Correlations in quantum spin ladders with site and bond dilution

Abstract

We investigate the effects of quenched disorder, in the form of site and bond dilution, on the physics of the S = 1/2 antiferromagnetic Heisenberg model on even-leg ladders. Site dilution is found to prune rung singlets and thus create localized moments which interact via a random, unfrustrated network of effective couplings, realizing a random-exchange Heisenberg model (REHM) in one spatial dimension. This system exhibits a power-law diverging correlation length as the temperature decreases. Contrary to previous claims, we observe that the scaling exponent is nonuniversal, i.e., doping dependent. This finding can be explained by the discrete nature of the values taken by the effective exchange couplings in the doped ladder. Bond dilution on even-leg ladders leads to a more complex evolution with doping of correlations, which are weakly enhanced in 2-leg ladders, and are even suppressed for low dilution in the case of 4-leg and 6-leg ladders. We clarify the different aspects of correlation enhancement and suppression due to bond dilution by isolating the contributions of rung-bond dilution and leg-bond dilution.

Magnetic responses of randomly depleted spin ladders

“…This was confirmed numerically in Ref. 33 in which results on depleted two-leg ladders are consistent with an upper bound of the order of z −2 reached for very low temperatures.…”

“…Interpretation in that sense was proposed on the same model through the study on correlation lengths. 33 Still, we observe that the RSRG argument does capture a lowering of the α(z) curve w.r.t. the 2ξz naive expectation.…”

“…Interesting questions arise then when a finite concentration of impurities is introduced in a spin ladder, as studied in a large number of theoretical works. [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33] Similar physics is also at play in other spin-gapped materials: spin-1 (Haldane) chains such as Y 2 BaNiO 5 , 34,35 or PbNi1 2 V 2 O 8 , 36 spin-Peierls chains such as CuGeO 3 [37][38][39][40][41][42][43][44][45] for instance. Indeed, a universal behavior can be observed for the impurity-induced three-dimensional ordering mechanism in such weakly coupled chains or ladder materials.…”

“…However, in the context of depleted ladders, universality for such thermodynamic quantities has been first questioned using quantum Monte Carlo (QMC) simulations by Miyazaki and co-workers 27 where no clear signature of universal low temperature scalings were found, in agreement with a more recent QMC study. 33 Despite the large number of works devoted to such systems in the absence of external magnetic field, much less is known regarding finite field effects. Indeed, as recently reviewed by Giamarchi and co-workers, 65 applying a finite external field on gapped AF systems leads to the analog of a Bose-Einstein condensation (BEC) of magnetic excitations 66,67 (hard-core bosons triplets) when the field is sufficiently strong to close the spin gap ∆ s .…”

Far-from-Equilibrium Quantum Magnetism with Ultracold Polar Molecules

“…Although we show results only for the homogeneous system, we have taken the trap into account and found that our conclusions remain valid [40]. Remarkably, relatives of such unusual models exist, and are employed to understand materials, 3 He-4 He mixtures, and disorder-induced phenomena [41][42][43][44][45][46][47][48][49].…”