  Landau theory's implicit assumption that microscopic details cannot affect
the system's phases has been challenged only recently in systems such as
antiferromagnetic quantum spin chains with periodic boundary conditions, where
topological frustration can be induced. In this work, we show that the latter
modifies the zero temperature phase diagram of the XY chain in a transverse
magnetic field by inducing new quantum phase transitions. In doing so, we come
across the first case of second order boundary quantum phase transition
characterized by a quartic dispersion relation. Our analytical results are
supported by numerical investigations and lay the foundation for understanding
the phase diagram of this frustrated model.
