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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We investigate the influence of quenched disorder on the dynamic structure factor of Heisenberg bilayers on the square, triangular, and kagome lattice in the quantum paramagnetic phase. Perturbative continuous unitary transformations and white graphs are employed to calculate the one-triplon contribution up to high orders in perturbation about the dimer limit for bimodal and continuous disorder. For the square lattice we find that the lifetime of the gap mode is increased by stronger quantum correlations while stronger disorder effects are observed for the triangular lattice due to geometric frustration. For intra-dimer disorder, in-band energy gaps are observed for both lattices which can be understood in terms of a level repulsion on dimers with low and high intra-dimer exchange that are close in energy at the momentum where the in-band gap opens. For the highly frustrated kagome lattice disorder even allows to decrease the gap energy. In addition, the localization length of the low-energy flat band is increased up to order 7 in perturbation theory. The interplay of quenched disorder, geometric frustration, and strong correlations leads therefore to rich structures in the dynamical structure factor of two-dimensional quantum magnets.

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