Chiral spin liquid in a frustrated anisotropic kagome Heisenberg model

Kalmeyer-Laughlin (KL) chiral spin liquid (CSL) is a type of quantum spin liquid without time-reversal symmetry, and it is considered as the parent state of an exotic type of superconductivity--anyon superconductor. Such exotic state has been sought for more than twenty years, however it remains unclear whether it can exist in realistic system where time-reversal symmetry is breaking (T-breaking) spontaneously. By using the density matrix renormalization group, we show that KL CSL exists in a frustrated anisotropic kagome Heisenberg model (KHM), which has spontaneously T-breaking. We find that our model has two topological degenerate ground states, which exhibit non-vanishing scalar chirality order and are protected by finite excitation gap. Further, we identify this state as KL CSL by the characteristic edge conformal field theory from the entanglement spectrum and the quasiparticles braiding statistics extracted from the modular matrix. We also study how this CSL phase evolves as the system approaches the nearest neighbor KHM.