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

Abstract

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.

Projective cluster-additive transformation for quantum lattice models

“…Examples range from the calculation of low-and high-field expansions for transverse-field Ising models [4,5], the analysis of phase transitions in triangular-lattice bilayer Heisenberg models [6] and spectral densities of two-particle excitations in dimerized Heisenberg quantum spin systems [2,7,8] to the study of critical and Griffiths-McCoy singularities in quantum Ising spin-glasses [9] or the derivation of spectral densities for Heisenberg quantum magnets with quenched disorder [10,11], or to the analysis of quantum phase diagrams of long-range transverse-field Ising models [12] and the application to quantum phases with intrinsic topological order [13][14][15]. Also questions such as the exploration of possible ground states in the kagome Heisenberg model [16] can be tackled with perturbation theory.…”

Series expansion studies of the $J_1$-$J_2$-Heisenberg bilayer

“…While in some cases the reduction of the dimer exchange may lead to condensation of triplons into sought-for quantum phases of some non-dimerized original model, bilayer systems host their own unique set of physics. For this reason, a variety of bilayer systems have previously been studied under various objectives, e.g., uncovering rich phase diagrams [49][50][51][52][53], examining the crossing to 3D bulk materials [54], investigating effects of disorder [55] and hole doping [56] or analyzing emergent bound states [57] and topological excitations [58]. On the material side, an extensive number of systems exist, which are related to this theme, including Li 2 VOSiO 4 [45], BaCuSi 2 O 6 [59,60], TlCuCl 3 [61], Ba 3 Mn 2 O 8 [62], and SrCu 2 (BO 3 ) 2 [63].…”

“…We will use the perturbative Continuous Unitary Transformation (pCUT) [67], based on the flow equation method [68], in order to perform a series expansion for the excitation energies directly in the thermodynamic limit. pCUT has been applied successfully to a large variety of dimerized and n-merized quantum spin systems, including, but not limited to ladders [69], tubes [70], planar pyrochlores [71], various SU(2)invariant Heisenberg bilayers [49,55], as well as to Kitaev bilayers [51,57].…”

Projective cluster-additive transformation for quantum lattice models

“…Albeit many other numerical techniques exist nowadays, high-order series expansions are used as a competitive technique to tackle quantum many-body problems [1][2][3]. Examples range from the calculation of low-and high-field expansions for transverse-field Ising models [4,5], the analysis of phase transitions in triangular-lattice bilayer Heisenberg models [6] and spectral densities of two-particle excitations in dimerized Heisenberg quantum spin systems [2,7,8] to the study of critical and Griffiths-McCoy singularities in quantum Ising spin-glasses [9] or the derivation of spectral densities for Heisenberg quantum magnets with quenched disorder [10,11], or to the analysis of quantum phase diagrams of long-range transverse-field Ising models [12] and the application to quantum phases with intrinsic topological order [13][14][15]. Also questions such as the exploration of possible ground states in the kagome Heisenberg model [16] can be tackled with perturbation theory.…”