Emergent Fermi-liquid-like phase by melting a holon Wigner crystal in a doped Mott insulator on the kagome lattice

The doped quantum spin liquid on the kagome lattice provides a fascinating platform to explore exotic quantum states, such as the reported holon Wigner crystal at low doping. By extending the doping range to $δ= 0.027$ - $0.36$, we study the kagome-lattice $t$-$J$ model using the state-of-the-art density matrix renormalization group calculation. On the $L_y=3$ cylinder ($L_y$ is the number of unit cells along the circumference direction), we establish a quantum phase diagram with increasing doping level. In addition to the charge density wave (CDW) states at lower doping, we find an emergent Fermi-liquid-like phase by melting the holon Wigner crystal at $δ\approx 0.15$, which is characterized by suppression of charge density oscillation and power-law decay of various correlation functions. On the wider $L_y = 4$ cylinder, the bond-dimension extrapolated correlation functions also support such a Fermi-liquid-like state, suggesting its stability with increasing system size. In a narrow doping range near $δ= 1/3$ on the $L_y = 3$ cylinder, we find a state with an exponential decay of single-particle correlation but the other correlation functions preserving the features in the Fermi-liquid-like phase, which may be a precursor of a superconducting state. Nevertheless, this peculiar state near $δ= 1/3$ disappears on the $L_y = 4$ cylinder, implying a possible lattice size dependence. Our results reveal a quantum melting from a holon Wigner crystal to a Fermi-liquid-like state with increasing hole density, and suggest a doping regime to explore superconductivity for future study.