We introduce a one-dimensional plaquette orbital model with a topology of a ladder and alternating interactions between
x and
z pseudospin components both along the ladder legs and on the rungs. We show by an exact transformation that it is equivalent to an effective spin model in a magnetic field, with spin dimers that replace plaquettes and are coupled along the chain by three-spin interactions in the Hilbert space reduced by a factor of 2. Using perturbative treatment and mean-field approaches with dimer correlations we study the ground state spin configuration and its defects in the lowest excited states. By the exact diagonalization approach we establish that the quantum effects are of purely short-range nature in the model and we find estimated values of the ground state energy and the gap in the thermodynamic limit from the system sizes up to
L=12 dimers. Finally, we study a class of excited states with classical-like defects accumulated in the central region of the chain to find that in this region the quantum entanglement measured by the mutual information of neighboring dimers is locally increased and coincides with disorder and frustration. Such islands of entanglement in an otherwise rather classical system may be of interest in the context of quantum computing devices.
With the advent of physical implementations of quantum walks, a general theoretical and efficient numerical framework is required for the study of their interactions with defects and disorder. In this paper, we derive analytic expressions for the eigenstates of a one-dimensional continuous-time quantum walk interacting with a single defect, before investigating the effects of multiple diagonal defects and disorder, with emphasis on its transmission and reflection properties. Complex resonance behavior is demonstrated, showing alternating bands of zero and perfect transmission for various defect parameters. Furthermore, we provide an efficient numerical method to characterize quantum walks in the presence of diagonal disorder, paving the way for selective control of quantum walks via the optimization of position-dependent defects. The numerical method can be readily extended to higher dimensions and multiple interacting walkers.
Using the conventional
T-matrix approach, we discuss gapped phases in one-, two-, and three-dimensional (3D) spin systems (both with and without a long-range magnetic order) with bond disorder and with weakly interacting bosonic elementary excitations. This work is motivated by recent experimental and theoretical activity in spin-liquid-like systems with disorder and in the disordered interacting boson problem. In particular, we apply our theory to both paramagnetic low-field and fully polarized high-field phases in dimerized spin-
21 systems and in integer-spin magnets with large single-ion easy-plane anisotropy
D with disorder in exchange coupling constants (and/or
D). The elementary excitation spectrum and the density of states are calculated in the first order in defects concentration $c\ensuremath{\ll}1$. In 2D and 3D systems, the scattering on defects leads to a finite damping of all propagating excitations in the band except for states lying near its edges. We demonstrate that the analytical approach is inapplicable for states near the band edges and our numerical calculations reveal their localized nature. We find that the damping of propagating excitations can be much more pronounced in considered systems than in magnetically ordered gapless magnets with impurities. In 1D systems, the disorder leads to localization of all states in the band, while those lying far from the band edges (short-wavelength excitations) can look like conventional wave packets.