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.