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arXiv:1405.7250 · Physical Review B

Fate of the false Mott-Hubbard transition in two dimensions

Thomas Schäfer, F. Geles, D. Rost, G. Rohringer, Enrico Arrigoni, Karsten Held, Nils Blümer, Markus Aichhorn, A. Toschi

Published Mar 3, 2015• 178 citations
arXivHTMLPDF

Abstract

We have studied the impact of nonlocal electronic correlations at all length scales on the Mott-Hubbard metal-insulator transition in the unfrustrated two-dimensional Hubbard model. Combining dynamical vertex approximation, lattice quantum Monte Carlo, and variational cluster approximation, we demonstrate that scattering at long-range fluctuations, i.e., Slater-like paramagnons, opens a spectral gap at weak-to-intermediate coupling, irrespective of the preformation of localized or short-range magnetic moments. This is the reason why the two-dimensional Hubbard model has a paramagnetic phase which is insulating at low enough temperatures for any (finite) interaction and no Mott-Hubbard transition is observed.

DOI
10.1103/physrevb.91.125109

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We have studied the impact of nonlocal electronic correlations at all length scales on the Mott-Hubbard metal-insulator transition in the unfrustrated two-dimensional Hubbard model. Combining dynamical vertex approximation, lattice quantum Monte Carlo, and variational cluster approximation, we demonstrate that scattering at long-range fluctuations, i.e., Slater-like paramagnons, opens a spectral gap at weak-to-intermediate coupling, irrespective of the preformation of localized or short-range magnetic moments. This is the reason why the two-dimensional Hubbard model has a paramagnetic phase which is insulating at low enough temperatures for any (finite) interaction and no Mott-Hubbard transition is observed.
Elucidating the physics of the single-orbital Hubbard model in its intermediate-coupling regime is a key missing ingredient to our understanding of metal-insulator transitions in real materials. Using recent nonperturbative many-body techniques that are able to interpolate between the spin-fluctuation-dominated Slater regime at weak coupling and the Mott insulator at strong coupling, we obtain the momentum-resolved spectral function in the intermediate regime and disentangle the effects of antiferromagnetic fluctuations and local electronic correlations in the formation of an insulating state. This allows us to identify the Slater and Heisenberg regimes in the phase diagram, which are separated by a crossover region of competing spatial and local electronic correlations. We identify the crossover regime by investigating the behavior of the local magnetic moment, shedding light on the formation of the insulating state at intermediate couplings.
The influence of spin and charge fluctuations on spectra of the two-dimensional fermionic Hubbard model is considered using the strong coupling diagram technique. Infinite sequences of diagrams containing ladder inserts, which describe the interaction of electrons with these fluctuations, are summed, and obtained equations are self-consistently solved for the ranges of Hubbard repulsions [Formula: see text], temperatures [Formula: see text] and electron concentrations [Formula: see text] with t the intersite hopping constant. For all considered U the system exhibits a transition to the long-range antiferromagnetic order at [Formula: see text]. At the same time no indication of charge ordering is observed. Obtained solutions agree satisfactorily with results of other approaches and obey moments sum rules. In the considered region of the U-T plane, the curve separating metallic solutions passes from [Formula: see text] at the highest temperatures to U = 2t at [Formula: see text] for half-filling. If only short-range fluctuations are allowed for the remaining part of this region is occupied by insulating solutions. Taking into account long-range fluctuations leads to strengthening of maxima tails, which transform a part of insulating solutions into bad-metal states. For low T, obtained results allow us to trace the gradual transition from the regime of strong correlations with the pronounced four-band structure and well-defined Mott gap for [Formula: see text] to the Slater regime of weak correlations with the spectral intensity having a dip along the boundary of the magnetic Brillouin zone due to an antiferromagnetic ordering for [Formula: see text]. For [Formula: see text] and [Formula: see text] doping leads to the occurrence of a pseudogap near the Fermi level, which is a consequence of the splitting out of a narrow band from a Hubbard subband. Obtained spectra feature waterfalls and Fermi arcs, which are similar to those observed in hole-doped cuprates.
