Localization of spin waves in disordered quantum rotors

We study the dynamics of excitations in a system of $O(N)$ quantum rotors in the presence of random fields and random anisotropies. Below the lower critical dimension $d_{\mathrm{lc}}=4$ the system exhibits a quasi-long-range order with a power-law decay of correlations. At zero temperature the spin waves are localized at the length scale $L_{\mathrm{loc}}$ beyond which the quantum tunneling is exponentially suppressed $c \sim e^{-(L/L_{\mathrm{loc}})^{2(\theta+1)}}$. At finite temperature $T$ the spin waves propagate by thermal activation over energy barriers that scales as $L^{\theta}$. Above $d_{\mathrm{lc}}$ the system undergoes an order-disorder phase transition with activated dynamics such that the relaxation time grows with the correlation length $\xi$ as $\tau \sim e^{C \xi^\theta/T}$ at finite temperature and as $\tau \sim e^{C' \xi^{2(\theta+1)}/\hbar^2}$ in the vicinity of the quantum critical point.Comment: 8 pages, 2 figures, revtex

Multifractality of correlated two-particle bound states in quasiperiodic chains

We consider the quasiperiodic Aubry-Andr\'e chain in the insulating regime with localised single-particle states. Adding local interaction leads to the emergence of extended correlated two-particle bound states. We analyse the nature of these states including their multifractality properties. We use a projected Green function method to compute numerically participation numbers of eigenstates and analyse their dependence on the energy and the system size. We then perform a scaling analysis. We observe multifractality of correlated extended two-particle bound states, which we confirm independently through exact diagonalisation.Comment: 7 pages, 8 figure

Chiral Flat Bands: Existence, Engineering and Stability

We study flat bands in bipartite tight-binding networks with discrete translational invariance. Chiral flat bands with chiral symmetry eigenenergy E = 0 and host compact localized eigenstates for finite range hopping. For a bipartite network with a majority sublattice chiral flat bands emerge. We present a simple generating principle of chiral flat band networks and as a showcase add to the previously observed cases a number of new potentially realizable chiral flat bands in various lattice dimensions. Chiral symmetry respecting network perturbations - including disorder and synthetic magnetic fields - preserve both the flatband and the modified compact localized states. Chiral flatbands are spectrally protected by gaps, and pseudogaps in the presence of disorder due to Griffiths effects

Avalanches and hysteresis in frustrated superconductors and XY-spin-glasses

We study avalanches along the hysteresis loop of long-range interacting spin-glasses with continuous XY-symmetry - which serves as a toy model of granular superconductors with long-range and frustrated Josephson couplings. We identify sudden jumps in the $T=0$ configurations of the XY-phases, as an external field is increased. They are initiated by the softest mode of the inverse susceptibility matrix becoming unstable, which induces an avalanche of phase updates (or spin alignments). We analyze the statistics of these events, and study the correlation between the non-linear avalanches and the soft mode that initiates them. We find that the avalanches follow the directions of a small fraction of the softest modes of the inverse susceptibility matrix, similarly as was found in avalanches in jammed systems. In contrast to the similar Ising spin-glass (Sherrington-Kirkpatrick) studied previously, we find that avalanches are not distributed with a scale-free power law, but rather have a typical size which scales with the system size. We also observe that the Hessians of the spin-glass minima are not part of standard random matrix ensembles as the lowest eigenvector has a fractal support.Comment: 17 pages, 12 figure

Non-Hermitian flatband generator in one dimension

Dispersionless bands -- flatbands -- have been actively studied thanks to their interesting properties and sensitivity to perturbations, which makes them natural candidates for exotic states. In parallel non-Hermitian systems have attracted much attention in the recent years as a simplified description of open system with gain or loss motivated by potential applications. In particular, non-Hermitian system with dispersionless energy bands in their spectrum have been studied theoretically and experimentally. Flatbands require in general fine-tuning of Hamiltonian or protection by a symmetry. A number of methods was introduced to construct non-Hermitian flatbands relying either on a presence of a symmetry, or specific frustrated geometries, often inspired by Hermitian models. We discuss a systematic method of construction of non-Hermitian flatbands using 1D two band tight-binding networks as an example, extending the methods used to construct systematically Hermitian flatbands. We show that the non-Hermitian case admits fine-tuned, non-symmetry protected flatbands and provides more types of flatbands than the Hermitian case.Comment: 14 pagers, 4 figure

Many-Body Flatband Localization

We generate translationally invariant systems exhibiting many-body localization from All-Bands- Flat single particle lattice Hamiltonians dressed with suitable short-range many-body interactions. This phenomenon - dubbed Many-Body Flatband Localization (MBFBL) - is based on symmetries of both single particle and interaction terms in the Hamiltonian, and it holds for any interaction strength. We propose a generator of MBFBL Hamiltonians which covers both interacting bosons and fermions for arbitrary lattice dimensions, and we provide explicit examples of MBFBL models in one and two lattice dimensions. We also explicitly construct an extensive set of local integrals of motion for MBFBL models. Our results can be further generalized to long-range interactions as well as to systems lacking translational invariance