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Using a perturbative renormalization group approach, we show that theextended ($J_1$-$J_2$-$J_d$) Heisenberg model on the kagome lattice with astaggered chiral interaction ($J_\chi$) can exhibit a gapless chiral quantumspin liquid phase. Within a coupled-chains construction, this phase can beunderstood as a chiral sliding Luttinger liquid with algebraic decay of spincorrelations along the chain directions. We calculate the low-energy propertiesof this gapless chiral spin liquid using the effective field theory and showthat they are compatible with the predictions from parton mean-field theorieswith symmetry-protected line Fermi surfaces. These results may be relevant tothe state observed in the kapellasite material.

Gapless chiral spin liquid from coupled chains on the kagome lattice