Frustrated Magnetism

Frustrated magnets are systems where local magnetic moments cannot be properly aligned at low temperatures. The resulting strong fluctuations can cause the system to stabilize exotic states of matter. This includes several (chiral) spin liquids and valence bond solids, for which I have demonstrated that they can emerge in rather simple Heisenberg antiferromagnets.

The mechanisms of high-temperature superconductivity are yet to be fully understood. The idea of electron-holes traveling in a background of strongly fluctuating magnetic moments has been proposed early as one of the most promising explanations . The fluctuating background spins have been envisioned to form an exotic state of matter, a so-called quantum spin liquid. Although quantum spin liquids have been proposed in the late 1980s, until very recently no simple model realizing this exotic physics has been known. Advances in numerical methods solved this problem around 2015. Using a combination of exact diagonalization and Gutzwiller projected ansatz wave functions I was among the first to show conclusive evidence for the emergence of a chiral spin liquid state in simple antiferromagnetic Heisenberg models on the kagome and triangular lattice . Different groups also confirmed my findings using the density matrix renormalization group (DMRG) method . Recently, we also discovered another kind of chiral spin liquid in a simple model with SU(3) degrees of freedom on the square lattice by a combination af various methods and a diamond valence bond solid in the kagome lattice.

Phase diagrams established for particular frustrated Heisenberg models on the triangular and kagome lattice. (Left) We found a chiral spin liquid being realized in an extended region of the phase diagram on the triangular lattice (Right) A diamond valence bond solid is stablized on the kagome lattice extending close to the nearest-neighbor only Heisenberg model.