We study the influence of ferromagnetic nonlocal exchange on correlated electrons in terms of an SU(2)-Hubbard-Heisenberg model and address the interplay of on-site interaction induced local moment formation and the competition of ferromagnetic direct and antiferromagnetic kinetic exchange interactions. In order to simulate thermodynamic properties of the system in a way that largely accounts for the on-site interaction driven correlations in the system, we advance the correlated variational scheme introduced in [M. Sch\"uler et al., Phys. Rev. Lett. 111, 036601 (2013)] to account for explicitly symmetry broken electronic phases by introducing an auxiliary magnetic field. After benchmarking the method against exact solutions of a finite system, we study the SU(2) Hubbard-Heisenberg model on a square lattice. We obtain the $U\ensuremath{-}J$ finite temperature phase diagram of a SU(2)-Hubbard-Heisenberg model within the correlated variational approach and compare it to static mean-field theory. While the generalized variational principle and static mean-field theory yield transitions from dominant ferromagnetic to antiferromagnetic correlations in similar regions of the phase diagram, we find that the nature of the associated phase transitions differs between the two approaches. The fluctuations accounted for in the generalized variational approach render the transitions continuous, while static mean-field theory predicts discontinuous transitions between ferro- and antiferromagnetically ordered states.
We study the influence of ferromagnetic nonlocal exchange on correlated electrons in terms of an SU(2)-Hubbard-Heisenberg model and address the interplay of on-site interaction induced local moment formation and the competition of ferromagnetic direct and antiferromagnetic kinetic exchange interactions. In order to simulate thermodynamic properties of the system in a way that largely accounts for the on-site interaction driven correlations in the system, we advance the correlated variational scheme introduced in [M. Sch"uler et al., Phys. Rev. Lett. 111, 036601 (2013)] to account for explicitly symmetry broken electronic phases by introducing an auxiliary magnetic field. After benchmarking the method against exact solutions of a finite system, we study the SU(2) Hubbard-Heisenberg model on a square lattice. We obtain the U\ensuremath−J finite temperature phase diagram of a SU(2)-Hubbard-Heisenberg model within the correlated variational approach and compare it to static mean-field theory. While the generalized variational principle and static mean-field theory yield transitions from dominant ferromagnetic to antiferromagnetic correlations in similar regions of the phase diagram, we find that the nature of the associated phase transitions differs between the two approaches. The fluctuations accounted for in the generalized variational approach render the transitions continuous, while static mean-field theory predicts discontinuous transitions between ferro- and antiferromagnetically ordered states.
Recent theoretical and experimental advances have opened new perspectives on the characterization of strongly correlated phases of matter, adding a new layer of understanding based on concepts and tools borrowed from quantum information theory. We join the effort by investigating, within dynamical mean-field theory (DMFT) and its cluster extension, the local and quasilocal (i.e. short-range) quantum information content of salient landmarks in the phase diagram of the two-dimensional Hubbard model, the cornerstone model for the description of the physics of cuprate materials, and of a closely related model for interacting topological states on the honeycomb lattice. In the first part of the thesis, we focus on the DMFT solution of the Kane-Mele-Hubbard model, at zero temperature. In the thermodynamic limit we find evidence of an interaction-driven discontinuous quantum phase transition between the Z2 quantum spin-Hall insulator and anisotropic antiferromagnetic solutions, with an intermediate regime of coexistence of nontrivial topology and magnetic order. A clear-cut interpretation of these results is given in terms of a rigorous quantification of quantum and classical correlations contained in a single local orbital (which we refer to as intra-orbital mutual information), providing a notion of "statistical distance" from the Hartree-Fock description of the system. The resulting analysis complements the established Green's function based understanding of the relationship between dynamical and static mean-field theories. In particular, we find the magnetic solutions of dynamical mean-field theory to asymptotically approach the corresponding uncorrelated Hartree-Fock states, in the strong coupling limit, in stark contrast with the paramagnetic Mott-Hubbard solution, which in turn reveals a maximally correlated local spin-orbital pair at large interaction strength. Furthermore, these findings cast some light on the relationship between Mott localization and the possible development of nonlocal entanglement. In the second part of the thesis, we provide