  The spontaneous breaking of a global discrete translational symmetry in the
finite, lattice quantum sine-Gordon model is demonstrated by a density matrix
renormalization group. A phase diagram in the coupling constant - inverse
system size plane is obtained. Comparison of the phase diagram with a
Woomany-Wyld finite-size scaling leads to an identification of the
Berezinskii-Kosterlitz-Thouless transition in the quantum sine-Gordon model as
the spontaneous symmetry breaking.
