Photoemission spectra of many-polaron systems

The crossover from low to high carrier densities in a many-polaron system is studied in the framework of the one-dimensional spinless Holstein model, using unbiased numerical methods. Combining a novel quantum Monte Carlo approach and exact diagonalization, accurate results for the single-particle spectrum and the electronic kinetic energy on fairly large systems are obtained. A detailed investigation of the quality of the Monte Carlo data is presented. In the physically most important adiabatic intermediate electron-phonon coupling regime, for which no analytical results are available, we observe a dissociation of polarons with increasing band filling, leading to normal metallic behavior, while for parameters favoring small polarons, no such density-driven changes occur. The present work points toward the inadequacy of single-polaron theories for a number of polaronic materials such as the manganites.

Figure 1

One-electron spectral function $A(k,\omega -\mu )$ from QMC for different band fillings $n$, $N=32$, $\beta t=8$, ${\overline{\omega }}_0=0.4$, and weak coupling $\lambda =0.1$.

Figure 2

One-electron density of states $\rho (\omega -\mu )$ from QMC for different band fillings $n$, $N=32$, $\beta t=8$, ${\overline{\omega }}_0=0.4$, and $\lambda =0.1$.

Figure 3

One-electron spectral function $A(k,\omega -\mu )$ from QMC for different band fillings $n$, $N=32$, $\beta t=8$, ${\overline{\omega }}_0=0.4$, and strong coupling $\lambda =2.0$.

Figure 4

Dispersion of the polaron band in $A(k,\omega -\mu )$ for $n=0.05$, $N=20$, and $\beta t=10$ (drawn to a larger scale as compared to Fig. 3). All other parameters as in Fig. 3.

Figure 5

One-electron density of states $\rho (\omega -\mu )$ from QMC for different band fillings $n$ and cluster sizes $N$, $\beta t=8$, ${\overline{\omega }}_0=0.4$, and $\lambda =2.0$.

Figure 6

One-electron spectral function $A(k,\omega -\mu )$ from QMC for different band fillings $n$ and cluster sizes $N$, $\beta t=8$, ${\overline{\omega }}_0=0.4$, and intermediate coupling $\lambda =1.0$.

Figure 7

(Color online) One-electron density of states $\rho (\omega -\mu )$ from QMC for different band fillings $n$, cluster sizes $N$, and inverse temperatures $\beta$. Here ${\overline{\omega }}_0=0.4$ and $\lambda =1.0$.

Figure 8

(Color online) One-electron spectral functions $A^{-}(k,\omega )$ (dot-dashed lines) and $A^{+}(k,\omega )$ (thin solid lines) from ED for different band fillings $n$, $N=10$, ${\overline{\omega }}_0=0.4$, and intermediate coupling $\lambda =1.0$. Also shown are the integrated spectral weights of $A^{-}$ and $A^{+}$ (dashed lines), as well as $A(k,\omega )$ from QMC for $N=10$ and $\beta t=8$ (thick solid lines).

Figure 9

(Color online) Comparison of the integrated spectral weight obtained from the QMC and ED data of Fig. 8a for three different momenta $k$.

Figure 10

(Color online) One-electron spectral functions $A^{-}(k,\omega )$ and $A^{+}(k,\omega )$ from ED for $N=10$, ${\overline{\omega }}_0=4.0$, and $\lambda =2.0$. Here $n=0.1$ ($A^{-}$: dashed two-dotted lines, $A^{+}$: dotted lines) and $n=0.3$ ($A^{-}$: dot-dashed lines, $A^{+}$: solid lines). Dashed lines correspond to the integrated spectral weight of $A^{-}(k,\omega )$ and $A^{+}(k,\omega )$, respectively.

Figure 11

Normalized kinetic energy as a function of EP coupling $\lambda$ for different band fillings $n$ and adiabatic ratios ${\overline{\omega }}_0$. Also shown are the results for a single polaron, obtained with the method of Ref. 28. Error bars are smaller than the symbols used and $\Delta \tau =0.05$.

Figure 12

Average sign ⟨sign⟩ [Eq. (A24)] of the fermionic weight $w_{\mathrm{f}}$ as a function of electron-phonon coupling $\lambda$ in one dimension (a) for different inverse temperatures $\beta$, and (b) for different values of the adiabatic ratio ${\overline{\omega }}_0$. Here and in subsequent figures, $\Delta \tau =0.05$, lines are guides to the eye only, and error bars are suppressed if smaller than the symbols shown.

Figure 13

Average sign as a function of (a) band filling $n$, and (b) system size $N$.