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We study the spin liquid candidate of the spin-$1/2$ $J_1$-$J_2$ Heisenbergantiferromagnet on the triangular lattice by means of density matrixrenormalization group (DMRG) simulations. By applying an external Aharonov-Bohmflux insertion in an infinitely long cylinder, we find unambiguous evidence forgapless $U(1)$ Dirac spin liquid behavior. The flux insertion overcomes thefinite size restriction for energy gaps and clearly shows gapless behavior atthe expected wave-vectors. Using the DMRG transfer matrix, the low-lyingexcitation spectrum can be extracted, which shows characteristic Dirac conestructures of both spinon-bilinear and monopole excitations. Finally, weconfirm that the entanglement entropy follows the predicted universal responseunder the flux insertion.

Dirac Spin Liquid on the Spin-1/2 Triangular Heisenberg Antiferromagnet