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Bulletin of the American Physical Society

Percolation and Quantum Criticality: a New Universality Class

Sean Fayfar, Alex Bretaña, Wouter Montfrooij, Thomas Heitmann

Published Mar 3, 2020• 0 citations
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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.
Abstract We present computer simulations on a class of percolative systems that forms a new universality class. We determine the universal critical exponents for this new class from simulations on lattices consisting of up to one billion sites. These new percolative systems differ from standard systems in that once a cluster breaks off the lattice spanning cluster, its sites become protected and cannot be removed. We demonstrate that despite this restriction on the evolution of isolated clusters, the scaling relationships between the critical exponents remain valid. Protected percolation closely mimics the situation in heavily-doped quantum critical systems where isolated magnetic clusters are protected from Kondo screening. We show that protected percolation in three dimensions violates the Harris criterion, explaining why universal exponents for quantum phase transitions have been elusive.
We present a new family of percolation models. We show, using theory and computer simulations, that these represent a new universality class. Interestingly, systems in this class appear to violate the Harris criterion, making model systems within these class ideal systems for studying the influence of disorder on critical behavior. We argue that such percolative systems have already been realized in practice in strongly correlated electron systems that have been driven to the quantum critical point by means of chemical substitution.