The subtle interplay of randomness and quantum fluctuations at low temperatures gives rise to a plethora of unconventional phenomena in systems ranging from quantum magnets and correlated electron materials to ultracold atomic gases. Particularly strong disorder effects have been predicted to occur at zero-temperature quantum phase transitions. Here, we demonstrate that the composition-driven ferromagnetic-to-paramagnetic quantum phase transition in Sr(1-x)Ca(x)RuO3 is completely destroyed by the disorder introduced via the different ionic radii of the randomly distributed Sr and Ca ions. Using a magneto-optical technique, we map the magnetic phase diagram in the composition-temperature space. We find that the ferromagnetic phase is significantly extended by the disorder and develops a pronounced tail over a broad range of the composition x. These findings are explained by a microscopic model of smeared quantum phase transitions in itinerant magnets. Moreover, our theoretical study implies that correlated disorder is even more powerful in promoting ferromagnetism than random disorder.

We investigate the effects of quenched disorder on first-order quantum phase transitions on the example of the N -color quantum Ashkin-Teller model. By means of a strong-disorder renormalization group, we demonstrate that quenched disorder rounds the first-order quantum phase transition to a continuous one for both weak and strong coupling between the colors. In the strong coupling case, we find a distinct type of infinite-randomness critical point characterized by additional internal degrees of freedom. We investigate its critical properties in detail and find stronger thermodynamic singularities than in the random transverse field Ising chain. We also discuss implications for higher spatial dimensions as well as unusual aspects of our renormalization group scheme.

We investigate the superfluid-insulator quantum phase transition of one-dimensional bosons with off-diagonal disorder by means of large-scale Monte-Carlo simulations. For weak disorder, we find the transition to be in the same universality class as the superfluid-Mott insulator transition of the clean system. The nature of the transition changes for stronger disorder. Beyond a critical disorder strength, we find nonuniversal, disorder-dependent critical behavior. We compare our results to recent perturbative and strong-disorder renormalization group predictions. We also discuss experimental implications as well as extensions of our results to other systems.Bosonic many-particle systems can undergo quantum phase transitions between superfluid and localized ground states due to interactions and lattice effects. These superfluid-insulator transitions occur in a wide variety of experimental systems ranging from helium in porous media, Josephson junction arrays, and granular superconductors to ultracold atomic gases [1][2][3][4][5][6][7][8]. In many of these applications, the bosons are subject to quenched disorder or randomness. Understanding the effects of disorder on the superfluid-insulator transition and on the resulting insulating phases is thus a prime question.The case of one space dimension is especially interesting because the superfluid phase is rather subtle and displays quasi-long-range order instead of true long-range order. Moreover, the Anderson localization scenario for non-interacting bosons suggests that disorder becomes more important with decreasing dimensionality.Giarmarchi and Schulz [9] studied the influence of weak disorder on the interacting superfluid by means of a perturbative renormalization group analysis. They found the superfluid-insulator transition to be of KosterlitzThouless (KT) type [10], with universal critical exponents and a universal value of the Luttinger parameter g = π √ ρ s κ at criticality (ρ s denotes the superfluid stiffness and κ the compressibility). This analysis was recently extended to second order in the disorder strength, with unchanged conclusion [11]. A different scenario emerges, however, from the realspace strong-disorder renormalization group approach. In a series of papers [12], Altman et al. studied onedimensional interacting lattice bosons in various types of disorder. In all cases, they found that the superfluidinsulator transition is characterized by KT-like scaling of lengths and times, but it occurs at a nonuniversal, disorder-dependent value of the Luttinger parameter. The transition is thus in a different universality class than the weak-disorder transition [9]. However, Monte-Carlo simulations [13] did not find any evidence in favor of the strong-disorder critical point.In view of these seemingly incompatible results, it is important to determine whether or not both types of superfluid-insulator critical points indeed exist in systems of interacting disordered bosons in one dimension. Moreover, it is important to study whether they can be reached f...

Phase transitions in random systems are smeared if individual spatial regions can order independently of the bulk system. In this paper, we study such smeared phase transitions (both classical and quantum) in substitutional alloys A1−xBx that can be tuned from an ordered phase at composition x = 0 to a disordered phase at x = 1. We show that the ordered phase develops a pronounced tail that extends over all compositions x < 1. Using optimal fluctuation theory, we derive the composition dependence of the order parameter and other quantities in the tail of the smeared phase transition. We also compare our results to computer simulations of a toy model, and we discuss experiments.

We study the ground-state phase diagram of the Ashkin-Teller random quantum spin chain by means of a generalization of the strong-disorder renormalization group. In addition to the conventional paramagnetic and ferromagnetic (Baxter) phases, we find a partially ordered phase characterized by strong randomness and infinite coupling between the colors. This unusual phase acts, at the same time, as a Griffiths phase for two distinct quantum phase transitions both of which are of infinite-randomness type. We also investigate the quantum multi-critical point that separates the two-phase and three-phase regions; and we discuss generalizations of our results to higher dimensions and other systems.