Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical review. B, Condensed matter

Dynamics of quasiparticles in the two-dimensional Hubbard model

Daniel Charles Mattis, Michael Dzierzawa, X. Zotos

Published Oct 1, 1990• 9 citations
Publisher

Abstract

The Hubbard model at half-filling is a collective, antiferromagnetic insulator. We study added electrons or holes. The insulating energy gap and the dispersion of the added carriers are calculated variationally in two dimensions with use of a Monte Carlo evaluation of the electronic correlation functions in the insulating phase. Both ${\mathit{E}}_{\mathit{g}}$ and ${\mathit{m}}^{\mathrm{*}}$ are found to be temperature dependent.

DOI
10.1103/physrevb.42.6787

Related papers

Tracking the Footprints of Spin Fluctuations: A MultiMethod, MultiMessenger Study of the Two-Dimensional Hubbard Model

Thomas Schäfer, Nils Wentzell, Fedor Šimkovic +23 more

The Hubbard model represents the fundamental model for interacting quantum systems and electronic correlations.Using the two-dimensional half-filled Hubbard model at weak coupling as a testing ground, we perform a comparative study of a comprehensive set of state-of-the-art quantum many-body methods.Upon cooling into its insulating antiferromagnetic ground state, the model hosts a rich sequence of distinct physical regimes with crossovers between a high-temperature incoherent regime, an intermediate-temperature metallic regime, and a low-temperature insulating regime with a pseudogap created by antiferromagnetic fluctuations.We assess the ability of each method to properly address these physical regimes and crossovers through the computation of several observables probing both quasiparticle properties and magnetic correlations, with two numerically exact methods (diagrammatic and determinantal quantum Monte Carlo methods) serving as a benchmark.By combining computational results and analytical insights, we elucidate the nature and role of spin fluctuations in each of these regimes.Based on this analysis, we explain how quasiparticles can coexist with increasingly longrange antiferromagnetic correlations and why dynamical mean-field theory is found to provide a remarkably accurate approximation of local quantities in the metallic regime.We also critically

arXiv:2006.10769•Physical Review X•Mar 23, 2021•222 citations

Single-particle dispersion and density of states of the half-filled two-dimensional Hubbard model

Gabe Schumm, Shiwei Zhang, Anders W. Sandvik

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 $\mathbf{k}=(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2)$ (the $\mathrm{\ensuremath{\Sigma}}$ points). We find saddle points at $\mathbf{k}=(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi},0),(0,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi})$ (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 $\mathrm{\ensuremath{\Sigma}}$. The fraction of quasiparticle states within the ledge is ${n}_{\mathrm{ledge}}\ensuremath{\approx}0.15$. Upon doping away from half filling, within the rigid-band approximation, these results support Fermi pockets around the $\mathrm{\ensuremath{\Sigma}}$ points, with states around the $X$ points becoming filled only at doping fractions $x\ensuremath{\ge}{n}_{\mathrm{ledge}}$. The high density of states away from the $\mathrm{\ensuremath{\Sigma}}$ gap edge may be an important clue for a finite minimum doping level for superconductivity and other instabilities of doped Mott insulators.

arXiv:2504.02614•Physical review. B./Physical review. B•Jul 29, 2025•5 citations

Quasiparticle dispersion of thet-Jand Hubbard models

Adriana Moreo, Stephan Haas, Anders W. Sandvik +1 more

The spectral weight A(p,\ensuremath{\omega}) of the two-dimensional t-J and Hubbard models has been calculated using exact diagonalization and quantum Monte Carlo techniques, at several densities 0.5\ensuremath{\le}〈n〉\ensuremath{\le}1.0. The photoemission (\ensuremath{\omega}0) region contains two dominant distinct features, namely a low-energy quasiparticle peak with bandwidth of order J, and a broad valence band peak at energies of order t. This behavior persists away from half-filling, as long as the antiferromagnetic correlations are robust. The results give support to theories of the copper oxide materials based on the behavior of holes in antiferromagnets, and they also provide theoretical guidance for the interpretation of experimental photoemission data for the cuprates.

arXiv:cond-mat/9412107•Physical review. B, Condensed matter•May 1, 1995•59 citations

Hole Dynamics in Two-Dimensional Antiferromagnetic Mott Insulators

Fakher F. Assaad, Masatoshi Imada

The dispersion relation of a doped hole in the half-filled 2D Hubbard model is shown to follow a k^4 law around the (0,pi) and (pi,0) points in the Brillouin zone. Upon addition of pair-hopping processes this dispersion relation is unstable towards a k^2 law. The above follows from T=0 Quantum Monte calculations of the single particle spectral function A(k, omega) on 16 X 16 lattices. We discuss finite dopings and argue that the added term restores coherence to charge dynamics and drives the system towards a d_x^2 - y^2 superconductor.

arXiv:cond-mat/9811384•Nov 27, 1998•0 citations

Filling-Control Metal-Insulator Transition in the Hubbard Model Studied by the Operator Projection Method

