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Description
Quantum spin liquids are tantalizing phases of quantum matter, but experimental evidence of their existence has remained elusive. Even theoretically, it is unclear whether many phases permitted by a mean-field classification can be realized as the stable ground states of a physical model. Recent theoretical and numerical studies have provided evidence that triangular-lattice Heisenberg antiferromagnets could host a U(1) Dirac spin liquid (DSL). This strongly coupled phase of matter with gapless spinon and gauge excitations is a two-dimensional analog of the Luttinger liquid description of the antiferromagnetic Heisenberg chain and its spin-disordered ground state. In this work, we find a spin-Peierls instability upon infinitessimal coupling of the DSL to a static lattice distortion. In analog to the Luttinger liquid, we find that explicitly breaking translational symmetry allows a relevant instanton to appear in the effective action — in our case, a lattice-monopole term. We calculate the effective free energy using conformal perturbation theory and show that an infinitesimal static coupling destroys the quantum spin-disordered ground state, resulting in a gapped 12-site valence bond solid with commensurate lattice distortion. Away from the static-distortion limit, we show that the possibility of establishing a DSL phase in experiment depends critically on the relationship between the lattice coupling and phonon frequency since there is a weak-coupling regime within which the spin-liquid phase remains stable. Our work presents a novel extension of the spin-Peierls mechanism to two-dimensional interacting fermions, which has profound implications for the stability and observability of general spin liquid states with gapless gauge excitations.
