Valence Bond States: Link models

TL;DR

This paper introduces a valence bond state model for isotropic antiferromagnetic quantum states on a square lattice, analyzing its correlations and relevance to real materials using theoretical and numerical methods.

Contribution

It presents a novel valence bond state construction for antiferromagnetic systems, with detailed correlation analysis and comparison to experimental data.

Findings

Correlation functions match neutron scattering data

Model captures key features of antiferromagnetic insulators

Numerical and analytical methods validate the state’s properties

Abstract

An isotropic anti-ferromagnetic quantum state on a square lattice is characterized by symmetry arguments only. By construction, this quantum state is the result of an underlying valence bond structure without breaking any symmetry in the lattice or spin spaces. A detailed analysis of the correlations of the quantum state is given (using a mapping to a 2D classical statistical model and methods in field theory like mapping to the non-linear sigma model or bosonization techniques) as well as the results of numerical treatments (regarding exact diagonalization and variational methods). Finally, the physical relevance of the model is motivated. A comparison of the model to known anti-ferromagnetic Mott-Hubbard insulators is given by means of the two-point equal-time correlation function obtained i) numerically from the suggested state and ii) experimentally from neutron scattering on cuprates in the anti-ferromagnetic insulator phase.