Ground-State Fidelity and Kosterlitz-Thouless Phase Transition for Spin 1/2 Heisenberg Chain with Next-to-the-Nearest-Neighbor Interaction

TL;DR

This paper investigates the Kosterlitz-Thouless phase transition in a spin 1/2 Heisenberg chain with next-to-nearest interactions using an advanced matrix product state algorithm, revealing pseudo symmetry breaking and a new order parameter.

Contribution

It introduces a generalized infinite matrix product state algorithm to study the transition, capturing pseudo symmetry breaking and defining a pseudo-order parameter.

Findings

Algorithm detects bifurcation in ground-state fidelity.

Pseudo symmetry spontaneous breakdown observed.

Pseudo-order parameter characterizes the transition.

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.