Fidelity susceptibility in the two-dimensional spin-orbit models

TL;DR

This paper investigates quantum phase transitions in two-dimensional spin-orbit models using fidelity susceptibility, revealing different transition orders and demonstrating the method's sensitivity and advantages in characterizing these critical phenomena.

Contribution

It provides new insights into phase transition detection in 2D spin-orbit models using fidelity susceptibility, including analytic expressions and scaling behavior analysis.

Findings

Fidelity susceptibility detects second-order phase transitions with power-law divergence.

Different types of quantum phase transitions are identified in Kitaev-Heisenberg model.

Reduced fidelity susceptibility indicates first-order transitions through scaling violation.

Abstract

We study the quantum phase transitions in the two-dimensional spin-orbit models in terms of fidelity susceptibility and reduced fidelity susceptibility. An order-to-order phase transition is identified by fidelity susceptibility in the two-dimensional Heisenberg XXZ model with Dzyaloshinsky-Moriya interaction on a square lattice. The finite size scaling of fidelity susceptibility shows a power-law divergence at criticality, which indicates the quantum phase transition is of second order. Two distinct types of quantum phase transitions are witnessed by fidelity susceptibility in Kitaev-Heisenberg model on a hexagonal lattice. We exploit the symmetry of two-dimensional quantum compass model, and obtain a simple analytic expression of reduced fidelity susceptibility. Compared with the derivative of ground-state energy, the fidelity susceptibility is a bit more sensitive to phase transition. The violation of power-law behavior for the scaling of reduced fidelity susceptibility at criticality suggests that the quantum phase transition belongs to a first-order transition. We conclude that fidelity susceptibility and reduced fidelity susceptibility show great advantage to characterize diverse quantum phase transitions in spin-orbit models.