Quenching across quantum critical points in periodic systems: dependence of scaling laws on periodicity

TL;DR

This paper investigates how the scaling laws of defect density during quantum quenches depend on the periodicity of the system, revealing deviations from universal behavior and effects of interactions.

Contribution

It demonstrates that the defect scaling law varies with the periodicity of the Hamiltonian and explores the influence of superpositions of periods and interactions.

Findings

Defect density scales as 1/τ^{q/(q+1)} for period 2q.

Scaling law depends only on the smallest period in superpositions at large τ.

Interactions modify the scaling law depending on q and interaction strength.

Abstract

We study the quenching dynamics of a many-body system in one dimension described by a Hamiltonian that has spatial periodicity. Specifically, we consider a spin-1/2 chain with equal xx and yy couplings and subject to a periodically varying magnetic field in the z direction or, equivalently, a tight-binding model of spinless fermions with a periodic local chemical potential, having period 2q, where q is a natural number. For a linear quench of the magnetic field strength (or potential strength) at rate 1/\tau across a quantum critical point, we find that the density of defects thereby produced scales as 1/\tau^{q/(q+1)}, deviating from the 1/\sqrt{\tau} scaling that is ubiquitous to a range of systems. We analyze this behavior by mapping the low-energy physics of the system to a set of fermionic two-level systems labeled by the lattice momentum k undergoing a non-linear quench as well as by performing numerical simulations. We also find that if the magnetic field is a superposition of different periods, the power law depends only on the smallest period for very large values of \tau although it may exhibit a cross-over at intermediate values of \tau. Finally, for the case where a zz coupling is also present in the spin chain, or equivalently, where interactions are present in the fermionic system, we argue that the power associated with the scaling law depends on a combination of q and interaction strength.