Single-Particle Dispersion and Density of States of the Half-Filled 2D Hubbard Model

Abstract

Implementing an improved method for analytic continuation and working with imaginary-time correlation functions computed using quantum Monte Carlo simulations, we resolve the single-particle dispersion relation and the density of states (DOS) of the two-dimensional Hubbard model at half-filling. At intermediate interactions of $U/t=4,6$, we find quadratic dispersion around the gap minimum at wave-vectors $\mathbf{k}=(\pm \pi /2,\pm \pi /2)$ (the $\Sigma$ points). We find saddle points at $\mathbf{k}=(\pm \pi ,0),(0,\pm \pi )$ (the X points) where the dispersion is approximately quartic, leading to a sharp DOS maximum above the almost flat ledge arising from the states close to $\Sigma$. The fraction of quasiparticle states within the ledge is $n_{\mathrm{ledge}}\approx 0.15$. Upon doping away from half-filling, within the rigid-band approximation, these results support Fermi pockets around the $\Sigma$ points, with states around the X points becoming filled only at doping fractions $x\ge n_{\mathrm{ledge}}$. The high density of states away from the $\Sigma$ gap edge may be an important clue for a finite minimum doping level for superconductivity and other instabilities of doped Mott insulators.

9 pages, 7 figures

References in corpus (16)

• Theory of Intertwined Orders in High Temperature Superconductors
• Fractionalized Fermi liquids
• Two Gaps Make a High Temperature Superconductor?
• Distinct Fermi-Momentum Dependent Energy Gaps in Deeply Underdoped Bi2212
• Two Energy Scales and two Quasiparticle Dynamics in the Superconducting State of Underdoped Cuprates
• The Ground State of the Pseudogap in Cuprate Superconductors
• Coexistence of superconductivity with partially filled stripes in the Hubbard model
• Nearly deconfined spinon excitations in the square-lattice spin-1/2 Heisenberg antiferromagnet
• Progress on stochastic analytic continuation of quantum Monte Carlo data
• Using the average spectrum method to extract dynamics from quantum Monte Carlo simulations
• Hole dynamics in an antiferromagnet across a deconfined quantum critical point
• The superconducting gap in the Hubbard model and the two gap energy scales in high-Tc cuprates
• The Average Spectrum Method for Analytic Continuation: Efficient Blocked Modes Sampling and Dependence on Discretization Grid
• Extending the average spectrum method: Grid points sampling and density averaging
• Angle-Resolved Photoemission from Cuprates with Static Stripes
• Cross Validation in Stochastic Analytic Continuation

Cited by in corpus (3)

• Twisting the Hubbard model into the Momentum-Mixing Hatsugai-Kohmoto Model
• Exact results for the Hubbard model on bipartite lattices in spatial dimensions $d>1$: Seven theorems from the full [SU(2)$\times$SU(2)$\times$U(1)]/${\mathbb{Z}}_2^2$ symmetry
• Single-hole spectral functions in one-dimensional quantum magnets with different ground states