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arXiv:1812.04277 · Physical review. B./Physical review. B

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

Camilla Buhl Larsen, Astrid Tranum Rømer, Sofie Holm-Janas, F. Treue, B. Mønsted, N. E. Shaik, Henrik Moodysson Rønnow, Kim Lefmann

Published Feb 27, 2019• 17 citations
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Abstract

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 four-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 $0J$ and 1.$5J$. We find that ring exchange induces a quantum phase transition from a $(\ensuremath{\pi},\ensuremath{\pi})$ ordered state to a $(\ensuremath{\pi}/2,\ensuremath{\pi}/2)$ 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 $\ensuremath{\sim}1.1$. At the quantum critical point, the dynamical correlation function shows a pseudocontinuum at $q$ values between the two competing ordering vectors.

DOI
10.1103/physrevb.99.054432

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