Local shortcut to adiabaticity for quantum many-body systems

TL;DR

This paper develops a method for implementing local shortcuts to adiabaticity in quantum many-body systems, enabling efficient state transitions near critical points using local control fields that scale polynomially.

Contribution

It introduces a universal approach to achieve local adiabatic shortcuts in spin chains and central spin models, reducing the need for non-local control Hamiltonians.

Findings

Local control fields scale polynomially with system size.

The method is exemplified using the transverse Ising model.

Extension to central spin models demonstrates versatility.

Abstract

We study the environment assisted local transitionless dynamics in closed spin systems driven through quantum critical points. In general shortcut to adaiabaticity (STA) in quantum critical systems requires highly non-local control Hamiltonians. In this work we develop an approach to achieve local shortcuts to adiabaticity (LSTA) in spin chains, using local control fields which scale polynomially with the system size, following universal critical exponents. We relate the control fields to reduced fidelity susceptibility and use transverse Ising model in one dimension to exemplify our generic results. We also extend our analysis to achieve LSTA in central spin models.