The magnetic responses of a spin-1/2 ladder doped with non-magnetic impurities are studied using various methods and including the regime where frustration induces incommensurability. Several improvements are made on the results of the seminal work o
f Sigrist and Furusaki [J. Phys. Soc. Jpn. 65, 2385 (1996)]. Deviations from the Brillouin magnetic curve due to interactions are also analyzed. First, the magnetic profile around a single impurity and effective interactions between impurities are analyzed within the bond-operator mean-field theory and compared to density-matrix renormalization group calculations. Then, the temperature behavior of the Curie constant is studied in details. At zero-temperature, we give doping-dependent corrections to the results of Sigrist and Furusaki on general bipartite lattice and compute exactly the distribution of ladder cluster due to chain breaking effects. Using exact diagonalization and quantum Monte-Carlo methods on the effective model, the temperature dependence of the Curie constant is compared to a random dimer model and a real-space renormalization group scenario. Next, the low-part of the magnetic curve corresponding to the contribution of impurities is computed using exact diagonalization. The random dimer model is shown to capture the bulk of the curve, accounting for the deviation from the Brillouin response. At zero-temperature, the effective model prediction agrees relatively well with density-matrix renormalization group calculations. Finite-temperature effects are displayed within the effective model and for large depleted ladder models using quantum Monte-Carlo simulations. In all, the effect of incommensurability does not display a strong qualitative effect on both the magnetic susceptibility and the magnetic curve. Consequences for experiments on the BiCu2PO6 compound and other spin-gapped materials are briefly discussed.
Using strong-disorder renormalization group, numerical exact diagonalization, and quantum Monte Carlo methods, we revisit the random antiferromagnetic XXZ spin-1/2 chain focusing on the long-length and ground-state behavior of the average time-indepe
ndent spin-spin correlation function C(l)=upsilon l^{-eta}. In addition to the well-known universal (disorder-independent) power-law exponent eta=2, we find interesting universal features displayed by the prefactor upsilon=upsilon_o/3, if l is odd, and upsilon=upsilon_e/3, otherwise. Although upsilon_o and upsilon_e are nonuniversal (disorder dependent) and distinct in magnitude, the combination upsilon_o + upsilon_e = -1/4 is universal if C is computed along the symmetric (longitudinal) axis. The origin of the nonuniversalities of the prefactors is discussed in the renormalization-group framework where a solvable toy model is considered. Moreover, we relate the average correlation function with the average entanglement entropy, whose amplitude has been recently shown to be universal. The nonuniversalities of the prefactors are shown to contribute only to surface terms of the entropy. Finally, we discuss the experimental relevance of our results by computing the structure factor whose scaling properties, interestingly, depend on the correlation prefactors.
