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arXiv · 0811.3658

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

Bo Li·Sheng-Hao Li·Huan-Qiang Zhou
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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.

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Bo Li, Sheng-Hao Li, Huan-Qiang Zhou. 2009-05-20. Quantum phase transitions in a two-dimensional quantum XYX model: Ground-state fidelity and entanglement. https://doi.org/10.1103/physreve.79.060101

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