Ultrabosonic behavior in photoexcited one-dimensional Mott insulators in the region of weak intersite Coulomb interaction

This paper reports a unique behavior expected for the optical excitations in one-dimensional Mott insulators. When the intersite Coulombic attraction does not work between two elementary charge excitations, i.e., a doublon and a holon, the lowest optical excitations are described as an unbound pair of them, still having finite mutual correlation due to the forbidden double occupancy on the same site. We find that, in such a situation, the pairs obey a particle statistics that exceeds that of ordinary bosons. This feature appears most directly in the enhancement factor of the matrix element for the pair photocreation. We discuss the possible mechanism for this ultrabosonic behavior and also demonstrate that this behavior is maintained even if we include a small amount of interiste Coulomibic interaction. Lastly, this enhancement factor almost coincides with that for ordinary bosons when the degree of the intersite interaction exceeds a certain value that switches on the formation of a bound doublon-holon pair.

Figure 1

(a) One-photon optical conductivity, $\sigma \left(\omega \right)$, calculated by the charge model with $(U,V)/T=(10,0)$ and $N=16$. The broadening factor $\gamma$ is $0.02T$. (b)–(h) Two-photon optical conductivity (red curve), ${\sigma }^{\left(2\right)}\left(\omega \right)$, with $\sigma \left(\omega \right)$ (green curve). In each spectrum of ${\sigma }^{\left(2\right)}\left(\omega \right)$, the initial state is the state that corresponds to each peak of (a), as shown by the arrows. (i) Schematic for the two spectra.

Figure 2

(a) Matrix elements for $N=16$. Upper and lower dashed curves follow $Csin(\pi k^{\prime }/(N/2))$, with $C=\pi \sqrt{2}$ and $2\sqrt{2}$, respectively. (b), (c) Fitting and extrapolations toward infinite $N$, with $k=N/4$. (d) Effective spectrum $S\left(\omega \right)$ (blue), $\omega \sigma \left(\omega \right)$ (green), and their difference (red).

Figure 3

Evaluation of ${\beta }^2$ values using (a) the minimum model and (b) the full model. The model parameters are $(U,V)/T=(10,0)$ commonly.

Figure 4

(a) Evaluation of ${\beta }^2$ values using approximate functions and the minimum model for $(U$, $V)/T=(10,3)$. The solid line is based on the simplest type of exciton function, while the exciton function is explicitly determined for circles. The squares show the results of the minimum model. (b) The evaluation of ${\beta }^2$, using approximate eigenfunctions for various $V/T$ values. The system size is $N=60$, 100, 200, and 400, and $U/T$ is fixed at 10.

Figure 5

Case of excitations from a two-DH-pair state to a three-DH-pair state. In (a), $N$ is chosen as $N=16$, 20,..., 44, and 48, from left to right.

Figure 6

Example of the number used in Eq. (A1). In this example, ($M=3)$, $\tau$ is $0+1+3=4$.

Figure 7

$N=16$, $U=10T$, $V=0$, $\gamma =0.1T$. Blue lines in (a)–(h) are $\omega \sigma \left(\omega \right)$ of the half-filled Hubbard model. Green lines in (b)–(h) are $\omega {\sigma }^{\left(2\right)}\left(\omega \right)$ of the half-filled Hubbard model. Red lines are $\omega \sigma \left(\omega \right)$ in (a) and $\omega {\sigma }^{\left(2\right)}\left(\omega \right)$ in (b)–(h) of the charge model ($M_{\max }=8$). Initial states of calculating $\omega {\sigma }^{\left(2\right)}\left(\omega \right)$ in (b)–(h) are corresponding excited states at the peaks of $\omega \sigma \left(\omega \right)$ in (a).

Figure 8

Details of the extrapolation $k=N/4$. The lines are for $N=16$, 20, 24,..., 40, and 48, from left to right.

Figure 9

Details of the extrapolation for (a)–(c) $k=N/8$ with $N=16$, 24, 32, 40, and 48, and (d) and (e) for the lowest $k$ at each $N$ ($k=1)$.

Figure 10

Extrapolation of the absolute value of the non-zero off-diagonal matrix element, $m_{10}$.

Figure 11

Details of the analysis using the minimum model for excitation at $k=N/8$. (a) Spectra for $N=48$ with $(U$, $V)/T=(10,0)$ and $\gamma =0.02T$. The three peak energies of $\omega \sigma \left(\omega \right)$, $e1\sim e3$, are defined in the main text. (b) Extrapolation of the intensity ratio toward infinite $N$.

Figure 12

Spectra of the full model with ($U$, $V)/T=(10,0)$. The other parameters are $N=20$ and $\gamma =0.02T$. $e1\sim e3$ are defined in the main text. The integrated intensities in $\left[(e1+e2)/2,(e2+e3)/2\right]$ are used to obtain Fig. 3 in the main text.

Figure 13

Details of the extrapolation using the minimum model with $(U,V)/T=(10,3)$. (a) Dependence of the intensity ratio on the $\gamma$ value. (b) Spectra for $N=200$.