Ordering near the percolation threshold in models of 2D interacting bosons with quenched dilution

Abstract

Randomly diluted quantum boson and spin models in two dimensions combine the physics of classical percolation with the well-known dimensionality dependence of ordering in quantum lattice models. This combination is rather subtle for models that order in two dimensions but have no true order in one dimension, as the percolation cluster near threshold is a fractal of dimension between 1 and 2: two experimentally relevant examples are the O(2) quantum rotor and the Heisenberg antiferromagnet. We study two analytic descriptions of the O(2) quantum rotor near the percolation threshold. First a spin-wave expansion is shown to predict long-ranged order, but there are statistically rare points on the cluster that violate the standard assumptions of spin-wave theory. A real-space renormalization group (RSRG) approach is then used to understand how these rare points modify ordering of the O(2) rotor. A new class of fixed points of the RSRG equations for disordered 1D bosons is identified and shown to support the existence of long-range order on the percolation backbone in two dimensions. These results are relevant to experiments on bosons in optical lattices and superconducting arrays, and also (qualitatively) for the diluted Heisenberg antiferromagnet.

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Cited by in corpus (15)

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• A Mott Glass to Superfluid Transition for Random Bosons in Two Dimensions
• Monopole Current and Unconventional Hall Response on Topological Insulator
• Quantum phase transitions of the diluted O(3) rotor model
• Quantum-criticality and percolation in dimer-diluted 2D antiferromagnets
• Nature of the low-energy excitations of two-dimensional diluted Heisenberg quantum antiferromagnets
• Low-energy dynamics of the two-dimensional S=1/2 Heisenberg antiferromagnet on percolating clusters
• Emergent Spin Excitations in a Bethe Lattice at Percolation
• Complex critical exponents for percolation transitions in Josephson-junction arrays, antiferromagnets, and interacting bosons
• Density-matrix based numerical methods for discovering order and correlations in interacting systems
• Schwinger boson mean field perspective on emergent spins in diluted Heisenberg antiferromagnets
• Percolation via combined electrostatic and chemical doping in complex oxide films
• Quadrupolar quantum criticality on a fractal