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arXiv:cond-mat/9701097 · Physical Review Letters

Pseudogaps and Their Interplay with Magnetic Excitations in the Doped 2D Hubbard Model

R. Preuss, Werner R. Hanke, C. Gröber, Hans Gerd Evertz

Published Aug 11, 1997• 114 citations
arXivHTMLPDF

Abstract

On the basis of quantum Monte Carlo simulations of the two-dimensional Hubbard model which cover the doping range from the underdoped to the overdoped regime, we find that the single-particle spectral weight $A(\stackrel{\ensuremath{\rightarrow}}{k},\ensuremath{\omega})$ qualitatively reproduces both the momentum ( ${d}_{{x}^{2}{\ensuremath{-}y}^{2}}$ symmetry) and doping dependence of the pseudogap as found in photoemission experiments. The drastic doping dependence of the spin response ${\ensuremath{\chi}}_{s}(\stackrel{\ensuremath{\rightarrow}}{q},\ensuremath{\omega})$, which is sharp in both $\stackrel{\ensuremath{\rightarrow}}{q}[\ensuremath{\approx}(\ensuremath{\pi},\ensuremath{\pi})]$ and $\ensuremath{\omega}$ in the underdoped regime but broad and structureless otherwise, identifies remnants of the antiferromagnetic order as the driving mechanism behind the pseudogap and its evolution with doping.

DOI
10.1103/physrevlett.79.1122

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We compute high-resolution angle-resolved photoemission spectroscopy of the Hubbard model using the unbiased determinant quantum Monte Carlo algorithm, revealing an asymmetry between electron and hole doping. Electron doping exhibits more coherent quasiparticles and stronger antiferromagnetic correlations compared to hole doping. At low doping, a nodal-antinodal dichotomy on the Fermi surface is observed, similar to cuprate experiments. The dichotomy reflects the momentum dependence of the Mott gap, as manifested in both the spectral function and the self-energy. For hole doping, we observe a transition towards the pseudogap, without signature of pocket formation. The simulated nuclear magnetic resonance pseudogap temperatures do not necessarily agree with the temperature determined by spectroscopy. These findings collectively suggest the pseudogap is a smooth crossover driven by strong correlations.
Using the dynamical cluster approximation and quantum Monte Carlo simulations we calculate the single-particle spectra of the Hubbard model with next-nearest neighbor hopping . In the underdoped region, we find that the pseudogap along the zone diagonal in the electron doped systems is due to long-range antiferromagnetic correlations. The physics in the proximity of (0, pi) is dramatically influenced by t' and determined by the short range correlations. The effect t' of on the low-energy angle-resolved photoemission spectroscopy spectra is weak except close to the zone edge. The short range correlations are sufficient to yield a pseudogap signal in the magnetic susceptibility and produce a concomitant gap in the single-particle spectra near (pi, pi/2), but not necessarily at a location in the proximity of the Fermi surface.
Abstract We investigate the interplay between the pseudogap state and d-wave superconductivity in the two-dimensional doped Hubbard model by employing an eight-site cluster dynamical mean-field theory method. By tuning electron hopping parameters, the strong-coupling pseudogap in the two-dimensional Hubbard model can be either enhanced or suppressed in the doped Mott insulator regime. We find that in underdoped cases, the closing of pseudogap leads to a significant enhancement of superconductivity, indicating competition between the two in the underdoped regime. In contrast, at large dopings, suppressing the pseudogap is accompanied by a concurrent decrease in the superconducting transition temperature T c, which can be attributed to a reduction in antiferromagnetic correlations behind both the pseudogap and superconductivity. We elucidate this evolving relationship between pseudogap and superconductivity across different doping regimes.
On the basis of quantum Monte Carlo results the evolution of the spectral weight $A(\mathbf{k},\ensuremath{\omega})$ of the two-dimensional Hubbard model is studied from insulating to metallic behavior. As observed in recent photoemission experiments for cuprates, the electronic excitations display essentially doping-independent features; a quasiparticlelike dispersive narrow band of width of the order of the exchange interaction JJJ and a broad valence- and conduction-band background. The continuous evolution is traced back to one and the same many-body origin: the doping-dependent antiferromagnetic spin-spin correlation.
Cluster perturbation theory is applied to the two-dimensional Hubbard $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}{t}^{\ensuremath{'}\ensuremath{'}}\ensuremath{-}U$ model to obtain doping and temperature-dependent electronic spectral function with $4\ifmmode\times\else\texttimes\fi{}4$ and 12-site clusters. It is shown that evolution of the pseudogap and electronic dispersion with doping and temperature is similar and in both cases it is significantly influenced by spin-spin short-range correlations. When short-range magnetic order is weakened by doping or temperature and Hubbard-I-like electronic dispersion becomes more pronounced, the Fermi arc turns into a large Fermi surface and the pseudogap closes. It is demonstrated how static spin correlations impact the overall dispersion's shape and how accounting for dynamic contributions leads to momentum-dependent spectral weight at the Fermi surface and broadening effects.
We investigate the doped two-dimensional Hubbard model at finite temperature using controlled diagrammatic Monte Carlo calculations allowing for the computation of spectral properties in the infinite-size limit and, crucially, with arbitrary momentum resolution. We show that three distinct regimes are found as a function of doping and interaction strength, corresponding to a weakly correlated metal with properties close to those of the non-interacting system, a correlated metal with strong interaction effects including a reshaping of the Fermi surface, and a pseudogap regime at low doping in which quasiparticle excitations are selectively destroyed near the antinodal regions of momentum space. We study the physical mechanism leading to the pseudogap and show that it forms both at weak coupling when the magnetic correlation length is large and at strong coupling when it is shorter. In both cases, we show that spin-fluctuation theory can be modified in order to account for the behavior of the non-local component of the self-energy. We discuss the fate of the pseudogap as temperature goes to zero and show that, remarkably, this regime extrapolates precisely to the ordered stripe phase found by ground-state methods. This handshake between finite temperature and ground-state results significantly advances the elaboration of a comprehensive picture of the physics of the doped Hubbard model.