Bifurcation in ground-state fidelity for a one-dimensional spin model with competing two-spin and three-spin interactions

TL;DR

This paper explores a one-dimensional quantum spin model with competing two-spin and three-spin interactions, using tensor network algorithms to analyze ground-state fidelity bifurcations and identify phase transitions.

Contribution

It introduces an adaptation of the infinite time-evolving block decimation algorithm for systems with three-spin interactions and characterizes phase transitions via fidelity bifurcations.

Findings

Fidelity per lattice site exhibits bifurcation at critical points.

Critical points are identified through fidelity analysis.

Local order parameters characterize different phases.

Abstract

A one-dimensional quantum spin model with the competing two-spin and three-spin interactions is investigated in the context of a tensor network algorithm based on the infinite matrix product state representation. The algorithm is an adaptation of Vidal's infinite time-evolving block decimation algorithm to a translation-invariant one-dimensional lattice spin system involving three-spin interactions. The ground-state fidelity per lattice site is computed, and its bifurcation is unveiled, for a few selected values of the coupling constants. We succeed in identifying critical points and deriving local order parameters to characterize different phases in the conventional Ginzburg-Landau-Wilson paradigm.