Shigeki Onoda, Masatoshi Imada

Thermodynamic and dynamical properties of filling-control metal-insulator transition (MIT) in the Hubbard model are studied by the operator projection method, especially in two dimensions. This is a non-perturbative analytic approach to many-body systems. The present theory incorporates the Mott-Hubbard, Brinkman-Rice and Slater pictures of the MIT into a unified framework, together with reproducing low-energy narrow band arising from spin-charge fluctuations. At half filling, single-particle spectra $A(ω, k)$ show formation of two Hubbard bands and their antiferromagnetic shadows separated by a Mott gap in the plane of energy $ω$ and momentum $k$ with lowering temperatures. These four bands produce splitting to two low-energy narrow bands and two SDW-like bands in the dispersion. Near half filling, the low-energy narrow band persists at low temperatures. This narrow band has a particularly weak dispersion and large weights around $(π, 0)$ and $(0, π)$ momenta. The velocity of these low-energy excitations is shown to vanish towards the MIT, indicating the mass divergence as in the Brinkman-Rice picture, but most prominently around $(π,0)$ and $(0,π)$ with strong momentum dependence. This reflects the suppression of the coherence near the MIT. Main structures in $A(ω, k)$ show remarkable similarities to quantum Monte-Carlo results in two dimensions as well as in the one-dimensional Hubbard model. The charge compressibility appears to diverge with decreasing doping concentration in both one and two dimensions in agreement with the exact and quantum Monte-Carlo results. We also discuss implications of the flat dispersion formed near the Fermi level to the observations in high-$\Tc$ cuprate superconductors.

arXiv:cond-mat/0107291•Journal of the Physical Society of Japan•Nov 1, 2001•33 citations

Electronic dynamic Hubbard model: Exact diagonalization study

J. E. Hirsch

A model to describe electronic correlations in energy bands is considered. The model is a generalization of the conventional Hubbard model that allows for the fact that the wave function for two electrons occupying the same Wannier orbital is different from the product of single-electron wave functions. We diagonalize the Hamiltonian exactly on a four-site cluster and study its properties as a function of band filling. The quasiparticle weight is found to decrease and the quasiparticle effective mass to increase as the electronic band filling increases, and spectral weight in one- and two-particle spectral functions is transferred from low to high frequencies as the band filling increases. Quasiparticles at the Fermi energy are found to be more ``dressed'' when the Fermi level is in the upper half of the band (hole carriers) than when it is in the lower half of the band (electron carriers). The effective interaction between carriers is found to be strongly dependent on band filling becoming less repulsive as the band filling increases and attractive near the top of the band in certain parameter ranges. The effective interaction is most attractive when the single-hole carriers are most heavily dressed, and in the parameter regime where the effective interaction is attractive, hole carriers are found to ``undress,'' hence become more like electrons, when they pair. It is proposed that these are generic properties of electronic energy bands in solids that reflect a fundamental electron-hole asymmetry of condensed matter. The relation of these results to the understanding of superconductivity in solids is discussed.

