Phase diagram of disordered quantum antiferromagnets

2014-10-24The presence of disorder can deeply affect the critical behavior of quantum spin systems. Disorder can localize the long-wavelength modes developed at the quantum phase transition of the clean systems, and thus introduce glassy phases. Furthermore, it has been shown that many novel phases can be induced by the simultaneous presence of both magnetic field and geometric randomness. For instance, in doped spin-gap ladders one observes a very rich phase diagram, with a sequence of magnetic field controlled phases, including superfluidity, Bose-Einstein condensate, Bose glass and full polarization. Geometric randomness can also induce local magnetic moments giving rise to long-range order through an order-by-disorder mechanism in a gapped quantum-disordered ground state. In this dissertation, we investigate the physical properties and phase diagrams of doped even-leg ladders. Even-leg ladders are the minimal system in which we can study these effects: pruned spins, bond vs. rung vacancies, and order-by-disorder. Furthermore, such minimal even-leg ladders do not have any intrinsic low-energy degrees of freedom, because the pure system is gapped. Thus the effects of impurity vacancies, introducing new low-energy features, can be cleanly studied. ❧ In the first part, we uncover the effects of quenched disorder in the form of site and bond dilution on the physics of the S=1/2 antiferromagnetic Heisenberg model in 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 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 non-universal, 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 of even-leg ladders leads to a more complex evolution with doping. Correlations 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. ❧ In the second part, we investigate random bond disorder in antiferromagnetic spin-1/2 Heisenberg ladders. We find that the effects of individual bond impurities vary strongly, depending on their positions on legs and rungs. We initially focus on how the distribution of local bond energies depends on the impurity concentration. Then we study how the phase diagram of even-leg ladders is affected by random bond doping. We observe Bose glass phases in two regimes (h' < h ≲ h{c₁} and h'' < h