiller variational theory to calculate the ground-state phase diagram and quasi-particle bands of LaOFeAs. The Fe3d--As4p Wannier-orbital basis obtained from density-functional theory defines the band part of our eight-band Hubbard model. The full atomic interaction between the electrons in the iron orbitals is parameterized by the Hubbard interaction U and an average Hund's-rule interaction J. We reproduce the experimentally observed small ordered magnetic moment over a large region of (U,J) parameter space. The magnetically ordered phase is a stripe spin-density wave of quasi-…
The experimental realization of time dependent ultracold lattice systems has paved the way towards the implementation of new Hubbard-like Hamiltonians. We show that in a one dimensional two components lattice dipolar Fermi gas the competition between long range repulsion and correlated hopping induced by periodically modulated on-site interaction allows for the formation of exotic hidden magnetic phases. The magnetism, characterized solely by string-like nonlocal order parameters, manifests itself both in the charge and, noticeably, in the spin degrees of freedom. Such behavior is enlighten by…
The influence of static magnetic correlations on the temperature-dependent superfluid density ρ_s(T) is calculated for d-wave superconductors. In self-consistent calculations, itinerant holes form incommensurate spin density waves (SDW) which coexist with superconductivity. In the clean limit, the density of states is gapped, and ρ_s(T << T_c) is exponentially activated. In inhomogeneously-doped cases, the SDW are disordered and both the density of states and ρ_s(T) obtain forms indistinguishable from those in dirty but pure d-wave superconductors, in accordance with experiments. We conclude t…
We study the effect of buckling and breathing phonons, relevant for cuprate superconductors, on the d-wave superconductivity in the two-dimensional Hubbard model by employing dynamical cluster Monte Carlo calculations. The interplay of electronic correlations and the electron-phonon interaction produces two competing effects, an enhancement of the effective d-wave pairing interaction, which favors d-wave superconductivity, and a strong renormalization of the single-particle propagator, which suppress superconductivity. Due to the later effect we find that buckling and breathing phonons suppres…
Using a dynamical cluster quantum Monte Carlo approximation we investigate the d-wave superconducting transition temperature $T_c$ in the doped 2D repulsive Hubbard model with a weak inhomogeneity. The inhomogeneity is introduced in the hoppings $\tp$ and $t$ in the form of a checkerboard pattern where $t$ is the hopping within a $2\times2$ plaquette and $\tp$ is the hopping between the plaquettes. We find inhomogeneity suppresses $T_c$. The characteristic spin excitation energy and the strength of d-wave pairing interaction decrease with decreasing $T_c$ suggesting a strong correlation betwee…
Building on the results of Ref. \cite{faye2018phase}, which identified an antiferromagnetic and Kondo singlet phases on the Kondo-Hubbard square lattice, we use the variational cluster approximation (VCA) to investigate the competition between these phases on a two-dimensional triangular lattice with $120^{o}$ spin orientation. In addition to the antiferromagnetic exchange interaction $J_{\perp}$ between the localized (impurity) and conduction (itinerant) electrons, our model includes the local repulsion $U$ of the conduction electrons and the Heisenberg interaction $J_H$ between the impuritie…
A treatment of many-electron polar and $s-d(f)$ exchange models is carried out in connection with the development of the theory of magnetism of transition and rare-earth metals, as well as their compounds. Particular emphasis is placed on the derivation of the many-electron Heisenberg, Hubbard, Anderson and $t-J$ models, as well as the internal relationship between them. Among the topics discussed are many-electron approaches in describing systems of $d$- and $f$-electrons, atomic representation of Hubbard's $X$-operators, slave-particle representations, the problem of strong itinerant magneti…
We report local probe ($μ$SR) measurements on the recently discovered tetragonal FeS superconductor which has been predicted to be electronically very similar to superconducting FeSe. Most remarkably, we find that low moment ($10^{-2}-10^{-3}μ_\mathrm{B})$ disordered magnetism with a transition temperature of $T_\mathrm{N}\approx 20$ K microscopically coexists with bulk superconductivity below $T_\mathrm{c}=4.3(1)$ K. From transverse field $μ$SR we obtain an in-plane penetration depth $λ_\mathrm{ab}(0)=223(2)$ nm for FeS. The temperature dependence of the corresponding superfluid density $λ_\m…
The realization of antiferromagnetic (AF) correlations in ultracold fermionic atoms on an optical lattice is a significant achievement. Experiments have been carried out in one, two, and three dimensions, and have also studied anisotropic configurations with stronger tunneling in some lattice directions. Such anisotropy is relevant to the physics of cuprate superconductors and other strongly correlated materials. Moreover, this anisotropy might be harnessed to enhance AF order. Here we numerically investigate, using Determinant Quantum Monte Carlo, a simple realization of anisotropy in the 3D …
Detailed analysis of the magnetic properties of the Hubbard model within dynamical mean-field theory (DMFT) is presented. Using a RPA-like decoupling of two-particle propagators we derive a universal form for susceptibilities, which captures essential aspects of localized and itinerant pictures. This expression is shown to be quantitatively valid whenever long-range coherence of particle-hole excitations can be neglected, as is the case in large parts of the phase diagram where antiferromag- netism is dominant. The applicability of an interpretation in terms of the two archetypical pictures of…
It is shown that a strong impurity potential induces short-range antiferromagnetic (ferrimagnetic) order around itself in a Hubbard model on a half-filled honeycomb lattice. This implies that short-range magnetic order is induced in monolayer graphene by a nonmagnetic defect such as a vacancy with full hydrogen termination or a chemisorption defect.
Cooperation and competition between the antiferromagnetic, d-wave superconducting and Mott-insulating states are explored for the two-dimensional Hubbard model including nearest and next-nearest-neighbor hoppings at zero temperature. Using the variational cluster approach with clusters of different shapes and sizes up to 10 sites, it is found that the doping-driven transition from a phase with microscopic coexistence of antiferromagnetism and superconductivity to a purely superconducting phase is discontinuous for strong interaction and accompanied by phase separation. At half-filling the syst…
