Low-lying excitations and thermodynamics of an antiferromagnetic Heisenberg fractal system of a dimension between one and two

TL;DR

This study explores the low-energy excitations and thermodynamic properties of a fractal-based antiferromagnetic Heisenberg model, revealing disordered ground states and spin gaps through advanced computational methods.

Contribution

It provides the first detailed analysis of a Heisenberg antiferromagnet on a fractal lattice, combining exact diagonalization and quantum Monte Carlo techniques.

Findings

Presence of a second maximum in specific heat at low temperatures

Evidence of a disordered ground state and spin gap

Similar thermodynamic behavior to kagome lattice antiferromagnets

Abstract

We investigate a frustrated Heisenberg spin-1/2 antiferromagnet on a fractal lattice of dimension d=ln3/ln2 (Sierpinski gasket). Calculations were performed using (a) exact diagonalization of all eigenstates and eigenvectors for systems up to N=15 and (b) the Decoupled-Cell Quantum-Monte-Carlo method for systems up to N=366. We present the low-lying spectrum and the specific heat. The specific heat shows a second maximum in the low-temperature region. This behavior is similar to the behavior of the quantum Heisenberg antiferromagnet on a kagome lattice and suggests a disordered ground state and a spin gap in the considered system.