Fate of Spinons at the Mott Point

Gapless spin liquids have recently been observed in several frustrated Mott insulators, with elementary spin excitations—“spinons”—reminiscent of degenerate Fermi systems. However, their precise role at the Mott point, where charge fluctuations begin to proliferate, remains controversial and ill understood. Here we present the simplest theoretical framework that treats the dynamics of emergent spin and charge excitations on the same footing, providing a new physical picture of the Mott metal-to-insulator transition at half filing. We identify a generic orthogonality mechanism leading to strong damping of spinons, arising as soon as the Mott gap closes. Our results indicate that spinons should not play a significant role within the high-temperature quantum critical regime above the Mott point—in striking agreement with all available experiments.

Figure 1

Proposed scheme to blend the static resonating valence bond (RVB) approach with the DMFT, using an impurity solver based on emergent spinon degrees of freedom. The spinon self-energy ${\mathrm{\Sigma }}_f(i\omega )$, usually absent from a mean-field RVB treatment, is extracted from a spinon-based DMFT framework. Using the RVB self-consistent determination of the spinon bandwidth $J_{\text{eff}}$, this in turn allows one to incorporate feedback effects due to scattering on charge excitations, which affect the gapless spin excitations in the Mott state.

Figure 2

Upper panel: electronic density of states across the Mott transition for $T=0.005D$ and $J/D=0.2$, with increasing values of the Coulomb interaction $U/D=1$, 2, 3. Lower panel: corresponding specific heat as a function of temperature. A striking linear in temperature contribution remains in $C_V$ at $U/D=3$, while quasiparticles have disappeared from the density of states in the Mott phase.

Figure 3

Phase diagram for $J/D=0.1$ (upper panel) and $J/D=0.4$ (lower panel) as a function of Coulomb strength $U/D$ and temperature $T/D$. Continuous lines denote the metal-insulator boundaries, and dashed lines indicate the true first-order transition based on the free energy. Also, the region bounded by dots shows the low-temperature onset of the spinon Fermi surface in the Mott insulator. The shaded region indicates that $J_{\text{eff}}^{\text{metal}}=0$ for the metallic state within the whole coexistence region. This demonstrates that spinons are only well-defined quasiparticles in the low-temperature Mott phase, and are never stable in the metal.

Figure 4

Frequency-dependent spinon self-energy ${\mathrm{\Sigma }}_f(i{\omega }_n)$ at temperature $T=0.005D$ for $U/D=1$ (metal) and $U/D=3$ (insulator). The strong enhancement in the metal is due to an x-ray edge effect, which is a hallmark of the spinon spectral density.