Ground-state fidelity and Kosterlitz–Thouless phase transition for the spin-1/2 Heisenberg chain with next-to-the-nearest-neighbor interaction

Abstract

The Kosterlitz–Thouless transition for the spin-1/2 Heisenberg chain with the next-to-the-nearest-neighbor interaction is investigated in the context of an infinite matrix product state algorithm, which is a generalization of the infinite time-evolving block decimation algorithm (Vidal 2007 Phys. Rev. Lett. 98 070201) to accommodate both the next-to-the-nearest-neighbor interaction and spontaneous dimerization. It is found that, in the critical regime, the algorithm automatically leads to infinite degenerate ground-state wavefunctions, due to the finiteness of the truncation dimension. This results in pseudo-symmetry spontaneous breakdown, which is reflected as a catastrophe point in the ground-state fidelity per lattice site. In addition, this allows the introduction of a pseudo-order parameter to characterize the Kosterlitz–Thouless transition. Our work demonstrates that the ground-state fidelity per lattice site is able to capture the Kosterlitz–Thouless transition, which is in sharp contrast to the fidelity susceptibility that fails to detect it.