Gaussian time-dependent variational principle for the finite-temperature anharmonic lattice dynamics

The anharmonic lattice is a representative interacting bosonic many-body system. The self-consistent harmonic approximation has been used to study the equilibrium properties of the anharmonic lattices. However, to study the dynamical properties within this method, one needs to resort to a specific self-energy ansatz, whose validity is yet to be proven. In this presentation, we apply the time-dependent variational principle, a recently emerging tool for studying the dynamical properties of interacting many-body systems, to the anharmonic lattices. Using the Gaussian variational states and the linearized equation of motion method, we theoretically prove the dynamical self-energy ansatz of the self-consistent harmonic approximation. The calculated dynamical and spectral properties of the lattice can be understood as that of interacting 1- and 2-phonon excitations. Our work lays the groundwork for a fully variational study of dynamical properties of the anharmonic lattice and also expands the range of applicability of time-dependent variational principle to first-principle lattice Hamiltonians.