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arXiv · 1105.3008

Bifurcation in ground-state fidelity and universal order parameter for two-dimensional quantum transverse Ising model

Sheng-Hao Li·Hong-Lei Wang·Qian-Qian Shi·Huan-Qiang Zhou
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Abstract

We establish an intriguing connection between quantum phase transitions and bifurcations in the ground-state fidelity per lattice site, and construct the universal order parameter for quantum Ising model in a transverse magnetic field on an infinite-size square lattice in two spatial dimensions, a prototypical model with symmetry breaking order. This is achieved by computing ground-state wave functions in the context of the tensor network algorithm based on the infinite projected entangled-pair state representation. Our finding is applicable to any systems with symmetry breaking order, as a result of the fact that, in the conventional Landau-Ginzburg-Wilson paradigm, a quantum system undergoing a phase transition is characterized in terms of spontaneous symmetry breaking captured by a local order parameter. In addition, a bifurcation in the reduced fidelity between two different reduced density matrices is also discussed.

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Sheng-Hao Li, Hong-Lei Wang, Qian-Qian Shi, Huan-Qiang Zhou. 2011-05-16. Bifurcation in ground-state fidelity and universal order parameter for two-dimensional quantum transverse Ising model. https://arxiv.org/abs/1105.3008

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