The anisotropic quantum antiferromagnet on the Sierpinski gasket: Ground state and thermodynamics

TL;DR

This study explores the quantum antiferromagnetic S=1/2 system on a Sierpinski gasket, revealing a disordered ground state with short-range correlations and a small spin gap, using a new numerical method.

Contribution

Introduces the configuration selective diagonalization (CSD) method and applies it to analyze the ground state and thermodynamics of the quantum antiferromagnet on a fractal lattice.

Findings

Disordered magnetic ground state with short correlation length (~1)

Presence of a very small spin gap

Results consistent for Heisenberg and XY models

Abstract

We investigate an antiferromagnetic s=1/2 quantum spin system with anisotropic spin exchange on a fractal lattice, the Sierpinski gasket. We introduce a novel approximative numerical method, the configuration selective diagonalization (CSD) and apply this method to the Sierpinski gasket with N=42. Using this and other methods we calculate ground state energies, spin gap, spin-spin correlations and specific heat data and conclude that the s=1/2 quantum antiferromagnet on the Sierpinski gasket shows a disordered magnetic ground state with a very short correlation length of about 1 and an, albeit very small, spin gap. This conclusion holds for Heisenberg as well a for XY exchange.