Quantum spin liquid from electron-phonon coupling

Abstract

A quantum spin liquid (QSL) is an exotic insulating phase with emergent gauge fields and fractionalized excitations. However, the unambiguous demonstration of the existence of a QSL in a "non-engineered" microscopic model (or in any material) remains challenging. Here, using numerically-exact sign-problem-free quantum Monte Carlo simulations, we show that a QSL arises in a non-engineered electron-phonon model. Specifically, we investigate the ground-state phase diagram of the bond Su-Schrieffer-Heeger (SSH) model on a 2D triangular lattice at half filling (one electron per site) which we show includes a QSL phase which is fully gapped, exhibits no symmetry-breaking order, and supports deconfined fractionalized holon excitations. This suggests new routes for finding QSLs in realistic materials and high-$T_c$ superconductivity by lightly doping them.

Figures (10)

• Figure 1: Zero-temperature phase diagram of the SSH electron-phonon model at half-filling on triangular lattice with varying EPC strength $\lambda$ and phonon frequency $\omega_0$, obtained from state-of-the-art QMC simulations. Here SC, sVBS, iVBS, and QSL denote superconducting, staggered VBS, incommensurate VBS, and quantum spin liquid, respectively. The QSL to SC transition is shown to be continuous and consistent with XY* universality, while the transition to the sVBS is first order over at least a portion of its extent.
• Figure 2: QMC results on the triangular lattice with size $L\times L$. (a) The correlation-length ratio for superconducting order as a function of $\omega_0$ with fixed $\lambda=2.16$. The crossing point for different system sizes indicates the transition point between SC disordered and ordered phases occurs at $\omega_0 \approx 1.2$. (b) The Binder ratio for sVBS order as a function of $\omega_0$ with fixed $\lambda=2.16$. The transition between sVBS disordered and ordered phases occurs at $\omega_0 \approx 0.7$.
• Figure 3: (a) Finite-size-scaling results of single-particle gap and spin gap in the QSL phase for $\lambda=2.16$ and $\omega_0 = 1.0$. Both single-particle and spin gaps are finite, confirming the nature of a gapped Mott insulating phase in the QSL regime. (b-d) QMC results for two holes doped away from half filling. We add large on-site impurity potential $V=30$ on two separated sites in the lattice to trap the doped holes. The EPC strength $\lambda=2.94$ and two representative values of $\omega_0$ (VBS for $\omega_0=0.6$ and QSL for $\omega_0=1.8$) are considered. The system size in the simulation is $L_x \times 8$. The following observable is considered in the simulation: (b) The correlation of hole density in the regimes around the two impurity potentials. (c) The correlation of $S^z$ in the regimes around the two impurity potentials. (d) The energy difference between the state of $N-2$ electrons with and without large impurity potentials.
• Figure 4: A schematic representation of the RK wave function on the triangular lattice. Each dimer represents two electrons occupying the bonding orbital between two neighboring sites.
• Figure S1: The results for VBS order and structure factor at adiabatic limit $\omega_0=0$. (a) The peak value of VBS structure factor at the corresponding ordering momentum ${\boldsymbol{q}}_{\mathrm{max}}$ as the function of $\lambda$. (b) The magnitude of ${\boldsymbol{q}}_{\mathrm{max}}$ in multiple of $\pi$ as the function of coupling strength $\lambda$. (c) The maximum difference of phonon displacement $\Delta X$ as the function of $\lambda$.