Dynamic Structure Factor of Disordered Quantum Spin Ladders

Abstract

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]

Dynamic structure factor of Heisenberg bilayer dimer phases in the presence of quenched disorder and frustration

“…a disordered chemical potential, in a nearest-neighbor one-triplon hopping Hamiltonian. For intra-dimer disorder in one dimension we found very characteristic structures in the DSF that had their origin in the fragmentation of the ladder into finite ladder segments [14]. This fragmentation could be understood by the fact that there is no percolation in one dimension.…”

“…Technically, we apply the method of pCUTs with the help of white graphs along the same lines as done for the disordered quasi one-dimensional Heisenberg ladder in Ref. 14. In order to be self-contained we nevertheless summarize the most important steps in the following.…”

“…Though, almost all eigenstates are still localized for such models except the ones in the band center [32; 33]. Differences between intra-and inter-dimer disorder in one dimension were already discussed in detail for antiferromagnetic Heisenberg spin ladders in [14].…”

“…For the antiferromagnetic Heisenberg spin-1/2 ladder, a quasi one-dimensional building block of a Heisenberg bilayer, high-order series expansions using the method of perturbative continuous unitary transformations (pCUTs) and white graphs allow to evaluate the DSF beyond the mean-field level in a wide window of coupling ratios [14]. In particular, the effect of quenched disorder on elementary triplon excitations [15] but also two-triplon continua and bound states has been determined.…”

“…Here, we advance from these calculations for the quasi one-dimensional Heisenberg ladder [14] and calculate the one-triplon properties of the DSF for two-dimensional Heisenberg bilayers within the gapped quantum paramagnetic dimer phase. A primary focus is laid on the interplay of quenched disorder and geometric frustration, which we study by comparing the unfrustrated square lattice Heisenberg bilayer with the frustrated cases on the triangular and kagome lattice.…”