Polarization-Driven Charge Frustration and Emergent Phases in the One-Dimensional Extended Hubbard Model

Abstract

Frustration is a key driver of exotic quantum phases, yet its role in charge dynamics remains largely unexplored. We show that charge frustration - induced by electronic polarization effects - stabilizes unconventional insulating states in the one-dimensional extended Hubbard model. Using exact diagonalization and density-matrix renormalization group, we uncover a charge-disordered phase that remains insulating despite lacking long-range order and possessing an effectively attractive on-site interaction - a behavior reminiscent of gapful spin liquids in frustrated spin systems. We also identify a fragile ferroelectric phase and a charge-density-wave state with emergent eight-site periodicity. These findings establish charge frustration, driven by charge-dipole interactions, as a robust mechanism for realizing exotic phases in low-dimensional correlated systems, with implications for organic conductors, transition-metal oxides, and ultracold polar molecules.

Figures (5)

• Figure 1: Phase diagram of the system \ref{['eq1']} in the atomic limit ($t=0$) within the ($V/U$, $P/U$) parameter space. The schematic electron configurations for each phase are illustrated, assuming an infinitesimally small $t$ to indicate the corresponding spin configurations. The FE, CDW I, and CDW III states are energetically degenerate along the dashed line.
• Figure 2: Ground-state phase diagrams of the model in Eq. \ref{['eq1']} for four values of $U/t$, plotted in the $(V/U, P/U)$ plane. Solid symbols denote phase boundaries determined via level-crossing analysis, while open symbols are obtained from DMRG. In (a), transitions of the same type are shown in the same color. Arrows in (b–d) indicate parameter paths used for analysis in subsequent sections.
• Figure 3: DMRG results for the FE state. (a) Charge density distribution at large and moderate $U/t$. (b, c) FE order parameter as a function of $t/U$ and $P/U$, respectively; the parameter path for (c) is shown in Fig. \ref{['fig2']}(d). (d) Local spin profile $\langle S_i^z \rangle$ for representative parameters. All parameters are given in the figure.
• Figure 4: DMRG results for the SDW and CDI phases. (a) Charge gap $\Delta_{\rm c}/t$ as a function of $V/U$; the parameter path for (a,b,d) is shown in Fig. \ref{['fig2']}(b). (b) Central charge $c$ versus $V/U$, with open circles marking the peak positions used for finite-size extrapolation. (c) Finite-size scaling analysis of the Tomonaga-Luttinger parameter $K_\rho$ within the CDI phase. (d) Double occupancy $\langle n_{i,\uparrow} n_{i,\downarrow} \rangle$ versus $V/U$, highlighting the transition from SDW to CDI phases. (e) Charge structure factor $\widetilde{C}(q)$ computed in the CDI phase; inset shows $\widetilde{C}(0)/N$ versus $1/N$. (f) Log-log plot of the spin-spin correlation function $|\langle S_i^z S_{i+r}^z \rangle|$ within the CDI phase. All parameters are given in the figure.
• Figure 5: DMRG results for the CDW III phase. (a) Charge structure factor $C(q)$ and (b) finite-size scaling of the normalized peak height at $q=3\pi/4$. (c) Density-density correlations. (d) Finite-size scaling of the CDW III order parameter. (e) Finite-size scaling of the spin gap. (f) Charge order parameter $\rho$ versus $P/U$; the parameter path for (f) is shown in Fig. \ref{['fig2']}(c). All parameters are given in the figure.