Exact diagonalization study of the Hubbard-parametrized four-spin ring exchange model on a square lattice

We have used exact numerical diagonalization to study the excitation spectrum and the dynamic spin correlations in the \(s=1/2\) next-next-nearest neighbor Heisenberg antiferromagnet on the square lattice, with additional 4-spin ring exchange from higher order terms in the Hubbard expansion. We have varied the ratio between Hubbard model parameters, \(t/U\), to obtain different relative strengths of the exchange parameters, while keeping electrons localized. The Hubbard model parameters have been parametrized via an effective ring exchange coupling, \(J_r\), which have been varied between 0\(J\) and 1.5\(J\). We find that ring exchange induces a quantum phase transition from the \((\pi, \pi)\) ordered Neèl state to a \((\pi/2, \pi/2)\) ordered state. This quantum critical point is reduced by quantum fluctuations from its mean field value of \(J_r/J = 2\) to a value of \(\sim 1.1\). At the quantum critical point, the dynamical correlation function shows a pseudo-continuum at \(q\)-values between the two competing ordering vectors.