Identifying spin nematic phases and parent Hamiltonians*

We are studying spin nematic phases and characterizing their properties. Traditionally quadrupolar moments have been theorized in S=1 biquadratic Hamiltonians on the sites and in S=½ Hamiltonians on the bonds [1]. These phases however are hard to experimentally detect because, unlike a magnetically ordered phase, they don’t have spin-dipoles that can couple to a magnetic field. Moreover, even theoretically these phases have been shown to be more elusive than originally thought. For instance, previously the regime in which nematic phases occur in the J1-J2 ferromagnetic-antiferromagnetic Heisenberg system was expected to be much larger than what recent DMRG studies have shown [2]. Building on the idea of the resonating valence bond picture of Quantum Spin Liquids [3], one can describe a spin-½ system in which triplets on the bonds are resonating with short range entanglement. One such study to do so found different potential spin nematic phases in the J1-J2 system using parton mean field theory [4]. However, although these phases were shown to be stable analytically, these phases did not align with the results of DMRG [2]. Our goal is to identify parent Hamiltonians for these elusive phases in which we can examine the stability nematic phase using parton mean field theory and complement our analysis with numerical DMRG simulations.

1. Lacroix, Claudine & Mendels, Philippe & Mila, Frédéric. (2011). Introduction to Frustrated Magnetism. Introduction to Frustrated Magnetism: Materials, Experiments, Theory, Springer Series in Solid-State Sciences, Volume 164. ISBN 978-3-642-10588-3. Springer-Verlag Berlin Heidelberg, 2011. -1. pp 331-362

2. Jiang, Shengtao et al. “Where is the Quantum Spin Nematic?.” Physical review letters vol. 130,11 (2023): 116701. doi:10.1103/PhysRevLett.130.116701

3. Savary, Lucile and Leon Balents. “Quantum spin liquids: a review.” Reports on Progress in Physics 80 (2016): n. pag.

4. Shindou, Ryuichi and Tsutomu Momoi. “SU(2) slave-boson formulation of spin nematic states in S=1/2 frustrated ferromagnets.” Physical Review B 80 (2009): 064410.