Condensed Matter

Frustrated magnets provide a fertile ground for discovering exotic states of matter, such as those with topologically non-trivial properties. Motivated by several near-ideal material realizations, we focus on aspects of the two-dimensional kagome antiferromagnet. I present two of our works in this area both involving the spin-1/2 XXZ antiferromagnetic Heisenberg model. First, guided by a previous field theoretical study, we explore the XY limit ($J_z=0$) for the case of 2/3 magnetization (i.e. 1/6 filling of hard-core bosons) 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 $J_z/J=-1/2$. This point in the phase diagram has "three coloring" states as its exact 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 certain aspects of the highly contentious Heisenberg case (in zero field) and suggest that it is possibly 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, under review.

Many model quantum spin systems have been proposed to realize critical points or phases described by 2+1 dimensional conformal gauge theories. On a torus of size L and modular parameter τ, the energy levels of such gauge theories equal (1/L) times universal functions of τ. We compute the universal spectrum of QED3, a U(1) gauge theory with Nf two-component massless Dirac fermions, in the large-Nf limit. We also allow for a Chern-Simons term at level k, and show how the topological k-fold ground state degeneracy in the absence of fermions transforms into the universal spectrum in the presence of fermions; these computations are performed at fixed Nf/k in the large-Nf limit.