Fate of Dirac spin liquids in the presence of spin-phonon interactions

Recent numerical calculations and theoretical studies have provided important evidence that Dirac spin liquid phases may be realized in highly frustrated spin systems on non-bipartite networks, e.g. on the kagome and triangular lattices [1]. We address the question of the stability of U(1) Dirac spin liquids in the presence of interactions between spins and lattice distortions (phonons) [2]. This scenario is modeled by considering a spin-phonon Hamiltonian in which the exchange interaction between the spins is modulated by lattice distortions. Adopting a variational Monte Carlo approach based on parton wave functions and spin-phonon Jastrow factors [3], which allow for a full quantum treatment of both spin and lattice degrees of freedom, we study the phase diagram of the spin-phonon Hamiltonian on the kagome and triangular lattices, away from the regime of static distortions. Our results indicate that Dirac spin liquid ground states are not immediately unstable and that competing valence-bond orders take over only above a critical value of the spin-phonon coupling.

[1] X.-Y. Song, C. Wang, A. Vishwanath, Y.-C. He, Nat Commun 10, 4254 (2019).

[2] U.F.P. Seifert, J. Willsher, M. Drescher, F. Pollmann, J. Knolle, arXiv:2307.12295 (2023).

[3] F. Ferrari, R. Valenti, F. Becca, Phys. Rev. B 104, 035126 (2021).