Textures of quantum intrinsically localized modes
Physical Review B
We have examined the lowest-energy members of the quantized ILMs of a generalization of the Fermi-Pasta-Ulam Hamiltonian to three-dimensions. The lowest energy ILMs are similar in form to multi-phonon bound states, except that the number of phonons is not conserved. The ILMs can be categorized as having a quasi-spin of either S = 2 or S = 0 and have other internal quantum numbers. We find that ILMs can form in three-dimensions at zero temperature, but only if the interaction exceeds a minimum
... exceeds a minimum value. Furthermore, as the temperature is raised, the magnitude of the minimal interaction required to stabilize the ILM is reduced. When the ILMs first form they split off from the top of the two-phonon continuum. The S = 0 ILMs form for lower values of the interaction than the S = 2 ILMs. The ILMs form preferentially for center of mass momentum q at the corner of the Brillouin zone. The tendency of ILMs to form at this momentum is traced to a confluence of van-Hove singularities in the (non-interacting) two-phonon density of states at the top of the two-phonon continuum. We have examined the ILM many-body wave functions and find that the relative coordinate part of the wave functions have symmetries associated with internal quantum numbers.