Spin-$S$ designer hamiltonians and the square lattice $S=1$ Haldane nematic

Abstract

We introduce a strategy to write down lattice models of spin rotational symmetric Hamiltonians with arbitrary spin-$S$ that are Marshall positive and can be simulated efficiently using world line Monte Carlo methods. As an application of our approach we consider a square lattice $S=1$ model for which we design a $3\times 3$ - spin plaquette interaction. By numerical simulations we establish that our model realizes a novel "Haldane nematic" phase that breaks lattice rotational symmetry by the spontaneous formation of Haldane chains, while preserving spin rotations, time reversal and lattice translations. By supplementing our model with a two-spin Heisenberg interaction, we present a study of the transition between Néel and Haldane nematic phase, which we find to be of first order.

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• One-dimensional model for deconfined criticality with ${\mathbb{Z}}_3\times {\mathbb{Z}}_3$ symmetry
• Stochastic Series Expansion Methods
• First-order Néel-cVBS transition in a model square lattice $S=1$ antiferromagnet
• Resummation-based updates for Stochastic Series Expansion Quantum Monte Carlo
• Phase diagram of the SU($N$) antiferromagnet of spin $S$ on a square lattice
• Competition between Neel, Haldane nematic, plaquette valence bond solid, and $(\pi ,\pi )$ valence bond solid phases in SU(N) analogs of $S=1$ square-lattice antiferromagnets
• Deconfined pseudocriticality in a model spin-1 quantum antiferromagnet
• First-order Néel-VBS transition in $S=3/2$ antiferromagnets