Metallic states induced by quantum lattice fluctuations

We developed a tractable many-body theory in which quantum lattice fluctuations beyond the adiabatic approximation, as well as electronic fluctuations, can be described. A many-body wave function is constructed by the superposition of direct products of Slater determinants for the electrons and the coherent states of phonons. The method was applied to a one-dimensional electron system with Su-Schrieffer-Heeger electron-phonon coupling. We show that, in the heavily doped regime, the quantum lattice fluctuations due to the collective motion of charged solitons cause a power-law singularity in the wave-number dependence of the electron density $n_k$ at the Fermi wave number $k=k_F$. This indicates that a metallic state is induced by heavy doping, and it is a Tomonaga-Luttinger liquid. The current results can solve a long-standing problem for the electronic state of heavily doped polyacetylene, the coexistence of Pauli paramagnetism along with a strong infrared-active light absorption.

Figure 1

Lattice structures for three of the five coherent states superposed to generate the wave function at half filling.

Figure 2

Lattice and electronic structures for three of the five coherent states superposed to generate the wave function at $N=198$ and $N_e=194$.

Figure 3

Alternating components of the lattice structure (upper panel), and alternating and net components of the charge density (middle and lower panels, respectively) with $N=198$ and $N_e=194$. The coherent states and Slater determinants in Fig. 2 are decomposed.

Figure 4

Alternating components of the lattice structure for all five configurations. We focus on the lattice points where the $\mathrm{A}Q$ value changes sign.

Figure 5

Alternating components of the lattice structure and charge density (left panels), overall and rescaled net components of the charge density (upper and middle panels right, respectively), and the spin density (right bottom panel) at $N=198,N_e=166$.

Figure 6

Doping dependence of $n_k$ for $N=198$. $k_F$ is given by $\frac{N_e\pi }{2N}$.

Figure 7

Size dependence of the absolute values of the first-order (a) and second-order (b) derivatives of $n_k$ at $k=k_F$ for $U=V=0$.

Figure 8

Lattice and electronic structures of three of the five coherent states superposed to generate the wave function for $(U,V)=(1.0,0.5)$ at $N=198$ and $N_e=194$.

Figure 9

Size dependence of the absolute values of the first-order (a) and second-order (b) derivatives of $n_k$ at $k=k_F$ for $(U,V)=(1.0,0.5)$.

Figure 10

$|k_F-k|$ dependence of $|n_{k_F}-n_k|$ for $N=198,N_e=166$, and $(U,V)=(1.0,0.5)$ in log-log scale.

Figure 11

Doping dependence of $|\frac{d^2{n}_k}{d{k}^2}{|\left(\mathrm{\Delta }k\right)}^2$ at $k=k_F$ for $(U,V)=(1.0,0.5)$ and $N=198$.

Figure 12

Schematic representation of the mechanism for the closing of the gap by quantum fluctuations due to charged lattice solitons.

Figure 13

$N_S$ dependence of $n_k$ for $(U,V)=(1.0,0.5)$ and $N_e=178$.