Small changes in an external parameter can often lead to dramatic qualitative changes in
the lowest energy quantum mechanical ground state of a correlated electron system. In …

It is known from the Mermin-Wagner theorem that magnetic long-range order can exist in two
dimensions only at zero temperature, but even then it can still be destroyed eg by quantum …

Perturbation series expansion methods are sophisticated numerical tools used to provide
quantitative calculations in many areas of theoretical physics. This book gives a …

Using both exact diagonalizations and diagonalizations in a subset of short-range valence-
bond singlets, we address the nature of the groundstate of the Heisenberg spin-1∕ 2 …

The resonating-valence-bond (RVB) theory for two-dimensional quantum antiferromagnets
is shown to be the correct paradigm for large enough “quantum frustration.” This scenario …

We revisit the phase transition from the Néel ordered to a valence bond solid (VBS) state in
the two-dimensional J 1-J 2 antiferromagnetic Heisenberg model. In the first part we address …

Abstract We study an S= 1/2 Heisenberg model on the honeycomb lattice with first and
second neighbor antiferromagnetic exchange (J 1–J 2 model), employing exact …

We report exact calculations of magnetic and superconducting pair-pair correlations for the
half-filled band Hubbard model on an anisotropic triangular lattice. Our results for the …

We study the zero-temperature phase diagram of the two-dimensional quantum J 1 XXZ–J 2
XXZ spin-1/2 anisotropic Heisenberg model on the square lattice. In particular, the effects of …

This review presents some theoretical advances in the field of quantum magnetism in two-
dimensional systems, and quantum spin liquids in particular. The first version published in …