Gapless chiral spin liquid in spin-1/2 triangular Heisenberg model

We study the ground state of spin-1/2 triangular-lattice antiferromagnet with first- (J1), second- (J2), and third-neighbor (J3) interactions, using large-scale density matrix renormalization group on cylinder geometry. By increasing the couplings, we establish a quantum phase diagram of the system. Besides the previously identified magnetic phases and J1-J2 spin liquid, we find a new gapless chiral spin liquid (CSL) phase with growing J3, which emerges at the neighbor of the J1-J2 spin liquid. This CSL spontaneously breaks time-reversal symmetry by showing a robust three-spin scalar chiral order and the chiral edge mode in the entanglement spectrum. The finite-size scaling of spin triplet gap strongly suggests gapless spin excitations, which is further supported by the logarithmic behavior of the subsystem length dependence of entanglement entropy that leads to a finite central charge. The fitted central charge grows rapidly with increasing system width, which does not support a U(1) Dirac spin liquid but indicates an emergent spinon Fermi surface. This CSL realizes an example of interacting topological phase with chiral edge mode and gapless bulk excitations.