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

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/τacross a quantum critical point, we find that the density of defects thereby produced scales as 1/τ^{q/(q+1)}, deviating from the 1/\sqrtτ 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 τalthough it may exhibit a cross-over at intermediate values of τ. 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.

13 pages including 11 figures

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Cited by in corpus (7)

• Slow quenches in a quantum Ising chain; dynamical phase transitions and topology
• Tuning the presence of dynamical phase transitions in a generalized $XY$ spin chain
• Non-equilibrium quantum relaxation across a localization-delocalization transition
• From fractional boundary charges to quantized Hall conductance
• Dynamical localization and slow thermalization in a class of disorder-free periodically driven one-dimensional interacting systems
• Nonequilibrium dynamics of the Ising chain in a fluctuating transverse field
• Fidelity susceptibility of one-dimensional models with twisted boundary conditions