From fidelity to entanglement of entropy of the one-dimensional transverse-field quantum compass model

TL;DR

This paper investigates quantum phase transitions in the one-dimensional transverse-field quantum compass model using fidelity, fidelity susceptibility, and von Neumann entropy, revealing second-order transitions and entanglement characteristics.

Contribution

It introduces a numerical analysis combining fidelity, fidelity susceptibility, and von Neumann entropy to characterize quantum phase transitions in the model.

Findings

Quantum phase transitions are second order, indicated by power-law divergence.

Von Neumann entropy effectively signals quantum critical points.

Entanglement depends more on exchange couplings connecting a block to the rest of the system.

Abstract

We study fidelity and fidelity susceptibility by addition of entanglement of entropy in the one-dimensional quantum compass model in a transverse magnetic field numerically. The whole four recognized gapped regions in the ground state phase diagram are in the range of our investigation. Power-law divergence at criticality accompanied by finite size scaling indicates the field induced quantum phase transitions are of second order as well as from the scaling behavior of the extremum of fidelity susceptibility is shown the quantum critical exponents are different in the various regions of phase diagram. We further calculate a recently proposed quantum information theoretic measure, von-Neumann entropy, and show that this measure provide appropriate signatures of the quantum phase transitions (QPT)s occurring at the critical fields. Von-Neumann entropy indicates a measure of entanglement between some-particle block and the rest of the system. We show the value of entanglement between a two-particle block with the rest of the system is more dependent on the power of exchange couplings connecting the block with the rest of the system than the power of exchange coupling between two particles in the block.