  Frustrated quantum magnets may exhibit fascinating collective phenomena. The
main goal of this dissertation is to provide conclusive evidence for the
emergence of novel phases of matter like quantum spin liquids in local quantum
spin models. We develop novel algorithms for large-scale Exact Diagonalization
computations. Sublattice coding methods for efficient use of lattice symmetries
in the procedure of diagonalizing the Hamiltonian matrix are proposed and
suggest a randomized distributed memory parallelization strategy. Benchmarks of
computations on various supercomputers with system size up to 50 spin-1/2
particles have been performed. Results concerning the emergence of a chiral
spin liquid in a frustrated kagome Heisenberg antiferromagnet are presented.
The stability and extent of this phase are discussed. In an extended Heisenberg
model on the triangular lattice, we establish another chiral spin liquid phase.
We discuss the special case of the Heisenberg $J_1$-$J_2$ model and present a
scenario where the critical point of phase transition from the 120-degree
N\'eel to a putative $\mathbf{Z}_2$ spin liquid is described by a Dirac spin
liquid. A generalization of the SU(2) Heisenberg model with SU(N) degrees of
freedom on the triangular lattice with an additional ring-exchange term is
discussed. We present our contribution to the project and the final results
that suggest a series of chiral spin liquid phases in an extended parameter
range. Finally, we present preliminary data from a Quantum Monte Carlo study of
an SU(N) version of the J-Q model on a square lattice for N=2,...,10, and
multi-column representations. We establish the phase boundary between the
N\'eel ordered phase and the disordered phases. The disordered phase in the
four-column representation is expected to be a two-dimensional analog of the
Haldane phase for the spin-1 Heisenberg chain.

Strongly Correlated Electrons