Fig. 3: Phase diagram and Kohn anomaly of the U(1) DSL with dynamical phonons.
From: Spin-Peierls instability of the U(1) Dirac spin liquid
a Scaling phase diagram for the spin-Peierls-VBS instability of the U(1) DSL, as a function of coupling g, temperature T and frequency ω0. The shaded regions indicate the unstable parameter regimes, based on the finite-temperature calculation in the classical (ω0 → 0) limit and the zero-temperature result for dynamical phonons (ω0 > 0). Phonon spectral function \(\log {S}_{{{{\rm{phonon}}}}}(\omega,{{{\bf{k}}}})\) plotted for b zero and c finite temperature along the momentum slice between Γ and Ka. Spin-phonon coupling is set to g = 0.3. The phonon spectral function is approximated by extending the interacting phonon propagator Ga(ω) = G(ω, Xa) to momenta Xa + q given a microscopic model for the bare phonon dispersion ω0(q) (white dashed line). We use a heuristic scaling form for the VBS correlator at finite temperatures for illustrative purposes (see “Methods”). At finite temperature T > TSP the phonon dispersion displays a Kohn anomaly, and at zero temperature, the quasiparticle picture breaks down.
