Percolation on Lieb lattices

Abstract

We study site- and bond-percolation on a class of lattices referred to as Lieb lattices. In two dimensions the Lieb lattice (LL) is also known as the decorated square lattice, or as the CuO${}_2$ lattice; in three dimensions it can be generalized to a layered Lieb lattice (LLL) or to a perovskite lattice (PL). Emergent electronic phenomena, such as topological states and ferrimagnetism, have been predicted to occur in these systems, which may be realized in optical lattices as well as in solid state. Since the study of the interplay between quantum fluctuations and disorder in these systems requires the availability of accurate estimates of geometrical critical parameters, such as percolation thresholds and correlation length exponents, here we use Monte Carlo simulations to obtain these data for Lieb lattices when a site (or bond) is present with probability $p$. We have found that the thresholds satisfy a mean-field (Bethe lattice) trend, namely that the critical concentration, $p_c$, increases as the average coordination number decreases; our estimates for the correlation length exponent are in line with the expectation that there is no change in the universality class.

arXiv comment5 pages, 5 figures

References in corpus (20)

• Many-Body Physics with Ultracold Gases
• Fermi-Hubbard physics with atoms in an optical lattice
• Tools for quantum simulation with ultracold atoms in optical lattices
• Coherent driving and freezing of bosonic matter wave in an optical Lieb lattice
• Topological Insulators on the Lieb and Perovskite Lattices
• Scaling corrections: site-percolation and Ising model in three dimensions
• Bond and Site Percolation in Three Dimensions
• Classical percolation transition in the diluted two-dimensional S=1/2 Heisenberg antiferromagnet
• Topological phase transitions driven by next-nearest-neighbor hopping in two-dimensional lattices
• Pseudorandom Number Generators and the Square Site Percolation Threshold
• An investigation of site-bond percolation on many lattices
• Ferromagnetism beyond Lieb's theorem
• Magnetism in the three-dimensional layered Lieb lattice: Enhanced transition temperature via flat-band and Van Hove singularities
• Compressible Ferrimagnetism in the depleted Periodic Anderson Model
• Destruction of Superconductivity by Impurities in the Attractive Hubbard Model
• Disordered two-dimensional superconductors: roles of temperature and interaction strength
• Enhancement of Long Range Antiferromagnetic Order by Nonmagnetic Impurities in the Hubbard Model
• Dynamical resilience to disorder: the dilute Hubbard model on the Lieb lattice
• Site percolation on lattices with low average coordination numbers
• Effect of site dilution in the two-dimensional attractive Hubbard model