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Disorder-induced localisation in the Mott-Hubbard model

Ričards Kristers Knipšis, Friedemann Queisser, Jesumony Jayabalan, Gael Reecht, Manuel Gruber, Uwe Bovensiepen, Ralf Schützhold

Abstract

For the Fermi-Hubbard model in the Mott insulator phase, we employ the hierarchy of correlations to study how doublon and holon quasi-particle excitations are affected by adding disorder to the system. We study two types of disorder: charge disorder, in the form of on-site potential randomness; and spin disorder, in the form of a fixed, randomly generated background spin arrangement. By analysing the quasi-particle eigen-spectra and quantifying the degree to which the corresponding eigen-states localise, we find both an energetic and spatial separation between localised and delocalised states in the charge disorder. In contrast, the spin disorder results in localised states throughout the quasi-particle bands. Finally, we repeat our calculations using strong-coupling perturbation theory, and compare the results obtained from both methods.

Disorder-induced localisation in the Mott-Hubbard model

Abstract

For the Fermi-Hubbard model in the Mott insulator phase, we employ the hierarchy of correlations to study how doublon and holon quasi-particle excitations are affected by adding disorder to the system. We study two types of disorder: charge disorder, in the form of on-site potential randomness; and spin disorder, in the form of a fixed, randomly generated background spin arrangement. By analysing the quasi-particle eigen-spectra and quantifying the degree to which the corresponding eigen-states localise, we find both an energetic and spatial separation between localised and delocalised states in the charge disorder. In contrast, the spin disorder results in localised states throughout the quasi-particle bands. Finally, we repeat our calculations using strong-coupling perturbation theory, and compare the results obtained from both methods.
Paper Structure (12 sections, 13 equations, 11 figures)

This paper contains 12 sections, 13 equations, 11 figures.

Table of Contents

  1. Introduction
  2. Setup
  3. Hierarchy of correlations
  4. Factorised equations of motion
  5. Charge disorder
  6. Square and honeycomb lattices
  7. Spin-fixed background
  8. Combined disorder
  9. Perturbation theory in $T/U$
  10. Charge disorder
  11. Spin-fixed background
  12. Conclusions and Outlook

Figures (11)

  • Figure 1: Holon and doublon quasi-particle excitation eigen-energy spectra obtained using the hierarchy of correlations for the hexagonal lattice with charge disorder at $r=26\%$ for (a) $V=0.00$ eV (b) $V=-0.10$ eV (c) $V=-0.20$ eV.
  • Figure 2: Holon (blue) and doublon (red) eigen-energy spectra for charge disordered hexagonal lattice with $V=-0.20$ eV and $r=26\%$. The shading visualises the proportion of localised states, with darker colours corresponding to more localised states.
  • Figure 3: Illustrations of selected holon eigen-states in the charge disordered hexagonal lattice. Dark outline corresponds to sites with on-site energy $V_{\mu} = V=-0.20$ eV, light outline corresponds to $V_{\mu} = 0$. The states have eigen-energies (a) $E\approx -0.315$ eV (bottom of doped holon sub-band) (b) $E\approx -0.161$ eV (top of doped holon sub-band) (c) $E\approx -0.031$ eV (middle of undoped holon sub-band).
  • Figure 4: Normalised distributions of the participation ratio for different lattice sizes in the case of charge disorder characterised by $V=-0.20$ eV and $r=26\%$.
  • Figure 5: Holon (blue) and doublon (red) eigen-energy spectra for charge disordered (a) square and (b) honeycomb lattices with $V=-0.20$ eV and $r=26\%$. The shading visualises the proportion of localised states, with darker colours corresponding to more localised states.
  • ...and 6 more figures