Impact of nonlocal correlations over different energy scales: A dynamical vertex approximation study

Abstract

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 (DΓA), 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 superexchangedriven (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.

Fluctuation diagnostics of the finite-temperature quasi-antiferromagnetic regime of the two-dimensional Hubbard model

“…Density dependence of the anti-ferromagnetic correlation length, ξ, for several interaction strengths U at T /t = 0.2. obtained from a fit of χsp(qx, qy, Ω = 0) with the function f (qx, ξ) = A/((q − (π, π)) 2 + ξ −2 ) + c, averaged over the qx = qy and (qx, qy) = (qx, π) directions. 14,29 electron or hole doping away from half-filling. 24,28 These observations at high temperature of a crossover with interaction strength are in-line with the long established cDMFT phase diagram.…”

Spin and Charge Correlations across the Metal-to-Insulator Crossover in the Half-Filled 2D Hubbard Model

“…This drastic qualitative difference between the limiting cases-a local scenario at strong coupling versus that local in the momentum space at weak coupling-makes physics at intermediate U ∼ t particularly intriguing and challenging to describe reliably.When extended AFM correlations are explicitly suppressed, a Mott insulator is expected to emerge by a first-order metal-to-insulator transition [15][16][17][18][19][20][21][22][23][24][25]. In the 2d Hubbard model (1) currently realized in experiments, extending correlations make the insulator develop in a smooth crossover [26][27][28][29]. Recent controlled results [29] by diagrammatic determinant Monte Carlo for the selfenergy (ΣDDMC) [30] and the dynamical cluster approximation [31] demonstrate that the crossover is non-trivial and involves a transitional non-Fermi-liquid (nFL) [32] regime with a partially gapped FS [27,28].…”

Magnetic susceptibility and simulated neutron signal in the two-dimensional Hubbard model

“…Left: Simulation results for Imχ(ω, q) at U/t = 8, t ′ /t = −0.3 and T /t = 0.2 at n = 1 (top row) and n = 0.95 (bottom row) for fixed frequencies in the qx and qy plane. Right: Doping dependence of the antiferromagnetic correlation length, ξ, for several interaction strengths U , obtained from a fit of χ along the direction (qx, qy) = (qx, π) with the function f (qx, ξ) = A/((qx − π) 2 + ξ −2 ) 66,67. …”