Abstract:

Strongly correlated electron and spin systems provide a fertile ground for discovering exotic states of matter, for example, those with topologically non-trivial properties. My talk will give a brief overview of the associated theoretical and computational challenges for studying these systems and then focus on our recent work in this area involving geometrically frustrated magnets. Motivated by near-ideal material realizations, I consider the two-dimensional kagome antiferromagnet, a problem with a rich history that still continues to baffle the community. In the first work, guided by a previous field theoretical study, we explore the XY limit ($J_z=0$) of the spin 1/2 XXZ-Heisenberg antiferromagnet for the case of 2/3 magnetization and perform exact numerical computations to search for a "chiral spin liquid phase". We provide evidence for this phase by analyzing the energetics, determining minimally entangled states and the associated modular matrices, and evaluating the many-body Chern number [1]. The second part of the talk follows from an unexpected outcome of the first work, which realized the existence of an exactly solvable point for the ratio of Ising to transverse coupling $J_z/J=-1/2$ [2]. This point in the phase diagram has "three coloring" states as its exact quantum ground states, exists for all magnetizations (fillings) and is found to be the source or "mother" of the observed phases of the kagome antiferromagnet. Using this viewpoint, I revisit aspects of the highly contentious Heisenberg case (in zero field, which is also experimentally relevant) and suggest that it is part of a line of critical points.

[1] K. Kumar, H. J. Changlani, B. K. Clark, E. Fradkin, Phys. Rev. B 94, 134410 (2016)
[2] H. J. Changlani, D. Kochkov, K. Kumar, B. K. Clark, E. Fradkin, arXiv 1703.04659, under review.