Spin excitation spectra of the spin-1/2 Kagome Heisenberg antiferromagnets

We present a large-scale numerical calculation on the dynamical correlation functions of spin-1/2 Kagome J1-J2 Heisenberg model using a state-of-the-art tensor network renormalization group method. The calculated results allow us to gain a comprehensive picture on the nature of spin excitation spectra of the Kagome J1-J2 Heisenberg model. The entire excitation spectra gradually gather from high energy to low energy as J2 decreases, and finally form a gapless low-energy continuum distributed in the J1 range when J2/J1 is less than about 0.05, implying that it has entered the gapless quantum spin liquid phase. Furthermore, combining with the static structure factor, we confirm that this gapless quantum spin liquid is more likely to be U(1) Dirac Spin Liquid, which is well consistent with our previous research (PRL 118, 137202 (2017)) on ground state properties.