Ground-State Fidelity and Kosterlitz-Thouless Phase Transition for 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 [G. Vidal, Phys. Rev. Lett. \textbf{98}, 070201 (2007)] 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 wave functions, due to the finiteness of the truncation dimension. This results in \textit{pseudo} symmetry spontaneous breakdown, as reflected in a bifurcation in the ground-state fidelity per lattice site. In addition, this allows to introduce a pseudo-order parameter to characterize the Kosterlitz-Thouless transition.

4 pages, 4 figures

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Cited by in corpus (5)

• Geometry of quantum phase transitions
• Fidelity at Berezinskii-Kosterlitz-Thouless quantum phase transitions
• Parity quantum numbers in the Density Matrix Renormalization Group
• Fidelity and entanglement entropy for infinite-order phase transitions
• Universal Order Parameters and Quantum Phase Transitions: A Finite-Size Approach