Kosterlitz–Thouless phase transition and ground state fidelity: a novel perspective from matrix product states

The Kosterlitz–Thouless transition is studied from the representation of the systems's ground state wavefunctions in terms of matrix product states for a quantum system on an infinite-size lattice in one spatial dimension. It is found that, in the critical regime for a one-dimensional quantum lattice system with continuous symmetry, the newly developed infinite matrix product state algorithm automatically leads to infinite degenerate ground states, due to the finiteness of the truncation dimension. This results in pseudo continuous symmetry spontaneous breakdown, which allows the introduction of a pseudo-order parameter that must be scaled down to zero, in order to be consistent with the Mermin–Wegner theorem. We also show that the ground state fidelity per lattice site exhibits a catastrophe point, thus resolving a controversy regarding whether or not the ground state fidelity is able to detect the Kosterlitz–Thouless transition. (letter)