Quenching across quantum critical points: Role of topological patterns

¹ Centre for High Energy Physics, Indian Institute of Science - Bangalore 560012, India
² Department of Physics, University of Illinois at Urbana-Champaign - 1110 W. Green St, Urbana, IL 61801, USA

^a diptiman@cts.iisc.ernet.in

Received: 20 July 2010
Accepted: 8 September 2010

Abstract

We introduce a one-dimensional version of the Kitaev model consisting of spins on a two-legged ladder and characterized by Z₂ invariants on the plaquettes of the ladder. We map the model to a fermionic system and identify the topological sectors associated with different Z₂ 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 ν being different in different sectors.