Title: Global phase diagram of doped quantum spin liquid on the Kagome lattice

Abstract: It has long been believed that doped quantum spin liquids (QSLs) can give rise to fascinating quantum phases, including the possibility of high-temperature superconductivity (SC) as proposed by P. W. Anderson's resonating valence bond (RVB) scenario. The Kagome lattice $t$-$J$ model is known to exhibit spin liquid behavior at half-filling, making it an ideal system for studying the properties of doped QSL. In this study, we employ the fermionic projected entangled simplex state (PESS) method to investigate the ground state properties of the Kagome lattice $t$-$J$ model with $t/J = 3.0$. Our results reveal a phase transition from charge density wave (CDW) states to uniform states around a critical doping level $\delta_c \approx 0.27$. Within the CDW phase, we observe different types of Wigner crystal (WC) formulated by doped holes that are energetically favored. As we enter the uniform phase, a non-Fermi liquid (NFL) state emerges within the doping range $0.27 < \delta < 0.32$, characterized by an exponential decay of all correlation functions. With further hole doping, we discover the appearance of a pair density wave (PDW) state within a narrow doping region $0.32 < \delta < 1/3$. We also discuss the potential experimental implications of our findings.