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arXiv · 1003.0058

Quenching across quantum critical points: role of topological patterns

Diptiman Sen·Smitha Vishveshwara
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Abstract

We introduce a one-dimensional version of the Kitaev model consisting of spins on a two-legged ladder and characterized by Z_2 invariants on the plaquettes of the ladder. We map the model to a fermionic system and identify the topological sectors associated with different Z_2 patterns in terms of fermion occupation numbers. Within these different sectors, we investigate the effect of a linear quench across a quantum critical point. We study the dominant behavior of the system by employing a Landau-Zener-type analysis of the effective Hamiltonian in the low-energy subspace for which the effective quenching can sometimes be non-linear. We show that the quenching leads to a residual energy which scales as a power of the quenching rate, and that the power depends on the topological sectors and their symmetry properties in a non-trivial way. This behavior is consistent with the general theory of quantum quenching, but with the correlation length exponent νbeing different in different sectors.

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Diptiman Sen, Smitha Vishveshwara. 2010-10-12. Quenching across quantum critical points: role of topological patterns. https://doi.org/10.1209/0295-5075%2F91%2F66009

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