Quantum phase transition in skewed ladders: an entanglement entropy and fidelity study

TL;DR

This study uses entanglement entropy and fidelity to accurately identify quantum phase transitions in frustrated antiferromagnetic spin systems on skewed ladders, addressing challenges with degeneracy.

Contribution

It demonstrates the effectiveness of EE and fidelity in detecting QPTs in skewed ladder systems and resolves issues related to degeneracy by symmetry-based calculations.

Findings

EE shows discontinuous change at QPTs

Fidelity exhibits sharp dips at transition points

Symmetry-based calculations resolve degeneracy issues

Abstract

Entanglement entropy (EE) of a state is a measure of correlation or entanglement between two parts of a composite system and it may show appreciable change when the ground state (GS) undergoes a qualitative change in a quantum phase transition (QPT). Therefore, the EE has been extensively used to characterise the QPT in various correlated Hamiltonians. Similarly fidelity also shows sharp changes at a QPT. We characterized the QPT of frustrated antiferromagnetic Heisenberg spin-1/2 systems on 3/4, 3/5 and 5/7 skewed ladders using the EE and fidelity analysis. It is noted that all the non-magnetic to magnetic QPT boundary in these systems can be accurately determined using the EE and fidelity, and the EE exhibits a discontinuous change, whereas fidelity shows a sharp dip at the transition points. It is also noted that in case of the degenerate GS, the unsymmetrized calculations show wild fluctuations in the EE and fidelity even without actual phase transition, however, this problem is resolved by calculating the EE and the fidelity in the lowest energy state of the symmetry subspaces, to which the degenerate states belong.