Quantum Spins and Quasiperiodicity: a real space renormalization group approach

TL;DR

This paper applies a real space renormalization group approach to study the antiferromagnetic spin-1/2 Heisenberg model on a quasiperiodic octagonal tiling, providing insights into its ground state properties.

Contribution

It introduces an approximate block spin renormalization scheme for quasiperiodic structures and compares results with Quantum Monte Carlo calculations.

Findings

Ground state energy estimated and compared with Monte Carlo results.

Local staggered magnetizations calculated for the quasiperiodic tiling.

Conjecture that the ground state energy matches that of the square lattice antiferromagnet.

Abstract

We study the antiferromagnetic spin-1/2 Heisenberg model on a two-dimensional bipartite quasiperiodic structure, the octagonal tiling -- the aperiodic equivalent of the square lattice for periodic systems. An approximate block spin renormalization scheme is described for this problem. The ground state energy and local staggered magnetizations for this system are calculated, and compared with the results of a recent Quantum Monte Carlo calculation for the tiling. It is conjectured that the ground state energy is exactly equal to that of the quantum antiferromagnet on the square lattice.