Studying interacting fermions in one dimension at high energy, we find a hierarchy in the spectral weights of the excitations theoretically, and we observe evidence for second-level excitations experimentally. Diagonalizing a model of fermions (without spin), we show that levels of the hierarchy are separated by powers of R^{2}/L^{2}, where R is a length scale related to interactions and L is the system length. The first-level (strongest) excitations form a mode with parabolic dispersion, like that of a renormalized single particle. The second-level excitations produce a singular power-law line shape to the first-level mode and multiple power laws at the spectral edge. We measure momentum-resolved tunneling of electrons (fermions with spin) from or to a wire formed within a GaAs heterostructure, which shows parabolic dispersion of the first-level mode and well-resolved spin-charge separation at low energy with appreciable interaction strength. We find structure resembling the second-level excitations, which dies away quite rapidly at high momentum.
In this paper, using the infinite time-evolving block decimation (iTEBD) algorithm and Bell-type inequalities, we investigate multipartite quantum nonlocality in an infinite one-dimensional quantum spin-
21XXZ system. High hierarchy of multipartite nonlocality can be observed in the gapless phase of the model, while only the lowest hierarchy of multipartite nonlocality is observed in most regions of the gapped antiferromagnetic phase. Thereby, Bell-type inequalities disclose different correlation structures in the two phases of the system. Furthermore, at the infinite-order quantum phase transition (QPT, or Kosterlitz-Thouless QPT) point of the model, the correlation measures always show a local minimum value, regardless of the length of the subchains. It indicates that relatively low hierarchy of multipartite nonlocality would be observed at the infinite-order QPT point in a Bell-type experiment. The result is in contrast to the existing results of the second-order QPT in the one-dimensional
XY model, where multipartite nonlocality with the highest hierarchy has been observed. Thus, multipartite nonlocality provides an alternative perspective to distinguish between these two kinds of QPTs. Reliable clues for the existence of tripartite quantum entanglement have also been found.
This paper gives a full account of the dynamical properties of single-mode inhomogeneously broadened lasers. The study divides itself into two parts. First, the integro-differential ``Maxwell-Bloch'' equations, which describe such systems, are numerically solved for a large scan of values of the various control parameters that govern the dynamical evolution of self-pulsing lasers. The instability hierarchies, delimited with respect to the excitation parameter, reveal that, along with the various decay rates of the interacting variables, the chosen number of velocity components, which divides the polarization integral into discrete intervals, also plays an important role in the dynamical evolution of the system, especially in the self-pulsing regime of operation. The second part of this paper concerns another approach to modeling single-mode inhomogeneously broadened laser dynamics that largely circumvents the infinite-dimensional complexity of the medium's polarization. A hierarchy of low-dimensional models, with increasing accuracy with respect to the infinite-dimensional ``Maxwell-Bloch'' equations, is constructed and adapted to describe correctly most of the properties of single-mode inhomogeneously broadened lasers.