Percolation quantum phase transitions in diluted magnets

Abstract

We show that the interplay of geometric criticality and quantum fluctuations leads to a novel universality class for the percolation quantum phase transition in diluted magnets. All critical exponents involving dynamical correlations are different from the classical percolation values, but in two dimensions they can nonetheless be determined exactly. We develop a complete scaling theory of this transition, and we relate it to recent experiments in La${}_2$Cu${}_{1-p}$(Zn,Mg)${}_p$O${}_4$. Our results are also relevant for disordered interacting boson systems.

4 pages, 3 eps figures, final version, as published

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• Effect of nonmagnetic dilution in honeycomb lattice iridates Na${}_2$IrO${}_3$ and Li${}_2$IrO${}_3$
• Stripe-like nanoscale structural phase separation and optimal inhomogeneity in superconducting BaPb${}_{1-x}$Bi${}_x$O${}_3$
• Quantum phase transitions of the diluted O(3) rotor model
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• Low-energy dynamics of the two-dimensional S=1/2 Heisenberg antiferromagnet on percolating clusters
• Quantum disorder and Griffiths singularities in bond-diluted two-dimensional Heisenberg antiferromagnets
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• Absorbing-state phase transitions on percolating lattices
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• Complex critical exponents for percolation transitions in Josephson-junction arrays, antiferromagnets, and interacting bosons
• Magnetic order in lightly doped cuprates: Coherent vs. incoherent hole quasiparticles and non-magnetic impurities
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• Quantum critical behavior of a three-dimensional superfluid-Mott glass transition
• Localization of the Higgs mode at the superfluid-Mott glass transition
• Quantum discontinuity fixed point and renormalization group flow of the SYK model
• Dynamic scaling of the restoration of rotational symmetry in Heisenberg quantum antiferromagnets
• The Griffiths Phase on Hierarchical Modular Networks with Small-world Edges
• Effect of long range connections on an infinite randomness fixed point associated with the quantum phase transitions in a transverse Ising model
• Two-dimensional percolation transition in two atomic layers of Fe on W(110): Direct measurement of a static percolation critical exponent in a two-dimensional Ising system
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• Superfluid-Mott glass quantum multicritical point on a percolating lattice
• Percolation transition in quantum Ising and rotor models with sub-Ohmic dissipation
• Quantum transitions from superfluid to insulating phases in disordered Bose systems
• Effects of dilution in a 2D topological magnon insulator
• Quadrupolar quantum criticality on a fractal