Ground-state fidelity and tensor network states for quantum spin tubes

TL;DR

This paper introduces an efficient tensor network algorithm to compute ground-state fidelity in quantum spin tubes, enabling the identification of quantum critical points and phase transitions.

Contribution

The paper develops a novel tensor network method for quantum spin tubes that efficiently detects quantum phase transitions via ground-state fidelity analysis.

Findings

Identification of two Kosterlitz-Thouless transitions in the spin tube model

Resolution of conflicting results on phase transitions using the new method

Efficient computation of ground-state fidelity per lattice site

Abstract

An efficient algorithm is developed for quantum spin tubes in the context of the tensor network representations. It allows to efficiently compute the ground-state fidelity per lattice site, which in turn enables us to identify quantum critical points, at which quantum spin tubes undergo quantum phase transitions. As an illustration, we investigate the isosceles spin 1/2 antiferromagnetic three-leg Heisenberg tube. Our simulation results suggest that two Kosterlitz-Thouless transitions occur as the degree of asymmetry of the rung interaction is tuned, thus offering an alternative route towards a resolution to the conflicting results on this issue arising from the density matrix renormalization group.