arXiv:cond-mat/0207369•Physical review. B, Condensed matter•Jan 6, 2003•32 citations
The Hubbard model at half-filling is a collective, antiferromagnetic insulator. We study added electrons or holes. The insulating energy gap and the dispersion of the added carriers are calculated variationally in two dimensions with use of a Monte Carlo evaluation of the electronic correlation functions in the insulating phase. Both Eg{\mathit{E}}_{\mathit{g}}Eg​ and m∗{\mathit{m}}^{\mathrm{*}}m∗ are found to be temperature dependent.
The Hubbard model represents the fundamental model for interacting quantum systems and electronic correlations.Using the two-dimensional half-filled Hubbard model at weak coupling as a testing ground, we perform a comparative study of a comprehensive set of state-of-the-art quantum many-body methods.Upon cooling into its insulating antiferromagnetic ground state, the model hosts a rich sequence of distinct physical regimes with crossovers between a high-temperature incoherent regime, an intermediate-temperature metallic regime, and a low-temperature insulating regime with a pseudogap created by antiferromagnetic fluctuations.We assess the ability of each method to properly address these physical regimes and crossovers through the computation of several observables probing both quasiparticle properties and magnetic correlations, with two numerically exact methods (diagrammatic and determinantal quantum Monte Carlo methods) serving as a benchmark.By combining computational results and analytical insights, we elucidate the nature and role of spin fluctuations in each of these regimes.Based on this analysis, we explain how quasiparticles can coexist with increasingly longrange antiferromagnetic correlations and why dynamical mean-field theory is found to provide a remarkably accurate approximation of local quantities in the metallic regime.We also critically
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=4,6U/t=4,6U/t=4,6, we find quadratic dispersion around the gap minimum at wave vectors $\mathbf{k}=(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2)$ (the $\mathrm{\ensuremath{\Sigma}}$ points). We find saddle points at $\mathbf{k}=(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi},0),(0,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi})$ (the XXX points), where the dispersion is approximately quartic, leading to a sharp DOS maximum above the almost flat ledge arising from the states close to $\mathrm{\ensuremath{\Sigma}}$. The fraction of quasiparticle states within the ledge is ${n}_{\mathrm{ledge}}\ensuremath{\approx}0.15$. Upon doping away from half filling, within the rigid-band approximation, these results support Fermi pockets around the $\mathrm{\ensuremath{\Sigma}}$ points, with states around the XXX points becoming filled only at doping fractions $x\ensuremath{\ge}{n}_{\mathrm{ledge}}$. The high density of states away from the $\mathrm{\ensuremath{\Sigma}}$ gap edge may be an important clue for a finite minimum doping level for superconductivity and other instabilities of doped Mott insulators.
The spectral weight A(p,\ensuremath{\omega}) of the two-dimensional t-J and Hubbard models has been calculated using exact diagonalization and quantum Monte Carlo techniques, at several densities 0.5\ensuremath{\le}〈n〉\ensuremath{\le}1.0. The photoemission (\ensuremath{\omega}0) region contains two dominant distinct features, namely a low-energy quasiparticle peak with bandwidth of order J, and a broad valence band peak at energies of order t. This behavior persists away from half-filling, as long as the antiferromagnetic correlations are robust. The results give support to theories of the copper oxide materials based on the behavior of holes in antiferromagnets, and they also provide theoretical guidance for the interpretation of experimental photoemission data for the cuprates.
The dispersion relation of a doped hole in the half-filled 2D Hubbard model is shown to follow a k^4 law around the (0,pi) and (pi,0) points in the Brillouin zone. Upon addition of pair-hopping processes this dispersion relation is unstable towards a k^2 law. The above follows from T=0 Quantum Monte calculations of the single particle spectral function A(k, omega) on 16 X 16 lattices. We discuss finite dopings and argue that the added term restores coherence to charge dynamics and drives the system towards a d_x^2 - y^2 superconductor.
Thermodynamic and dynamical properties of filling-control metal-insulator transition (MIT) in the Hubbard model are studied by the operator projection method, especially in two dimensions. This is a non-perturbative analytic approach to many-body systems. The present theory incorporates the Mott-Hubbard, Brinkman-Rice and Slater pictures of the MIT into a unified framework, together with reproducing low-energy narrow band arising from spin-charge fluctuations. At half filling, single-particle spectra A(ω,k)A(ω, k)A(ω,k) show formation of two Hubbard bands and their antiferromagnetic shadows separated by a Mott gap in the plane of energy ωωω and momentum kkk with lowering temperatures. These four bands produce splitting to two low-energy narrow bands and two SDW-like bands in the dispersion. Near half filling, the low-energy narrow band persists at low temperatures. This narrow band has a particularly weak dispersion and large weights around (π,0)(π, 0)(π,0) and (0,π)(0, π)(0,π) momenta. The velocity of these low-energy excitations is shown to vanish towards the MIT, indicating the mass divergence as in the Brinkman-Rice picture, but most prominently around (π,0)(π,0)(π,0) and (0,π)(0,π)(0,π) with strong momentum dependence. This reflects the suppression of the coherence near the MIT. Main structures in A(ω,k)A(ω, k)A(ω,k) show remarkable similarities to quantum Monte-Carlo results in two dimensions as well as in the one-dimensional Hubbard model. The charge compressibility appears to diverge with decreasing doping concentration in both one and two dimensions in agreement with the exact and quantum Monte-Carlo results. We also discuss implications of the flat dispersion formed near the Fermi level to the observations in high-$\Tc$ cuprate superconductors.
A model to describe electronic correlations in energy bands is considered. The model is a generalization of the conventional Hubbard model that allows for the fact that the wave function for two electrons occupying the same Wannier orbital is different from the product of single-electron wave functions. We diagonalize the Hamiltonian exactly on a four-site cluster and study its properties as a function of band filling. The quasiparticle weight is found to decrease and the quasiparticle effective mass to increase as the electronic band filling increases, and spectral weight in one- and two-particle spectral functions is transferred from low to high frequencies as the band filling increases. Quasiparticles at the Fermi energy are found to be more ``dressed'' when the Fermi level is in the upper half of the band (hole carriers) than when it is in the lower half of the band (electron carriers). The effective interaction between carriers is found to be strongly dependent on band filling becoming less repulsive as the band filling increases and attractive near the top of the band in certain parameter ranges. The effective interaction is most attractive when the single-hole carriers are most heavily dressed, and in the parameter regime where the effective interaction is attractive, hole carriers are found to ``undress,'' hence become more like electrons, when they pair. It is proposed that these are generic properties of electronic energy bands in solids that reflect a fundamental electron-hole asymmetry of condensed matter. The relation of these results to the understanding of superconductivity in solids is discussed.