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arXiv:cond-mat/9902015

Hubbard Fermi surface in the doped paramagnetic insulator

C. Gröber, M. G. Zacher, R. Eder

Published Feb 1, 1999• 0 citations
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Abstract

We study the electronic structure of the doped paramagnetic insulator by finite temperature Quantum Monte-Carlo simulations for the 2D Hubbard model. Throughout we use the moderately high temperature T=0.33t, where the spin correlation length has dropped to < 1.5 lattice spacings, and study the evolution of the band structure with hole doping. The effect of doping can be best described as a rigid shift of the chemical potential into the lower Hubbard band, accompanied by some transfer of spectral weight. For hole dopings <20% the Luttinger theorem is violated, and the Fermi surface volume, inferred from the Fermi level crossings of the `quasiparticle band', shows a similar topology and doping dependence as predicted by the Hubbard I and related approximations.

DOI
10.48550/arxiv.cond-mat/9902015

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We study the electronic structure of the doped paramagnetic insulator by finite temperature Quantum Monte-Carlo simulations for the 2D Hubbard model. Throughout we use the moderately high temperature T=0.33t, where the spin correlation length has dropped to < 1.5 lattice spacings, and study the evolution of the band structure with hole doping. The effect of doping can be best described as a rigid shift of the chemical potential into the lower Hubbard band, accompanied by some transfer of spectral weight. For hole dopings <20% the Luttinger theorem is violated, and the Fermi surface volume, inferred from the Fermi level crossings of the `quasiparticle band', shows a similar topology and doping dependence as predicted by the Hubbard I and related approximations.
We study the transition from paramagnetic metal to paramagnetic insulator by finite temperature Quantum Monte-Carlo simulations for the 2D Hubbard model at half-filling. Working at the moderately high temperature T=0.33*t where the spin correlation length has dropped to 1.5 lattice spacings, and scanning the interaction strength U, we observe an unambiguous metal-insulator transition with onset at U_c=4t. In the metallic phase there are no indications of any `correlation narrowing' of the band width, nor for any decrease of spectral weight at the Fermi energy. The Mott-Hubbard gap opens gradually with increasing U and is accompanied by the formation of side bands near the Fermi energy. In the first stages of gap formation the gap opens at (pi,0), reminiscent of the `pseudogap' phenomenology in cuprate superconductors.
We present results of a systematic quantum Monte Carlo study for the single-band Hubbard model. Thereby we evaluated single-particle spectra (PES and IPES), two-particle spectra (spin and density correlation functions), and the dynamical correlation function of suitably defined diagnostic operators, all as a function of temperature and hole doping. The results allow us to identify different physical regimes. Near half-filling we find an anomalous ``Hubbard-I phase,'' where the band structure is, up to some minor modifications, consistent with the Hubbard-I predictions. At lower temperatures, where the spin response becomes sharp, additional dispersionless ``bands'' emerge due to the dressing of electrons/holes with spin excitations. We present a simple phenomenological fit that reproduces the band structure of the insulator quantitatively. The Fermi surface volume in the low-doping phase, as derived from the single-particle spectral function, is not consistent with the Luttinger theorem, but qualitatively in agreement with the predictions of the Hubbard-I approximation. The anomalous phase extends up to a hole concentration of $\ensuremath{\approx}15%,$ i.e., the underdoped region in the phase diagram of high-Tc{T}_{c}Tc​ superconductors. We also investigate the nature of the magnetic ordering transition in the single-particle spectra. We show that the transition to a spin-density wave-like band structure is not accomplished by the formation of any resolvable ``precursor bands,'' but rather by a (spectroscopically invisible) band of spin-3/2 quasiparticles. We discuss implications for the ``remnant Fermi surface'' in insulating cuprate compounds and the shadow bands in the doped materials.
The concentration dependences of the band structure, spectral weight, density of states, and Fermi surface in the paramagnetic state are studied in the Hubbard model within cluster pertubation theory with 2 × 2 clusters. Representation of the Hubbard X operators makes it possible to control conservation of the spectral weight in constructing cluster perturbation theory. The calculated value of the ground-state energy is in good agreement with the results obtained using nonperturbative methods such as the quantum Monte Carlo method, exact diagonalization of a 4 × 4 cluster, and the variational Monte Carlo method. It is shown that in the case of hole doping, the states in the band gap (in-gap states) lie near the top of the lower Hubbard band for large values of U and near the bottom of the upper band for small U . The concentration dependence of the Fermi surface strongly depends on hopping to second ( t ′) and third ( t ″) neighbors. For parameter values typical of HTSC cuprates, the existence of three concentration regions with different Fermi surfaces is demonstrated. It is shown that broadening of the spectral electron density with an energy resolution typical of contemporary ARPES leads to a pattern of arcs with a length depending on the concentration. Only an order-of-magnitude decrease in the linewidth makes it possible to obtain the true Fermi surface from the spectral density. The kinks associated with strong electron correlations are detected in the dispersion relation below the Fermi level.
We study the electronic state of the doped Mott-Hubbard insulator within the dynamical mean field theory. The evolution of the finite temperature spectral functions as a function of doping show large redistributions of spectral weight in both antiferromagnetic and paramagnetic phases. In particular, a metallic antiferromagnetic state is obtained with a low frequency Slater-splitted quasiparticle peak coexisting with Hubbard bands. In the high temperature paramagnetic metallic phase, upon reducing doping, the system has a crossover through a ``bad metal'' state characterized by an anomalous shift of the quasiparticle peak away from the Fermi energy. We find that the charge compressibility of the antiferromagnetic metal is dramatically enhanced upon approaching the second order N\'eel line.
We present determinant quantum Monte Carlo simulations of the hole-doped single-band Hubbard-Holstein model on a square lattice, to investigate how quasiparticles emerge when doping a Mott insulator (MI) or a Peierls insulator (PI). The MI regime at large Hubbard interaction UUU and small relative e-ph coupling strength $\ensuremath{\lambda}$ is quickly suppressed upon doping, by drawing spectral weight from the upper Hubbard band and shifting the lower Hubbard band towards the Fermi level, leading to a metallic state with emergent quasiparticles at the Fermi level. On the other hand, the PI regime at large $\ensuremath{\lambda}$ and small UUU persists out to relatively high doping levels. We study the evolution of the ddd-wave superconducting susceptibility with doping, and find that it increases with lowering temperature in a regime of intermediate values of UUU and $\ensuremath{\lambda}$.
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.