Complex critical exponents in quantum percolation transitions

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Date/Time:Thursday, 09 Dec 2010 - Thursday, 09 Dec 2010
Channel:Condensed Matter Physics
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Rafael M. Fernandes Ames Laboratory and Iowa State University

The ubiquitous presence of disorder in real materials can significantly change their behavior close to a phase transition. In percolative systems, disorder is introduced via random dilution, leading to geometric fluctuations that diverge at the percolation threshold. Although the effects of percolation in classical phase transitions have been widely studied, the investigation of the interplay between geometric and quantum fluctuations is rather recent.

In this seminar, I will discuss the thermodynamic properties of a variety of diluted quantum systems at the percolation threshold, such as Josephson-junction arrays, quantum antiferromagnets and interacting bosons. In particular, I will show that the critical behavior of these systems is dramatically affected by their Berry phase 2 Rho. For rational Rho, large clusters of occupied sites govern the low-energy properties, leading to power-law behavior with the same critical exponents as in the case with no Berry phase. However, for irrational Rho, the low-energy excitations at the quantum percolation critical point change completely and are given by emergent spinless fermions with fractal spectrum. Physically, degenerate clusters of intermediate size and arbitrarily low energy dominate the low-temperature physics. As a result, critical properties that cannot be described by the usual Ginzburg-Landau-Wilson theory of phase transitions emerge, such as complex critical exponents and dynamically broken scale invariance.