Magnetoroton modes of the ultraquantum crystal: Numerical study

The field-induced spin-density-wave phases observed in quasi-one-dimensional conductors of the Bechgaard salts family under magnetic field exhibit both spin-density-wave order and a quantized Hall effect, which may exhibit sign reversals. The original nature of the condensed phases is evidenced by the collective mode spectrum. Besides the Goldstone modes, a quasiperiodic structure of magnetoroton modes, predicted to exist for a monotonic sequence of Hall quantum numbers, is confirmed, and a second mode is shown to exist within the single-particle gap. We present numerical estimates of the magnetoroton mode energies in a generic case of the monotonic sequence. The mass anisotropy of the collective mode is calculated. We show how differently the magnetoroton spectrum evolves with magnetic field at low and high fields. The collective mode spectrum should have specific features, in the sign-reversed ``Ribault Phase,'' as compared to modes of the majority sign phases. We investigate numerically the collective mode in the Ribault phase, and find in this latter case a previously unnoticed field-independent low-energy magnetoroton mode at an intermediate wave vector. The occurrence of the Ribault phase depends sensitively on the electron-electron interactions. A byproduct of our study deals with the metal-ultraquantum-crystal instability line: we find, in a monotonic sequence, a reentrant behavior of the metallic phase, at a given temperature, as a function of field, which has been observed experimentally. This behavior is also sensitive to the strength of electron-electron interactions.