an alternative view of both the interaction-driven and density-driven paramagnetic Mott transitions in the two-dimensional Hubbard model, in terms of rigorous measures of entanglement and correlation between two spatially separated electronic orbitals, with no contribution from their environment. A space-resolved analysis of cluster dynamical mean-field theory results elucidates the prominent role of the nearest-neighbor entanglement in probing Mott localization: two traditional upper bounds and two recently introduced lower bounds for its magnitude sharply increase at the metal-insulator transition, in contrast with the moderate variation found at all interaction strengths that are sufficiently far from the transition point. At half-filling, the two-site entanglement beyond nearest neighbors is shown to be quickly damped as the inter-site distance is increased within the cluster, suggesting that Mott-Hubbard insulators may follow an area law. However, the size of the simulated clusters does not allow a quantitative analysis of the decay, so that a precise classification of the spatial entanglement properties of the system is left for future study. In the presence of hole-doping, we show how the pseudogap metal separating the Mott-Hubbard insulator from the hole-dominated Fermi liquid features quasilocal entanglement properties that are strikingly similar to the localized Mott phase, while it is separated from the low-entangled Fermi liquid by a discontinuous jump in all the computed entanglement and correlation measures. All the presented results ultimately resolve a conundrum of previous analyses based on the single-site von Neumann entropy, which has been found to monotonically decrease when the interaction is increased, defeating the purpose of capturing and understanding strong electronic correlations with the aid of quantum information concepts. Both the intra-orbital mutual information and the quasilocal two-site entanglement, on the other hand, recover instead the distinctive character of Mott insulators and pseudogap metals as strongly correlated many-body states, demonstrating its central role in future advancements in the field of quantum materials.
The influence of local disorder on the thermodynamics of interacting electrons is studied within the infinite-dimensional disordered Hubbard model.Using a finite-temperature quantum Monte Carlo method, the averaged local moment and staggered susceptibility are calculated and the magnetic phase diagram at half-filling is constructed.From the averaged compressibility in the paramagnetic and antiferromagnetic phase we determine the metalinsulator transitions of the system.A rich transition scenario is revealed.Quite unexpectedly the disorder is found to stabilize the magnetic order in the strong-coupling limit.Randomness can significantly influence the low-temperature behaviour of interacting systems.In particular, it may lead to new phases which have no analogue in non-random systems [l].In the case of electrons, the simplest lattice model including both interactions and random potentials is the disordered Hubbard model.It is now known that even in the .mean-field.limit d + CQ [2,3] the Hubbard interaction remains dynamical [4] and leads to a highly non-trivial single-site problem with infinitely many coupled quantum degrees of freedom [5].This problem is, in fact, equivalent to an Anderson impurity model complemented by a self-consistency condition [6] and is thus amenable to numerical investigations [7] within a finite-temperature quantum Monte Carlo approach [81.In the absence of disorder this technique was already used by several groups to investigate the magnetic phase diagram [7,9], the Mott-Hubbard transition [lo, 1 1 1 and lately also superconductivity in a two-band version [12] of the Hubbard model in d = C Q ; thereby important new insight was gained.In this letter we wish to concentrate on the combined effect of disorder and interaction.We will study the effect of diagonal disorder on the low-temperature properties of the Hubbard model in d = CQ , in particular the competition between correlation-induced
We consider the extended Hubbard model and introduce a corresponding Heisenberg-like problem written in terms of spin operators. The derived formalism is reminiscent of Anderson's idea of the effective exchange interaction and takes into account nonlocal correlation effects. The results for the exchange interaction and spin susceptibility in the magnetic phase are expressed in terms of single-particle quantities. This fact not only can be used for realistic calculations of multiband systems but also allows us to reconsider a general description of many-body effects in the most interesting physical regimes, where the physical properties of the system are dominated by collective (bosonic) fluctuations. In the strongly spin-polarized limit, when the local magnetic moment is well defined, the exchange interaction reduces to a standard expression of the density functional theory that has been successfully used in practical calculations of magnetic properties of real materials.