We investigate the properties of a two-orbital Hubbard model with unequal bandwidths on the square lattice in the framework of the dynamical cluster approximation (DCA) combined with a continuous-time quantum Monte Carlo algorithm. We explore the effect of short-range spatial fluctuations on the nature of the metal-insulator transition and the possible occurrence of an orbital-selective Mott transition (OSMT) as a function of cluster size N{c}. We observe that for N{c}=2 no OSMT is present, instead a band insulator state for both orbitals is stabilized at low temperatures due to the appearance of an artificial local ordered state. For N{c}=4 the DCA calculations suggest the presence of five different phases which originate out of the cooperation and competition between spatial fluctuations and orbitals of different bandwidths and an OSMT phase is stabilized. Based on our results, we discuss the nature of the gap opening.
We study the interplay between electron correlation and disorder in the two-dimensional Hubbard model at half filling by means of a variational wave function that can interpolate between Anderson and Mott insulators. We give a detailed description of our improved variational state and explain how the physics of the Anderson-Mott transition can be inferred from equal-time correlations functions, which can be easily computed within the variational Monte Carlo scheme. The ground-state phase diagram is worked out in both the paramagnetic and the magnetic sector. Whereas in the former a direct second-order Anderson-Mott transition is obtained, when magnetism is allowed variationally, we find evidence for the formation of local magnetic moments that order before the Mott transition. Although the localization length increases before the Mott transition, we have no evidence for the stabilization of a true metallic phase. The effect of a frustrating next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$ is also studied in some detail. In particular, we show that ${t}^{\ensuremath{'}}$ has two primary effects. The first one is the narrowing of the stability region of the magnetic Anderson insulator, also leading to a first-order magnetic transition. The second and most important effect of a frustrating hopping term is the development of a ``glassy'' phase at strong couplings, where many paramagnetic states, with disordered local moments, may be stabilized.
The nature of the metal-insulator Mott transition at zero temperature has been discussed for a number of years. Whether it occurs through a quantum critical point or through a first-order transition is expected to profoundly influence the nature of the finite-temperature phase diagram. In this paper, we study the zero temperature Mott transition in the two-dimensional Hubbard model on the square lattice with the variational cluster approximation. This takes into account the influence of antiferromagnetic short-range correlations. By contrast to single-site dynamical mean-field theory, the transition turns out to be first order even at zero temperature.
In this paper, we investigate how nonlocal correlations affect, selectively, the physics of correlated electrons over different energy scales, from the Fermi level to the band edges. This goal is achieved by applying a diagrammatic extension of dynamical mean field theory (DMFT), the dynamical vertex approximation $(\mathrm{D}\mathrm{\ensuremath{\Gamma}}\mathrm{A})$, to study several spectral and thermodynamic properties of the unfrustrated Hubbard model in two and three dimensions. Specifically, we focus first on the low-energy regime by computing the electronic scattering rate and the quasiparticle mass renormalization for decreasing temperatures at a fixed interaction strength. This way, we obtain a precise characterization of the several steps through which the Fermi-liquid physics is progressively destroyed by nonlocal correlations. Our study is then extended to a broader energy range, by analyzing the temperature behavior of the kinetic and potential energy, as well as of the corresponding energy distribution functions. Our findings allow us to identify a smooth but definite evolution of the nature of nonlocal correlations by increasing interaction: They either increase or decrease the kinetic energy w.r.t. DMFT depending on the interaction strength being weak or strong, respectively. This reflects the corresponding evolution of the ground state from a nesting-driven (Slater) to a superexchange-driven (Heisenberg) antiferromagnet (AF), whose fingerprints are, thus, recognizable in the spatial correlations of the paramagnetic phase. Finally, a critical analysis of our numerical results of the potential energy at the largest interaction allows us to identify possible procedures to improve the ladder-based algorithms adopted in the dynamical vertex approximation.