New preprint entitled „Symmetry breaking and competing valence bond states in the star lattice Heisenberg antiferromagnet“
New preprint arXiv:2508.05133 entitled “Symmetry breaking and competing valence bond states in the star lattice Heisenberg antiferromagnet”. This work is a nice collaboration with Pratyay Ghosh, Samuel Nyckees, and Frederic Mila from EPF Lausanne and LEP members Jan Alexander Koziol and Kai Phillip Schmidt.
In this work we investigate the ground state phase diagram of the spin-1/2 antiferromagnetic Heisenberg model on the star lattice using infinite projected entangled pair states (iPEPS) and high-order series expansions. The model includes two distinct couplings: Jd on the dimer bonds and Jt on the trimer bonds. While it is established that the system hosts a valence bond solid (VBS) phase for Jd≥Jt, the ground state phase diagram for Jd<Jt has remained unsettled.
Our iPEPS simulations uncover a first-order phase transition at Jd/Jt≈0.18, significantly lower than previously reported estimates. Beyond this transition, we identify a close competition between two valence bond crystal (VBC) states: a columnar VBC and a 3–√×3–√ VBC, with the latter consistently exhibiting lower energy across all finite bond dimensions.
The high-order series expansion supports this by finding that the 3–√×3–√ VBC state indeed becomes energetically favorable, but only at sixth order in perturbation theory, revealing the subtle nature of the competition between candidate states.