Quantum phase transitions in a two-dimensional quantum XYX model: Ground-state fidelity and entanglement

TL;DR

This paper investigates quantum phase transitions in a 2D anisotropic spin-1/2 XYX model using tensor network algorithms, fidelity measures, and entanglement estimators to identify critical points and phase boundaries.

Contribution

It introduces an innovative tensor network method to analyze quantum phase transitions and employs fidelity and entanglement measures for precise characterization.

Findings

Identified a continuous quantum phase transition via fidelity pinch point.

Quantitatively determined the factorizing field and critical point.

Derived local order parameter from tensor network ground state representations.

Abstract

A systematic analysis is performed for quantum phase transitions in a two-dimensional anisotropic spin 1/2 anti-ferromagnetic XYX model in an external magnetic field. With the help of an innovative tensor network algorithm, we compute the fidelity per lattice site to demonstrate that the field-induced quantum phase transition is unambiguously characterized by a pinch point on the fidelity surface, marking a continuous phase transition. We also compute an entanglement estimator, defined as a ratio between the one-tangle and the sum of squared concurrences, to identify both the factorizing field and the critical point, resulting in a quantitative agreement with quantum Monte Carlo simulation. In addition, the local order parameter is "derived" from the tensor network representation of the system's ground state wave functions.