Thermodynamics of the Antiferromagnetic Heisenberg Model on the Checkerboard Lattice

TL;DR

This study uses advanced numerical methods to analyze the thermodynamic properties of the antiferromagnetic Heisenberg model on the checkerboard lattice, revealing how frustration affects phase transitions and magnetic orderings at low temperatures.

Contribution

It introduces the application of numerical linked-cluster expansions combined with extrapolation techniques to explore low-temperature behaviors of the model, surpassing previous limitations of exact diagonalization.

Findings

High-temperature peak in specific heat decreases with increased frustration.

Disappearance of long-range antiferromagnetic order beyond J'=0.75J.

Large susceptibilities for stripe and Neel order at J'=4J.

Abstract

Employing numerical linked-cluster expansions (NLCEs) along with exact diagonalizations of finite clusters with periodic boundary condition, we study the energy, specific heat, entropy, and various susceptibilities of the antiferromagnetic Heisenberg model on the checkerboard lattice. NLCEs, combined with extrapolation techniques, allow us to access temperatures much lower than those accessible to exact diagonalization and other series expansions. We find that the high-temperature peak in specific heat decreases as the frustration increases, consistent with the large amount of unquenched entropy in the region around maximum classical frustration, where the nearest-neighbor and next-nearest neighbor exchange interactions (J and J', respectively) have the same strength, and with the formation of a second peak at lower temperatures. The staggered susceptibility shows a change of character when J' increases beyond 0.75J, implying the disappearance of the long-range antiferromagnetic order at zero temperature. For J'=4J, in the limit of weakly coupled crossed chains, we find large susceptibilities for stripe and Neel order with Q=(pi/2,pi/2) at low temperatures with antiferromagnetic correlations along the chains. Other magnetic and bond orderings, such as a plaquette valence-bond solid and a crossed-dimer order suggested by previous studies, have also been investigated.