We show that a broad class of quantum critical points can be stable against locally correlated disorder even if they are unstable against uncorrelated disorder. Although this result seemingly contradicts the Harris criterion, it follows naturally from the absence of a random-mass term in the associated order-parameter field theory. We illustrate the general concept with explicit calculations for quantum spin-chain models. Instead of the infinite-randomness physics induced by uncorrelated disorder, we find that weak locally correlated disorder is irrelevant. For larger disorder, we find a line of critical points with unusual properties such as an increase of the entanglement entropy with the disorder strength. We also propose experimental realizations in the context of quantum magnetism and cold-atom physics.
We show that a broad class of quantum critical points can be stable against locally correlated disorder even if they are unstable against uncorrelated disorder. Although this result seemingly contradicts the Harris criterion, it follows naturally from the absence of a random-mass term in the associated order-parameter field theory. We illustrate the general concept with explicit calculations for quantum spin-chain models. Instead of the infinite-randomness physics induced by uncorrelated disorder, we find that weak locally correlated disorder is irrelevant. For larger disorder, we find a line of critical points with unusual properties such as an increase of the entanglement entropy with the disorder strength. We also propose experimental realizations in the context of quantum magnetism and cold-atom physics.
This work provides a full description of the critical behavior of the XX spin-1/2 chain under correlated quenched disorder.Previous investigations have shown that the introduction of correlation between couplings in the random XX model gives rise to a novel critical behavior, where the infinite-randomness critical point of the uncorrelated case is replaced by a family of finite-disorder critical points that depends on the disorder strength.Here it is shown that most of the critical exponents of the XX model with correlated randomness are equal to clean (without disorder) chain values and do not depend on disorder strength, except the critical dynamical exponent and the anomalous dimension.The former increases monotonically with disorder strength, whereas the results obtained for the latter are unreliable.Furthermore, the scaling relations between the critical exponents were also tested and it was found that those involving the system dimensionality, namely the hyperscaling and Fisher's scaling relations, are not respected.Measurements of the Rényi entanglement entropy of the system at criticality have also been performed, and it is shown that the scaling behavior of the correlated-disorder case is similar to the theoretical prediction for the clean chain, displaying the same finite-size correction and a disorder-dependent effective central charge in the leading term of the scaling.Further corrections to the scaling of the entanglement entropy were also investigated, but the results are inconclusive.The model was studied via exact numerical diagonalization of the corresponding Hamiltonian.
We employ scaling arguments and optimal fluctuation theory to establish a general relation between quantum Griffiths singularities and the Harris criterion for quantum phase transitions in disordered systems. If a clean critical point violates the Harris criterion, it is destabilized by weak disorder. At the same time, the Griffiths dynamical exponent z' diverges upon approaching the transition, suggesting unconventional critical behavior. In contrast, if the Harris criterion is fulfilled, power-law Griffiths singularities can coexist with clean critical behavior, but z' saturates at a finite value. We present applications of our theory to a variety of systems including quantum spin chains, classical reaction-diffusion systems and metallic magnets, and we discuss modifications for transitions above the upper critical dimension. Based on these results we propose a unified classification of phase transitions in disordered systems.
We study quantum phase transitions in transverse-field Ising spin chains in which the couplings are random but hyperuniform, in the sense that their large-scale fluctuations are suppressed. We construct a one-parameter family of disorder models in which long-wavelength fluctuations are increasingly suppressed as a parameter $\ensuremath{\alpha}$ is tuned. For $\ensuremath{\alpha}=0$, one recovers the familiar infinite-randomness critical point. For $0<\ensuremath{\alpha}<1$, we find a line of infinite-randomness critical points with continuously varying critical exponents; however, the Griffiths phases that flank the critical point at $\ensuremath{\alpha}=0$ are absent at any $\ensuremath{\alpha}>0$. When $\ensuremath{\alpha}>1$, randomness is a dangerously irrelevant perturbation at the clean Ising critical point, leading to a state we call the critical Ising insulator. In this state, thermodynamics and equilibrium correlation functions behave as in the clean system. However, all finite-energy excitations are localized, thermal transport vanishes, and autocorrelation functions remain finite in the long-time limit. We characterize this line of hyperuniform critical points using a combination of perturbation theory, renormalization-group methods, and exact diagonalization.
This work provides a full description of the critical behavior of the XX spin-1/2 chain under correlated quenched disorder. Previous investigations have shown that the introduction of correlation between couplings in the random XX model gives rise to a novel critical behavior, where the infinite-randomness critical point of the uncorrelated case is replaced by a family of finite-disorder critical points that depends on the disorder strength. Here it is shown that most of the critical exponents of the XX model with correlated randomness are equal to clean (without disorder) chain values and do not depend on disorder strength, except the critical dynamical exponent and the anomalous dimension. The former increases monotonically with disorder strength, whereas the results obtained for the latter are unreliable. Furthermore, the scaling relations between the critical exponents were also tested and it was found that those involving the system dimensionality, namely the hyperscaling and Fisher´s scaling relations, are not respected. Measurements of the Rényi entanglement entropy of the system at criticality have also been performed, and it is shown that the scaling behavior of the correlated-disorder case is similar to the theoretical prediction for the clean chain, displaying the same finite-size correction and a disorder-dependent effective central charge in the leading term of the scaling. Further corrections to the scaling of the entanglement entropy were also investigated, but the results are inconclusive. The model was studied via exact numerical diagonalization of the corresponding Hamiltonian.
We study the scaling properties of entanglement entropy (EE) near the quantum critical points in interacting random antiferromagnetic (AFM) spin chains. Using density-matrix renormalization group, we compute the half-chain EE near the topological phase transition between the Haldane and random singlet phases in a disordered spin-1 chain. It is found to diverge logarithmically in system size with an effective central charge ceff=1.17(4) at the quantum critical point (QCP). Moreover, a scaling analysis of EE yields the correlation length exponent $\ensuremath{\nu}=2.28(5)$. Our unbiased calculation establishes that the QCP is in the universality class of the infinite-randomness fixed point predicted by previous studies based on the strong disorder renormalization group technique. However, in the disordered spin-1/2 Majumdar-Ghosh chain, where a valence bond solid phase is unstable to disorder, the crossover length exponent obtained from a scaling analysis of EE disagrees with the expectation based on the Imry-Ma argument. We provide a possible explanation.
We study the effects of topological (connectivity) disorder on phase transitions. We identify a broad class of random lattices whose disorder fluctuations decay much faster with increasing length scale than those of generic random systems, yielding a wandering exponent of ω=(d-1)/(2d) in d dimensions. The stability of clean critical points is thus governed by the criterion (d+1)ν>2 rather than the usual Harris criterion dν>2, making topological disorder less relevant than generic randomness. The Imry-Ma criterion is also modified, allowing first-order transitions to survive in all dimensions d>1. These results explain a host of puzzling violations of the original criteria for equilibrium and nonequilibrium phase transitions on random lattices. We discuss applications, and we illustrate our theory by computer simulations of random Voronoi and other lattices.