Quantum fidelity for one-dimensional Dirac fermions and two-dimensional Kitaev model in the thermodynamic limit

Mukherjee, Victor and Dutta, Amit and Sen, Diptiman (2012) Quantum fidelity for one-dimensional Dirac fermions and two-dimensional Kitaev model in the thermodynamic limit. In: Physical Review B: Condensed Matter and Materials Physics, 85 (2).

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Abstract

We study the scaling behavior of the fidelity (F) in the thermodynamic limit using the examples of a system of Dirac fermions in one dimension and the Kitaev model on a honeycomb lattice. We show that the thermodynamic fidelity inside the gapless as well as gapped phases follow power-law scalings, with the power given by some of the critical exponents of the system. The generic scaling forms of F for an anisotropic quantum critical point for both the thermodynamic and nonthermodynamic limits have been derived and verified for the Kitaev model. The interesting scaling behavior of F inside the gapless phase of the Kitaev model is also discussed. Finally, we consider a rotation of each spin in the Kitaev model around the z axis and calculate F through the overlap between the ground states for the angle of rotation eta and eta + d eta, respectively. We thereby show that the associated geometric phase vanishes. We have supplemented our analytical calculations with numerical simulations wherever necessary.

Item Type:	Journal Article
Publication:	Physical Review B: Condensed Matter and Materials Physics
Publisher:	The American Physical Society
Additional Information:	Copyright of this article belongs to The American Physical Society.
Department/Centre:	Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited:	07 Feb 2012 08:00
Last Modified:	07 Feb 2012 08:00
URI:	http://eprints.iisc.ac.in/id/eprint/43377

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