Dynamic Structure Factor of Disordered Quantum Spin Ladders

We investigate the impact of quenched disorder on the zero-temperature dynamic structure factor of two-leg quantum spin ladders. Using linked-cluster expansions and bond-operator mean-field theory, huge effects on individual quasiparticles but also on composite bound states and two-quasiparticle continua are observed. This leads to intriguing quantum structures in dynamical correlation functions well observable in spectroscopic experiments.

Figure 1

(a) QSL with bimodal disorder. The two different rung ($J_{(1,2)}^{\perp }$) and leg ($J_{(1,2)}^{\parallel }$) couplings are shown as red and blue bonds. The unit cell $\nu$ is indicated by the rectangular box. (b) Spectrum of the clean QSL for $J^{\parallel }/J^{\perp }=1/2$ as a function of momentum $k$ including one-triplon dispersion (black line), two-triplon continuum (gray), as well as spin-one two-triplon bound state (red line) calculated by perturbative continuous unitary transformations (pCUTs).

Figure 2

One-triplon contribution to the antisymmetric DSF $S_{-}(k,\omega )$ for pure rung (A-S rung) or leg (A-S leg) disorder and to the symmetric DSF $S_{+}(k,\omega )$ for pure leg disorder (S leg). A-S rung: bimodal rung disorder with $p=0.5$ and rung exchanges $J_1^{\perp }=1.4$ and $J_2^{\perp }=0.6$. The constant leg exchange is $J^{\parallel }=0.4$. White lines represent one-triplon dispersions for a clean QSL with $J^{\parallel }=0.4$ and $J^{\perp }=1.4$ (dashed) or $J^{\perp }=0.6$ (dashed-dotted). Horizontal white lines indicate the lowest one-triplon energy ${\epsilon }_1^{(L)}$ of open ladder segments of length $L$ with $J^{\perp }=0.6$. A-S/S leg: bimodal leg disorder with $p=0.5$ and leg exchanges $J_1^{\parallel }=0.1$ and $J_2^{\parallel }=0.4$. The black dashed line represents the one-triplon dispersion with mean hopping amplitudes.

Figure 3

Two-triplon contribution to the symmetric DSF $S_{+}(k,\omega )$ for pure rung (S rung) or leg (S leg) disorder and to the antisymmetric DSF $S_{-}(k,\omega )$ for pure leg disorder (A-S leg). S rung: bimodal rung disorder with $p=0.5$ and rung exchanges $J_1^{\perp }=1.4$ and $J_2^{\perp }=0.6$. The constant leg exchange is $J^{\parallel }=0.4$. The three dashed lines represent the dispersion of the two-triplon bound state for the clean QSL using $J^{\perp }=1.4$, $J^{\perp }=1.0$, and $J^{\perp }=0.6$. S/A-S leg: bimodal leg disorder with $p=0.5$ and leg exchanges $J_1^{\parallel }=0.1$ and $J_2^{\parallel }=0.4$. The dashed lines represent the dispersion of the two-triplon bound state for the clean QSL with $J_1^{\parallel }$ (white) and $J_2^{\parallel }$ (black).