Quenching across quantum critical points: role of topological patterns

TL;DR

This paper studies how linear quenches across quantum critical points in a topologically patterned 1D Kitaev ladder affect residual energy, revealing sector-dependent scaling behaviors linked to topological invariants and symmetry properties.

Contribution

It introduces a 1D Kitaev ladder model with Z_2 invariants, mapping it to fermions, and analyzes how topological sectors influence quenching dynamics and residual energy scaling.

Findings

Residual energy scales as a power of quenching rate.

Scaling exponents vary with topological sectors.

Different sectors exhibit distinct correlation length exponents.

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 \nu being different in different sectors.