For Na2Ti3Cl8, the high-temperature magnetic Hamiltonian has a spin-nematic (quadrupolar) ground state, and the breathing lattice distortion, driven by spin-lattice coupling, is required to stabilize the experimentally observed trimerized phase.
Spin-$S$ designer hamiltonians and the square lattice $S=1$ Haldane nematic
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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 N\'eel and Haldane nematic phase, which we find to be of first order.
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Spin--lattice coupling and the emergence of the trimerized phase in the $S=1$ Kagome antiferromagnet Na$_2$Ti$_3$Cl$_8$
For Na2Ti3Cl8, the high-temperature magnetic Hamiltonian has a spin-nematic (quadrupolar) ground state, and the breathing lattice distortion, driven by spin-lattice coupling, is required to stabilize the experimentally observed trimerized phase.