Quenching across quantum critical points: Role of topological patterns
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
Accepted: 8 September 2010
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.
PACS: 64.70.Tg – Quantum phase transitions / 75.10.Jm – Quantized spin models, including quantum spin frustration
© EPLA, 2010