We investigate the impact of quenched disorder on the dynamical correlation functions of twoleg quantum spin ladders. Perturbative continuous unitary transformations with the help of white graphs and bond-operator mean-field theory are used to calculate the one-and two-triplon contribution of the zero-temperature dynamical structure factor. Disorder results in huge effects on quasi-particles as well as composite bound states due to localization. This leads to intriguing quantum structures in dynamical correlation functions well observable in spectroscopic experiments.Disorder is an inevitable ingredient of any condensed matter. On the one hand disorder can change or even destroy the physical behaviour of the associated clean systems [1][2][3] or, on the other hand, it can induce fundamentally new physics. This is especially true for correlated quantum materials where the interplay of disorder and quantum fluctuations can result in technological challenges or exotic phases of quantum matter like many-body localization [4][5][6][7]. One important aspect in the collective behaviour of correlated quantum matter is the formation of quasi-particles and their role in quantum critical behaviour. While many studies have investigated the static and thermodynamic properties of such systems in the presence of disorder [8][9][10][11][12][13][14][15][16], the fate of quasi-particles under disorder is only rarely studied. Experimentally, however, increasingly improving resolution in spectroscopy like inelastic neutron or light scattering as well as intentional doping to control disorder in quantum materials [17][18][19][20][21][22][23], demands theoretical predictions for dynamical correlation functions of correlated quantum matter in the presence of disorder. Disordered QSL -The Hamiltonian of the disordered QSL for a fixed disorder configuration {J} is given byJ ν,n S ν,n · S ν+1,n ,(1) where the sum runs over all rungs and n = 1, 2 denotes arXiv:1806.01717v1 [cond-mat.str-el]

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Recent experimental findings have reported the presence of unconventional charge orders in the enlarged (2 × 2) unit-cell of kagome metals AV3Sb5 (A = K, Rb, Cs) and hinted towards specific topological signatures. Motivated by these discoveries, we investigate the types of topological phases that can be realized in such kagome superlattices. In this context, we employ a recently introduced statistical method capable of constructing topological models for any generic lattice. By analyzing large data sets generated from symmetry-guided distributions of randomized tight-binding parameters, and labeled with the corresponding topological index, we extract physically meaningful information. We illustrate the possible real-space manifestations of charge and bond modulations and associated flux patterns for different topological classes, and discuss their relation to present theoretical predictions and experimental signatures for the AV3Sb5 family. Simultaneously, we predict higher-order topological phases that may be realized by appropriately manipulating the currently known systems.

Electronic systems living on Archimedean lattices such as kagome and square–octagon networks are presently being intensively discussed for the possible realization of topological insulating phases. Coining the most interesting electronic topological states in an unbiased way is however not straightforward due to the large parameter space of possible Hamiltonians. A possible approach to tackle this problem is provided by a recently developed statistical learning method (Mertz and Valentí in Phys Rev Res 3:013132, 2021. https://doi.org/10.1103/PhysRevResearch.3.013132), based on the analysis of a large data sets of randomized tight-binding Hamiltonians labeled with a topological index. In this work, we complement this technique by introducing a feature engineering approach which helps identifying polynomial combinations of Hamiltonian parameters that are associated with non-trivial topological states. As a showcase, we employ this method to investigate the possible topological phases that can manifest on the square–octagon lattice, focusing on the case in which the Fermi level of the system lies at a high-order van Hove singularity, in analogy to recent studies of topological phases on the kagome lattice at the van Hove filling.