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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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|
|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|
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