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

The anharmonic lattice is a representative example of an interacting, bosonic, many-body system. The self-consistent harmonic approximation has proven versatile for the study of the equilibrium properties of anharmonic lattices. However, the study of dynamical properties therein resorts to an ansatz, whose validity has not yet been theoretically proven. Here we apply the time-dependent variational principle, a recently emerging useful tool for studying the dynamic properties of interacting many-body systems, to the anharmonic lattice Hamiltonian at finite temperature using the Gaussian states as the variational manifold. We derive an analytic formula for the position-position correlation function and the phonon self-energy, proving the dynamical ansatz of the self-consistent harmonic approximation. We establish a fruitful connection between time-dependent variational principle and the anharmonic lattice Hamiltonian, providing insights in both fields. Our work expands the range of applicability of the time-dependent variational principle to first-principles lattice Hamiltonians and lays the groundwork for the study of dynamical properties of the anharmonic lattice using a fully variational framework.

Automated summary

The self-consistent harmonic approximation is proven useful for studying the equilibrium properties of anharmonic lattices, but the study of dynamical properties still requires further exploration. By applying the time-dependent variational principle, an analytical formula for position-position correlation function and phonon self-energy in anharmonic lattice is derived, confirming the dynamical ansatz of the self-consistent harmonic approximation. This work establishes a fruitful connection between the time-dependent variational principle and anharmonic lattice Hamiltonian, providing insights in both fields.