Spontaneous symmetry breaking in the finite lattice quantum sine-gordon model

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.