We develop a variational perturbation expansion around dynamical mean-field theory (DMFT) that systematically incorporates nonlocal correlations beyond the local correlations treated by DMFT. We apply this approach to investigate how the DMFT critical temperature is suppressed from its mean-field value and how the critical behavior near the finite-temperature phase transition evolves from the mean-field to the Heisenberg universality class. By identifying the symmetry breaking of paramagnetic diagrammatic expansions as a signature of the Néel transition, we accurately predict the Néel temperature of the three-dimensional cubic Hubbard model across all interaction strengths with low computational cost. Introducing a variational order parameter, our method can be applied to both paramagnetic and long-range ordered states, such as antiferromagnetic order. We compute magnetization and antiferromagnetic susceptibility, demonstrating minor corrections to DMFT solutions in the weak-coupling regime while revealing significant modifications to these properties in the intermediate correlation regime. From the analysis of critical exponents, we establish the emergence of Heisenberg critical behavior beyond the mean-field nature of DMFT.
We present an efficient diagrammatic method to describe nonlocal correlation effects in lattice fermion Hubbard-type models, which is based on a change of variables in the Grassmann path integrals. The new fermions are dual to the original ones and correspond to weakly interacting quasiparticles in the case of strong local correlations in the Hubbard model. The method starts with dynamical mean-field theory as a zeroth-order approximation and includes nonlocal effects in a perturbative way. In contrast to cluster approaches, this method utilizes an exact transition to a dual set of variables. It therefore becomes possible to treat vertices of an effective single-impurity problem as small parameters. This provides a very efficient interpolation between bandlike weak-coupling and atomic limits. The method is illustrated on the two-dimensional Hubbard model. The antiferromagnetic pseudogap, Fermi-arc formations, and non-Fermi-liquid effects due to the Van Hove singularity are correctly reproduced by the lowest-order diagrams. Extremum properties of the dual fermion approach are discussed in terms of the Feynman variational principle.
We analyze the impact of the lattice geometry on the thermodynamic transition to magnetically ordered phases in strongly interacting electron systems for various Bravais lattices in three, four, and five dimensions, including both local and nonlocal correlation effects. In a first step we use the dynamical mean-field theory (DMFT), which takes into account purely local correlations, to calculate the magnetic susceptibilities of the Hubbard model on three- (3d-sc), four- (4d-sc), and five- dimensional (5d-sc) simple cubic/hypercubic, as well as on three- dimensional body- (bcc) and face-centered (fcc) cubic lattices, and determine the transition temperature to the corresponding magneticallyordered state. In a second step, we exploit the dynamical vertex approximation ( D Γ A ) , a diagrammatic extension of DMFT, to include the effect of nonlocal correlations which are particularly important in the vicinity of the corresponding phase transition. For the bipartite 3d-sc, 4d-sc, 5d-sc, and bcc lattices nonlocal fluctuations lead to a substantial reduction of the DMFT transition temperature consistent to the overall tendency of mean-field approaches to overestimate the stability of ordered phases. As expected, the magnitude of the difference between the DMFT, being exact in the limit of large connectivity/dimensions, and D Γ A transition temperatures decreases with increasing coordination number. On a more practical perspective, these results also provide a reasonable guidance to evaluate the expected overestimation of the DMFT ordering temperature for different material geometries. For the fcc lattice, on the other hand, the ordered phase observed in DMFT vanishes completely within D Γ A which is consistent with the existence of strong geometric frustration in this lattice.