Alladi Ramakrishnan Hall

The mother of all states of the kagome quantum antiferromagnet

Hitesh J. Changlani, Florida State University

Assistant professor, Florida State University

Strongly correlated systems provide a fertile ground for discovering exotic
states of matter, such as those with topologically non-trivial properties.
Among these are geometrically frustrated magnets, which harbor spin liquid
phases with fractional excitations. On the experimental front, this has
motivated the search for new low dimensional quantum materials. On the
theoretical front, this area of research has led to analytical and
numerical advances in the study of quantum many-body systems.

I will present aspects of our theoretical and numerical work in the area of
frustrated magnetism, focusing on the kagome geometry, which has seen a
flurry of research activity owing to several near-ideal material
realizations. On the theoretical front, the kagome problem has a rich
history and poses multiple theoretical puzzles which continue to baffle the
community. First, I will present a study of the spin-1 antiferromagnet,
where our numerical calculations indicate that the ground state is a
trimerized valence bond (simplex) solid with a spin gap [1], contrary to
previous proposals. I will show evidence from recent experiments that
support our findings but also pose new questions [2]. The second part of
the talk follows from an unexpected outcome of my general investigations in
the area for the well-studied spin-1/2 case [3]. I will highlight our
discovery of an exactly solvable point in the XXZ-Heisenberg model for the
ratio of Ising to transverse coupling $J_z/J=-1/2$ [4]. This point in the
phase diagram has "three-coloring" states as its exact quantum ground
states and is macroscopically degenerate. It exists for all magnetizations
and is the origin or "mother" of many of the observed phases of the kagome
antiferromagnet. I will revisit aspects of the contentious and
experimentally relevant Heisenberg case and discuss its relationship to the
newly discovered point [4,5].

[1] H. J. Changlani, A.M. Lauchli, Phys. Rev. B 91, 100407(R) (2015).
[2] A. Paul, C.M. Chung, T. Birol, H. J. Changlani, arXiv:1909.02020 (2019).
[3] K. Kumar, H. J. Changlani, B. K. Clark, E. Fradkin, Phys. Rev. B 94,
134410 (2016).
[4] H. J. Changlani, D. Kochkov, K. Kumar, B. K. Clark, E. Fradkin, Phys.
Rev. Lett. 120, 117202 (2018).
[5] H. J. Changlani, S. Pujari, C.M. Chung, B. K. Clark, Phys. Rev. B.
99,104433 (2019)