Single-particle spectral function of the Holstein-Hubbard bipolaron

Martin Hohenadler, Markus Aichhorn, and Wolfgang von der Linden

Phys. Rev. B 71, 014302 – Published 14 January 2005

Abstract

The one-electron spectral function of the Holstein-Hubbard bipolaron in one dimension is studied using cluster perturbation theory together with the Lanczos method. In contrast to other approaches, this allows one to calculate the spectrum at continuous wave vectors and thereby to investigate the dispersion and the spectral weight of quasiparticle features. The formation of polarons and bipolarons, and their manifestation in the spectral properties of the system, is studied for the cases of intermediate and large phonon frequencies, with and without Coulomb repulsion. A good agreement is found with the most accurate calculations of the bipolaron band dispersion available. Pronounced deviations of the bipolaron band structure from a simple tight-binding band are observed, which can be attributed to next-nearest-neighbor hopping processes.

Received 25 May 2004

DOI:https://doi.org/10.1103/PhysRevB.71.014302

Authors & Affiliations

Martin Hohenadler^*, Markus Aichhorn, and Wolfgang von der Linden

Institute for Theoretical and Computational Physics, Graz University of Technology, Petersgasse 16, 8010 Graz, Austria

^*Electronic address: hohenadler@itp.tugraz.at

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Vol. 71, Iss. 1 — 1 January 2005

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Images

Figure 1
(Color online) Spectral functions $A_{↑} (k, ϵ)$ (solid lines) and $A_{↓} (k, ϵ)$ (dashed lines) calculated with CPT for different values of the el-ph coupling $λ$ , using $η = 0.05 t$ [see Eq. (5)]. All other parameters as indicated in the figures. The truncation errors are $Δ <$ (a) $5.3 \times 10^{- 6}$ , (b) $1.0 \times 10^{- 5}$ , (c) $2.4 \times 10^{- 7}$ , (d) $6.7 \times 10^{- 6}$ (see text). The vertical lines correspond to VDM results for the polaron and bipolaron band dispersions $E^{↑} (0) + E^{↑} (k)$ (dashed) and $E^{↑ ↓} (k)$ (solid), respectively (Ref. 44).Reuse & Permissions
Figure 2
(Color online) Density plot of the spectral function $A_{↑} (k, ϵ)$ for $\bar{ω} = 4.0$ , $\bar{U} = 0$ , and $λ = 0.5$ , as shown in Fig. 1a. The symbols correspond to VDM results for $E^{↑} (0) + E^{↑} (k)$ (squares) and $E^{↑ ↓} (k)$ (crosses), respectively (Ref. 44).Reuse & Permissions
Figure 3
(Color online) Spectral functions $A_{↑} (k, ε)$ (solid lines) and $A_{↓} (k, ε)$ (dashed lines) calculated with CPT for different values of the el-ph coupling $λ$ , using $η = 0.05 t$ . All other parameters as indicated in the figures. The truncation errors are $Δ <$ (a) $9.1 \times 10^{- 5}$ , (b) $9.0 \times 10^{- 5}$ , (c) $1.2 \times 10^{- 7}$ , (d) $2.4 \times 10^{- 6}$ . The vertical lines correspond to variational diagonalization results for the polaron and bipolaron band dispersions $E^{↑} (0) + E^{↑} (k)$ (dashed) and $E^{↑ ↓} (k)$ (solid), respectively (Ref. 44).Reuse & Permissions
Figure 4
(Color online) Spectral functions $A_{↑} (k, ϵ)$ (solid lines) and $A_{↓} (k, ϵ)$ (dashed lines) calculated with CPT for different values of the el-ph coupling $λ$ , using $η = 0.05 t$ . All other parameters as indicated in the figures. The truncation errors are $Δ <$ (a) $3.3 \times 10^{- 5}$ , (b) $2.0 \times 10^{- 5}$ , (c) $9.9 \times 10^{- 6}$ , (d) $6.7 \times 10^{- 7}$ . The vertical lines correspond to variational diagonalization results for the polaron and bipolaron band dispersions $E^{↑} (0) + E^{↑} (k)$ (dashed) and $E^{↑ ↓} (k)$ (solid), respectively (Ref. 44).Reuse & Permissions
Figure 5
Comparison of the spectral function $A_{↑} (0, ϵ)$ calculated with ED and CPT, respectively, for different cluster sizes $N$ , using $η = 0.05 t$ . The crosses correspond to the VDM result for the bipolaron energy $E^{↑ ↓} (0)$ (Ref. 44).Reuse & Permissions
Figure 6
Bipolaron dispersion $E^{↑ ↓} (k)$ as a function of the wave vector $k$ (Ref. 44). Also shown is the bare tight-binding dispersion for nearest-neighbor hopping, and a fit to the results for $\bar{U} = 4$ , $λ = 0.5$ using a dispersion for nearest- and next-nearest-neighbor hopping (see text). All curves have been scaled to the interval [−1,0], with the actual bandwidths given in the legend.Reuse & Permissions

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