Inhomogeneity induced shortcut to adiabaticity in Ising chains with long-range interactions

TL;DR

This paper demonstrates that in long-range interacting Ising chains, an inhomogeneous transition can be made adiabatic by moving the critical front below a specific velocity, leveraging an energy gap induced by inhomogeneity.

Contribution

It reveals a novel mechanism where inhomogeneity induces an energy gap, enabling adiabatic transitions in long-range systems without a sonic horizon.

Findings

Adiabatic transitions are achievable when the front velocity is below a crossover velocity.

Inhomogeneity opens an energy gap in the quasiparticle spectrum.

The results enable efficient adiabatic quantum state preparation in long-range systems.

Abstract

Driving a homogeneous system across a quantum phase transition in a quench-time $\tau_Q$ generates excitations on wavelengths longer than the Kibble-Zurek (KZ) length $\hat\xi\propto\tau_Q^{\nu/(1+z\nu)}$ within the KZ time window $\hat t\propto\tau_Q^{z\nu/(1+z\nu)}$, where $z$ and $\nu$ are the critical exponents. Quenches designed with local time-dependent inhomogeneity can introduce a gap in the spectrum. For a variety of setups with short-range interactions, they have been shown to suppress excitations if the spatial velocity of the inhomogenous front is below the characteristic KZ velocity $\hat v \propto \hat\xi/\hat t$. Ising-like models with long-range interactions can have no sonic horizon, spreading information instantaneously across the system. Usually, this should imply that inhomogenous transitions will render the dynamics adiabatic regardless of the front velocity. However, we show that we get an adiabatic transition with no defects only when the inhomogeneous front moves slower than a characteristic crossover velocity $\tilde v \propto \theta^{(z-1)\nu/(1+\nu)}$, where $\theta$ is the slope of the inhomogeneous front at the critical point. The existence of this crossover velocity and adiabaticity of the model is a consequence of the energy gap in the quasiparticle spectrum that is opened by the inhomogeneity. This effect can be employed for efficient adiabatic quantum state preparation in systems with long-range interactions.