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.

arXiv comment9 pages, 7 figures

References in corpus (44)

• 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
• Scattering and Pairing in Cuprate Superconductors
• Two Energy Scales and two Quasiparticle Dynamics in the Superconducting State of Underdoped Cuprates
• The remarkable underlying ground states of cuprate superconductors
• Absence of superconductivity in the pure two-dimensional Hubbard model
• Nodal metallic behavior of lightly-doped La${}_{2-x}$Sr${}_x$CuO${}_4$
• The Ground State of the Pseudogap in Cuprate Superconductors
• Quasiparticle Dispersion of the 2D Hubbard Model: From an Insulator to a Metal
• Quantum Monte Carlo study of the two-dimensional fermion Hubbard Model
• Coexistence of superconductivity with partially filled stripes in the Hubbard model
• Carrier relaxation, pseudogap, and superconducting gap in high-Tc cuprates: A Raman scattering study
• Nearly deconfined spinon excitations in the square-lattice spin-1/2 Heisenberg antiferromagnet
• Algorithms for optimized maximum entropy and diagnostic tools for analytic continuation
• Constrained sampling method for analytic continuation
• Single hole dynamics in the t-J model on a square lattice
• Benchmark study of the two-dimensional Hubbard model with auxiliary-field quantum Monte Carlo method
• Ab initio effective Hamiltonians for cuprate superconductors
• Progress on stochastic analytic continuation of quantum Monte Carlo data
• Analytic Continuation of Quantum Monte Carlo Data by Stochastic Analytical Inference
• Using the average spectrum method to extract dynamics from quantum Monte Carlo simulations
• Single hole spectral function and spin-charge separation in the t-J model
• Hole dynamics in an antiferromagnet across a deconfined quantum critical point
• Luttinger-volume violating Fermi liquid in the pseudogap phase of the cuprate superconductors
• Computation of dynamical correlation functions for many fermion systems with auxiliary-field quantum Monte Carlo
• Quantum criticality around metal-insulator transitions of strongly correlated electrons
• Fully Gapped Single-Particle Excitations in the Lightly Doped Cuprates
• The amplitude mode in three-dimensional dimerized antiferromagnets
• Insulator-Metal Transition in the One and Two-Dimensional Hubbard Models
• Renormalization group analysis of the pair-density-wave and charge order within the fermionic hot-spot model for cuprate superconductors
• The novel metallic states of the cuprates: Fermi liquids with topological order, and strange metals
• Validity of the rigid band picture for the t-J model
• Critical Doping for the Onset of Fermi-Surface Reconstruction by Charge-Density-Wave Order in the Cuprate Superconductor La${}_{2-x}$Sr${}_x$CuO${}_4$
• 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
• Spin-charge interplay in antiferromagnetic La${}_{2-x}$Sr${}_x$CuO${}_4$ studied by the muons, neutrons, and ARPES techniques
• Spin density wave order, topological order, and Fermi surface reconstruction
• Extending the average spectrum method: Grid points sampling and density averaging
• Doping induced metal-insulator transition in two-dimensional Hubbard, $t-U$, and extended Hubbard, $t-U-W$, models
• Analytic continuation average spectrum method for quantum liquids
• Angle-Resolved Photoemission from Cuprates with Static Stripes
• Cross Validation in Stochastic Analytic Continuation

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