Fast preparation of critical ground states using superluminal fronts

TL;DR

This paper introduces a superluminal front protocol for rapidly preparing ground states of gapless models, significantly reducing the time compared to adiabatic methods, with exact solutions for free particles and numerical tests on spin chains.

Contribution

It presents a novel spatio-temporal quench method that achieves fast ground state preparation in gapless systems using superluminal fronts, with exact solutions and numerical demonstrations.

Findings

Protocol produces near-ground states in time proportional to system size L.

Exact solutions provided for free bosons and fermions in various dimensions.

Numerical simulations confirm effectiveness on quantum spin chains.

Abstract

We propose a spatio-temporal quench protocol that allows for the fast preparation of ground states of gapless models with Lorentz invariance. Assuming the system initially resides in the ground state of a corresponding massive model, we show that a superluminally-moving `front' that $\textit{locally}$ quenches the mass, leaves behind it (in space) a state $\textit{arbitrarily close}$ to the ground state of the gapless model. Importantly, our protocol takes time $\mathcal{O} \left( L \right)$ to produce the ground state of a system of size $\sim L^d$ ($d$ spatial dimensions), while a fully adiabatic protocol requires time $\sim \mathcal{O} \left( L^2 \right)$ to produce a state with exponential accuracy in $L$. The physics of the dynamical problem can be understood in terms of relativistic rarefaction of excitations generated by the mass front. We provide proof-of-concept by solving the proposed quench exactly for a system of free bosons in arbitrary dimensions, and for free fermions in $d = 1$. We discuss the role of interactions and UV effects on the free-theory idealization, before numerically illustrating the usefulness of the approach via simulations on the quantum Heisenberg spin-chain.