Enhanced carrier binding and bond correlations in the Hubbard-Su-Schrieffer-Heeger model with dispersive optical phonons

Abstract

Electron-phonon (e-ph) interactions play a crucial role in determining many properties of materials. In this context, the Su-Schrieffer-Heeger (SSH) model, where atomic motion modulates the electronic hopping, has gained significant attention due to its potential for strong electron pairing in relation to high-Tc superconductivity. Previous studies of the SSH models have addressed many aspects of this problem, but have focused heavily on either dilute or half-filled models with dispersionless (Einstein) phonons. Here, we study the effects of dispersive optical phonons on the lightly doped one-dimensional optical Hubbard-SSH model using the density matrix renormalization group. We observe a significant enhancement in singlet binding driven by phonon dispersion; however, by calculating various correlation functions, we find that the enhanced binding does not translate to increased superconducting correlations but rather robust bond correlations in the studied parameter regime. Nevertheless, the significant impact of phonon dispersion on these correlations highlights the need to go beyond the Einstein phonon limit while modeling realistic quantum materials.

Figures (4)

• Figure 1: (a) Phonon dispersion of the optical branch with different values of $\Omega^{\prime}/\Omega$. (b) Ground state expectation values of the lattice distortion for the doped HSSH model for the same values of $\Omega^{\prime}/\Omega$ as in panel (a). (c-d) Binding energy $\mathrm{\Delta_{\mathrm{b}}}$ as a function of $\Omega^{\prime}/\Omega$ for the HSSH and HH models. All results were obtained for an $L=90$ site 1D chain with $U=8t$, $\Omega=t$, $g=0.4$ (HSSH), $g=1.13$ (HH), (b-c) $\rho = 6.67\%$, and (d) $N=2$, with different values of $\Omega^{\prime}/\Omega$ as indicated.
• Figure 2: Dynamical spin structure factor $S(q,\omega)$ for the doped HSSH model with dispersive optical phonons calculated for an $L=30$ sites 1D chain with $U=8t$, $\Omega=t$, $\rho = 6.67\%$ with different values of $g$ and $\Omega^{\prime}/\Omega$ as indicated.
• Figure 3: (a) Finite size scaling of the spin $\mathrm{\Delta_{spin}}$ and charge $\mathrm{\Delta_{charge}}$ gaps as a function of cluster size $L$. (b)-(g) Ground state expectation values and correlations functions obtained on an $L=90$ site chain. All results were obtained for $U=8t$, $\Omega=t$, $g=0.4$, $\rho = 6.67\%$, and with varying $\Omega^{\prime}/\Omega$ as indicated in the legend of panels (a), (d), and (g). Panel (b) plots the average electron density, (c) the expectation of double occupancy, (d) spin-spin, (e) density-density, (f) bond-bond, and (g) singlet/triplet correlation functions. The correlation functions in panels (d)-(g) are plotted as a function of $r = j-c$ measured from the chain's center site $c$ and plotted on a log-log scale.
• Figure 4: (a) Binding energy of the HSSH model as a function of hole doping $\rho$. (b-e) Bond-bond, singlet, and triplet correlation functions as a function of distance $r$ from the center site, plotted on a log-log scale, for different values of $\rho$ as indicated in each panel. All the results are calculated for an $L=90$ site chain with $U=8t$, $\Omega=t$, $g=0.4$ and $\Omega^{\prime}/\Omega=0.1$. (f) Power-law exponents for bond, singlet, and triplet correlations as a function of $\Omega^{\prime}/\Omega$ for $\rho=6.67\%$.