  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.
