Citation: Hamma, A., et al. "Entanglement, fidelity, and topological entropy in a quantum phase transition to topological order." Physical Review B—Condensed Matter and Materials Physics 77.15 (2008): 155111.
Web: https://arxiv.org/abs/0705.0026
Tags: Physical, Phase-transition, Information-theory
This paper presents a numerical study of a quantum phase transition of a spin 1/2 particle system on the torus. This phase transitions takes a spin-polarized system to a topological system. In the classical theory of phase transitions, there is a notion of the "order" of the phase transition with an associated "order parameter". In topological systems we are beyond Landau theory, and there is no more good notion of "order" for a phase transition. This paper makes the observation that topological entanglement entropy quite like an standard order parameter would in this case. In this way, it seems TEE can serve as a foundational tool in the study of topological quantum phase transitions.
This paper has led to a series of detailed theoretical and numerical works about the microscopic nature of topological quantum phase transitions, and how topological entanglement entropy behaves during these transitions:
> Castelnovo, Claudio, and Claudio Chamon. "Quantum topological phase transition at the microscopic level." Physical Review B—Condensed Matter and Materials Physics 77.5 (2008): 054433.
> Isakov, Sergei V., Matthew B. Hastings, and Roger G. Melko. "Topological entanglement entropy of a Bose-Hubbard spin liquid." Nature Physics 7.10 (2011): 772-775.
> Halász, Gábor B., and Alioscia Hamma. "Probing topological order with Rényi entropy." Physical Review A—Atomic, Molecular, and Optical Physics 86.6 (2012): 062330.