In this thesis we present results from quantum Monte Carlo for the fully-frustrated honeycomb lattice. The XXZ model is of interest in the classical limit, as there is a mapping between the classical fully-frustrated honeycomb Ising model groundstates and the classical hard-core dimer model groundstate. The aim of this work is to explore the effect of quantum fluctuations on the fully-frustrated honeycomb model to see what sort of interesting physics arises. One might expect unusual physics due to the quantum hard-core dimer model, where interesting physics are known to exist. This is because there is a duality mapping between the classical dimer model and the classical fully-frustrated honeycomb Ising model. Indeed, by studying the fully-frustrated honeycomb XXZ model we find that in some cases the system orders into crystal-like structures, a case of order-by-disorder. The most interesting case, when the frustrating bonds are chosen randomly, reveals to us a novel state without any discernible order while at the same time avoiding the freezing one would expect of a glass. This state is a featureless system lacking low temperature magnetic susceptibility---a candidate ``quantum spin liquid''. Future work that might more easily measure quantum spin liquid criteria is suggested.

In this thesis we present results from quantum Monte Carlo for the fully-frustrated honeycomb lattice. The XXZ model is of interest in the classical limit, as there is a mapping between the classical fully-frustrated honeycomb Ising model groundstates and the classical hard-core dimer model groundstate. The aim of this work is to explore the effect of quantum fluctuations on the fully-frustrated honeycomb model to see what sort of interesting physics arises. One might expect unusual physics due to the quantum hard-core dimer model, where interesting physics are known to exist. This is because there is a duality mapping between the classical dimer model and the classical fully-frustrated honeycomb Ising model. Indeed, by studying the fully-frustrated honeycomb XXZ model we find that in some cases the system orders into crystal-like structures, a case of order-by-disorder. The most interesting case, when the frustrating bonds are chosen randomly, reveals to us a novel state without any discernible order while at the same time avoiding the freezing one would expect of a glass. This state is a featureless system lacking low temperature magnetic susceptibility---a candidate ``quantum spin liquid''. Future work that might more easily measure quantum spin liquid criteria is suggested.

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