Ground State Properties of a Fully Frustrated Quantum Spin System

А. А. Овчинников, V. Ya. Krivnov, Д. В. Дмитриев

Hidetsugu Kitatani, 北谷 英嗣

Jianjun Jiang

Élliott H. Lieb, Peter Schupp

We find that ground states of the quantum Heisenberg antiferromagnet on the geometrically frustrated pyrochlore checkerboard lattice are singlets and can be expressed in terms of positive matrices. The magnetization at zero external field vanishes for each frustrated tetrahedral unit separately, and there is an upper bound of 1/8 in natural units on the susceptibility both for the ground state and at finite temperature. These results are the first exact ones in this field and generalize to some other lattices. The approach is also of interest for other spin systems.

Shu Tanaka

In this paper we show quantum fluctuation effect of fully frustrated Ising spin systems. Quantum annealing has been expected to be an efficient method to find ground state of optimization problems. However it is not clear when to use the quantum annealing. In order to clarify when the quantum annealing works well, we have to study microscopic properties of quantum annealing. In fully frustrated Ising spin systems, there are macroscopically degenerated ground states. When we apply quantum annealing to fully frustrated systems, we cannot obtain each ground state with the same probability. This nature is consistent with "order by disorder" which is well-known mechanism in frustrated systems.

Kenn Kubo, Tota Nakamura