Quantum phase transitions in impurity models and percolating lattices

Sean Fayfar

We describe a new universality class - dubbed protected percolation - that we show to be relevant to quantum critical systems. Percolation theory describes phase transitions where long-range order is lost when parts of a system become disconnected from other parts; in the vicinity of the transition, critical behavior is observed, captured by universal power laws. Protected percolation has the added restriction that only sites from the system spanning connection can be removed. We developed a new technique to simulate protected percolation, and we used it to determine the critical exponents of this new universality class in 2, 3, and 4 dimensions. We relate the exponents analytically to those of standard percolation. The Harris criterion predicts whether a phase transition is stable against impurities. We prove that protected percolation violates this criterion in 3 dimensions and higher, implying that impurities result in the loss of universal behavior in systems governed by protected percolation. We investigated the change in critical exponents for various types of impurities, focusing on the case for three dimensions where protected percolation models quantum critical systems. We detail how our simulations can be used for direct comparison to experimental results on such quantum critical systems.

Gérard G. Emch, Chuang Liu

Pedro L. Garrido, Joaquín Marro

The authors study d-dimensional lattice model systems whose dynamics consist of competing independent processes which may induce nonequilibrium steady states. Interesting phase transitions and critical phenomena ensue which are influenced, even dominated, by a sort of dynamical bond disorder. The latter, which may occur in natural systems, reminds one of the disorder in more familiar bond-diluted and other impure models, for example, percolation-like phenomena arise in some of the model cases. Exact solutions for d=1, some exact results for d<1, and a comparison with more standard, either quenched or annealed, magnetically diluted models are reported.

Brent T. Fultz

Amit Dutta, G. Aeppli, Bikas K. Chakrabarti +3 more

Hisatoshi Yokoyama, Ryo Sato, Kenji Kobayashi +2 more

An impurity Hubbard model with strong correlation on a square lattice with diagonal hopping is studied for an antiferromagnetic state, using a variational Monte Carlo method.If the impurity potential is repulsive with moderate strength and the density of impurity sites is equal to or larger than the doping rate in a partially filled band, the state becomes insulating.When the impurity density is increased, an insulator-to-metal transition takes place through a mechanism of percolation.