  Quantum phase transitions are sudden changes in the ground-state wavefunction
of a many-body system that can occur as a control parameter such as a
concentration or a field strength is varied. They are driven purely by the
competition between quantum fluctuations and mutual interactions among
constituents of the system, not by thermal fluctuations; hence they can occur
even at zero temperature. Examples of quantum phase transitions in many-body
physics may be found in systems ranging from high-temperature superconductors
to topological insulators. A quantum phase transition usually can be
characterized by nonanalyticity/discontinuity in certain order parameters or
divergence of the ground state energy eigenvalue and/or its derivatives with
respect to certain physical quantities. Here in a circular one-dimensional spin
model with Heisenberg XY interaction and no magnetic field, we observe critical
phenomena for the $n_0=1/N\rightarrow0$ Mott insulator caused by a qualitative
change of the boundary condition. We demonstrate in the vicinity of the
transition point a sudden change in ground-state properties accompanied by an
avoided level-crossing between the ground and the first excited states.
Notably, our result links conventional quantum phase transitions to microscopic
boundary conditions, with significant implications for quantum information,
quantum control, and quantum computing.
