Numerical Investigations of SO(4) Emergent Extended Symmetry in Spin-1/2 Heisenberg Antiferromagnetic Chains

TL;DR

This paper uses quantum Monte Carlo simulations to numerically investigate the emergent SO(4) extended symmetry in spin-1/2 Heisenberg antiferromagnetic chains, confirming its effects on correlation functions.

Contribution

It demonstrates the emergence of SO(4) symmetry in a modified Heisenberg chain and confirms its influence on correlation functions through numerical analysis.

Findings

Correlation functions approach conformal field theory predictions

Extended symmetry constrains spin and dimer correlations

Logarithmic corrections are effectively avoided in the modified model

Abstract

The antiferromagnetic Heisenberg chain is expected to have an extended symmetry, [SU(2)xSU(2)]/Z 2 , in the infrared limit, whose physical interpretation is that the spin and dimer order parameters form the components of a common 4-dimensional vector. Here we numerically in- vestigate this emergent symmetry using quantum Monte Carlo simulations of a modified Heisenberg chain (the J-Q model) in which the logarithmic scaling corrections of the conventional Heisenberg chain can be avoided. We show how the two- and three-point spin and dimer correlation func- tions approach their forms constrained by conformal field theory as the system size increases and numerically confirm the expected effects of the extended symmetry on various correlation functions.